Description
In finance, an investment strategy is a set of rules, behaviors or procedures, designed to guide an investor's selection of an investment portfolio. Usually the strategy will be designed around the investor's risk-return tradeoff: some investors will prefer to maximize expected returns by investing in risky assets, others will prefer to minimize risk, but most will select a strategy somewhere in between.
Financial Study on A Simulation And Analysis of The Overreaction Hypothesis Market Anomaly As An Investment Strategy For Individual And Hedge Fund Investors
TABLE OF CONTENTS LIST OF TABLES AND FIGURES ABSTRACT I. II. Introduction Surrounding Issues II. A. II. B. Market Efficiency Long-Term Overreaction Institutional Constraints to Short Selling vii viii 1 3 3 6 7 7 10 10 22 26 26 28 29 31 31 32
II. B. 1. II. C. III.
Hedge Funds Literature Review The Overreaction Hypothesis Regulations that Prevent Unconstrained Investment Hedge Funds Regulations Operating Characteristics
III. A. III. B. III. C.
III. C. 1. III. C. 2.
III. C. 2. a. Hedge Funds vs. Mutual Funds III. C. 3. Hedge Fund Styles
III. C. 3. a. Market Trend III. C. 3. b. Other Styles
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III. C. 4. III. C. 5.
A Focus on Market Neutral Hedge Funds Risk Exposures of Market Neutral Hedge Funds
34 34 36 37 38 39 41 42 42 43 43 44 47 47 51 51 51 54 58 59
III. C. 5. a. Return Persistence III. C. 5. b. Non-Normality of Returns III. C. 5. c. Absolute Versus Relative Return Targets III. C. 5. d. The Role of Leverage III. C. 5. e. Dynamic Versus Passive Strategies III. C. 5. f. Biases in Databases III. C. 5. f. 1) Survivorship Bias III. C. 5. f. 2) Self-Selection Bias III. C. 5. f. 3) Instant History Bias III. C. 6. IV. Alternative Risk Measures
Hypotheses and Model Development
IV. A. Hypotheses to Test V. Data and Results V. A. V. B. V. C. Data Collection DT85 Cumulative Abnormal Returns DT85 Buy-and-Hold Returns Unexpected Positive Momentum Coefficients
V. C. 1. V. D.
Personal Asset Management
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V. D. 1. V. E. V. F. V. G. VI.
Results of Personal Asset Management
66 69 71 72 75 79
Additional Hedge Fund Expenses Changes in Risk Other Results Conclusion and Directions for Future Research
BIBLIOGRAPHY
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LIST OF TABLES AND FIGURES Table 1: Cumulative Abnormal Return Differentials Table 2: Buy-and-Hold Return Differentials Table 3: Regression Results on Buy-and-Hold Return Differentials Table 4: Regression Results on Buy-and-Hold Return Differentials and Loser and Winner Portfolios Table 4a: NYSE Stocks Table 4b: NYSE/AMEX/NASDAQ Stocks Table 4c: AMEX/NASDAQ Stocks Table 5: Comparison of 36-Month Testing Period Returns Table 6: Regression Results on Personal Asset Management Returns and Loser and Winner Portfolios Table 7: Regression Results on Hedge Fund Investment Returns and Loser and Winner Portfolios Table 8: Momentum Regression Results for All Approaches Figure 1a: Personal Asset Management Simulation Flowchart Figure 1b: Hedge Fund Simulation Flowchart Figure 2: Average Monthly Returns for Each 36-Month Testing Period Figure 3: Momentum Model Intercepts for Each 36-Month Testing Period Figure 4: Average Monthly Returns for Each Calendar Month Figure 5: Momentum Model Intercepts for Each Calendar Month
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86 87 88
90 91 92 93 94
95
96 97 98 99 100 101 102 103
ABSTRACT This study revisited the overreaction hypothesis studied by DeBondt and Thaler (1985) to determine its suitability as a strategy for private investment. Using their same filters from January 1986 through January 2004, prior NYSE losers only outperformed prior NYSE winners by 0.02% over the subsequent three years. The inclusion of AMEX and NASDAQ stocks resulted in a cumulative abnormal return differential of 28.60%; this difference increased to 34.85% when the requirement of preexisting data was reduced from seven years to five years. Qualitatively similar results were found when the analysis shifted from looking at cumulative abnormal returns to looking at buy-and-hold returns. While the buy-and-hold return results faced significant exposure to market, size, book-tomarket, and momentum-based risk, the explanatory power of models incorporating these factors was relatively low (maximum 13.82%), and there still existed significant risk-adjusted returns as determined by the intercept of the regressions of up to 0.824% per month. Additionally,
breaking down the factor analysis to be run on the losers and winners separately showed that both losers and winners experienced reversals in their returns and that these reversals were stronger in the winners than the losers. An investor looking to exploit these return differences could earn up to 51.44% over a three-year period, 23.22% of which would be considered risk-adjusted return, by using the maximum amount of leverage allowed by Regulation T. If this investor desires to instead invest in a hypothetical hedge fund following this same strategy, he could still earn 32.54% over three years, 11.52% of which would be risk-adjusted, while the hedge fund manager extracts 17.92% of the initial investment over the same three-year period in the form of management and performance fees. While the institutional constraints in place designed to protect investors who
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engage in the type of short selling required to implement this strategy succeed in reducing the investor's general exposure to various risk factors, the legal use of maximum leverage actually eliminates most of the risk-reducing benefits of these constraints without providing compensation in the form of additional returns (either on a raw or risk-adjusted basis). Even though the initial study was published in 1985, there is little evidence that arbitrageurs have reduced the difference in the returns between prior losers and winners. There also appears to be a pronounced January effect in the returns to investing by this strategy. Finally, there is no indication of the extent to which this strategy is followed in practice.
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I. Introduction This dissertation will analyze the possibility of taking advantage of a controversial statistical anomaly in an investment strategy that is subject to the constraints that actual investors must face. The overreaction hypothesis was explained in detail by DeBondt and Thaler (1985, henceforth DT85) as return reversals experienced by the stocks with the most extreme returns over a three- to five-year period. While the original article's results were scrutinized by
researchers, this study intends to focus on whether this phenomenon still exists in the time period since the publication of their findings and whether it can be applied in a profitable manner. This study is feasible in spite of previous refutations of DT85 because (1) direct refutations of DT85 were themselves scrutinized, leaving the general issue open-ended, (2) the necessity of prior refutations to focus on time frames heavily overlapping the original article's study neglects the issue of whether investors using this hypothesis since its publication could have profited from it, and (3) research that was well-designed to analyze DT85 (e.g. Fama and French (1996)) analyzed the entire pool of stocks looking for general patterns in returns and risk factors based on prior returns instead of looking for those patterns in the specific securities that would have been chosen by the DT85 filter. I will test my hypotheses that DT85 will work for investors since its publication, first by replicating the DT85 results in the years since the original article came out. I will then adjust this filter and the testing metric to more realistically reflect long-term investors' buy-and-hold strategies. Once this adjustment shows that the overreaction hypothesis still holds the potential to be used by investors to earn profits, I will apply the DT85 filter to two possible investing scenarios that could take advantage of it: personally investing and managing one's own assets through a broker and investing one's assets in a hedge fund that follows a similar strategy. Due
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to some of the objections raised by researchers towards the original article (such as in the aforementioned Fama and French (1996) article), I will not only look for profits from raw returns but also for profits from risk-adjusted returns. The remainder of this paper is structured as follows. Part II will briefly introduce the main issues that this study confronts. Part III will detail some of the major regulations that will need to be taken into consideration in the models developed later. It will also overview a significant portion of the overreaction literature that relates to hedge funds, focusing at certain points on the class of hedge funds most relevant to the models being used in this study, and the overreaction hypothesis, which will be the basis for the investment strategy used in those models. Part IV explains the hypotheses that will be tested. Part V details data collection and the results of tests of the hypotheses. Part VI concludes and details potential next steps in this line of research.
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II. Surrounding Issues II. A. Market Efficiency Market efficiency is a core concept in financial research and practice. In its present form, it implies an inability to profit on a risk-adjusted basis from predictions of future asset prices based on current knowledge. Should any anomalies (underpriced or overpriced assets) arise, market forces would work swiftly to offset these deviations. If an asset is underpriced, potential buyers would be quick to enter the market and force the price up to fair value. Similarly, overpriced assets would see a large quantity of long and short sellers in the market. However, while anyone can make an offer to purchase an underpriced asset, there are limitations to market participants' ability to make an offer to sell. Whereas the owners of an overpriced asset can simply offer the item for sale at the market price, not everyone who notices and wants to take advantage of the overpricing may own the asset. While such individuals have the option to take a short position in the asset, there are restrictions on their ability to do so. They, or their broker, must be able to find one or more current owners willing to lend their asset to the individual who feels it is overpriced for the purpose of selling it. Since they are selling another person's property, they are also liable to purchase the asset at the market price should it be recalled by the original owner for any reason (such as an increase in its price to a point where the owner wants to liquidate their position in the asset), thus prematurely closing out their short position. Note that while the use of street name securities in such transactions often makes premature closeout unlikely, it is still a potential restriction to be considered. In addition to the raw mechanics that restrict investors' ability to engage in short sales, there are other institutional constraints that make short selling a costly endeavor. For example, the short seller must post some collateral in addition to the proceeds of the short sale, preventing him from using those funds for some other
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potentially profitable opportunity, whereas the long seller simply needs to make an offer to sell what they already own. So, while a long seller gains the use of all the post-commission proceeds of the sale, a short seller would be able to use only a portion of those proceeds once they are netted out against the lost availability of the collateral posted. And while it is true that an investor with bearish sentiment towards an asset has other ways to exercise his belief that do not come with the same level of additional restrictions, any such choice is counterbalanced by an equally viable route for a bullish investor, assuming these alternative choices are available for that particular asset. For example, put and call options balance each other out, and they are not publicly traded for many listed securities. Overall, the problem this creates is that there is a potential extra level of expenses for investors who choose to exercise their bearish sentiment regarding an asset than for those exercising a bullish sentiment. Efficiency proponents would argue that economic agents will only look to take advantage of asset mispricing as long as the level of the mispricing (and thus the potential gains to be made) is greater than the costs involved with establishing their desired positions in the asset. As such, ceteris paribus, there should be a smaller pool of investors who can exercise bearish sentiments than of those who can exercise bullish sentiments. Thus, market overpricings would exist in greater quantities and magnitudes and with greater persistence than market underpricings. This, however, also creates an opportunity for astute investors to search for ways to exploit market mispricings at lower costs, thus taking advantage of opportunities that others are not able to and reaping potentially large profits. To this end, the hedge fund industry seems to have reduced the discrepancy between the costs of exercising bullish sentiment and exercising bearish sentiment. Hedge fund managers are able to avoid some of the institutional restrictions
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on short selling that mutual funds face by keeping their number of investors, assets under management, and beneficial ownership of individual securities within specified limits. This in itself creates a different set of restrictions on these economic agents, but their continued existence implies that these restrictions are worth it for the profits they will generate as a result of adhering to these restrictions. Ultimately, hedge funds can exist for the same reason most businesses exist: because they are profitable for those who run them. While some of these profits come from their relaxed restrictions relative to mutual funds, hedge funds, like mutual funds, are also able to extract profits by charging fees to those who invest in them (the difference between the fee structures of hedge funds and mutual funds will be described in Part III of this paper). This then creates a dilemma for the individual who wants to invest but cannot establish his own hedge fund. Assuming this person is a wise investor who sees a mispricing he wants to exploit for arbitrage profits, he has two choices. He can take his concept to the markets on his own and establish the proper long and short positions he desires, incurring all the costs and being subject to all the restrictions applicable to such a strategy. On the other hand, he could search for a hedge fund that employs a strategy similar to what he sees as potentially profitable and that is accepting new investors, saving himself the time going forward that he would otherwise require to maintain his arbitrage position and some of the costs of transacting in the markets, but incurring the additional fees that the hedge fund manager will extract from his investment and not being able to follow his intended strategy as precisely as he would desire. Part of this paper will look at the return difference between these two options.
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II. B. Long-Term Overreaction The work in this paper will be based on the results of DT85, which revealed a pattern in some long-term investments. They observed evidence that in the long-run, securities with extreme positive or negative returns over a period of a few years (three or five in their study) tend to reverse direction for a similar period of time. This creates an easily observable
opportunity for astute investors to exploit in the search for increased returns. DT85 also found a few patterns within this general pattern. Since the focus of this paper is on a realistic investor's opportunities to profit, I will also discuss and explore those patterns in terms of their applicability and potential profitability over and above the profitability provided by the general pattern itself, if any. The first avenue I will explore will be to attempt to replicate DT85's findings in the years since the publication of their work. If proponents of market efficiency are correct, then the announcement of such an inefficiency would lead arbitrageurs to work to profit from it. Investors would search for the securities that performed the poorest over the previous three years1 (losers) to purchase. They would also sell off or establish short positions in any securities that performed the best over the previous three years (winners). That should then result in the inefficiency being eliminated relatively quickly. Another possibility includes a ?slow burn? of the inefficiency, where it exists early on while investors determine the best way to exploit it, and their aptitude at doing so increases over time. Here, the magnitude of the difference between the returns of the losers and winners should decline over time to some equilibrium difference. Otherwise, the inefficiency may be robust to any efforts to arbitrage it away, and its magnitude may fluctuate over time but never really diminish by a significant amount. As long as the
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Three years was the primary time frame on which DT85 focused. 6
inefficiency of DT85's original model still exists, the next step will be to change the setup of the model to make it more relevant for investors. II. B. 1. Institutional Constraints to Short Selling While pure efficiency theory would suggest the inefficiencies would be eliminated once they are publicized, the existence of various forms of transactions costs, as mentioned earlier, would prevent this inefficiency from being fully arbitraged away. The Federal Reserve's
Regulations T and U are the two main institutional constraints that create these costs that are imposed on investors who desire to engage in borrowing to help finance stock purchases. These regulations set the limits on the amount of leverage investors can utilize to finance securities transactions. Additionally, the Financial Industry Regulatory Authority (FINRA)2 establishes requirements that exceed those laid out by Regulations T and U. Whereas Regulations T and U focus on the activities of the financial intermediaries (broker-dealers in the case of Regulation T and other lenders in the case of Regulation U) in their dealings with investors, the FINRA regulations focus on the investors who utilize these intermediaries' services and allow the relevant intermediaries to establish margin requirements in excess of the FINRA minimum standards. II. C. Hedge Funds Over the past several years, the hedge fund industry has grown from being a tiny piece of the investment community to a significant factor that has grabbed the attention of investors and regulators alike. While the academic community has done its part to attempt to explain the underlying factors that have led to the success and growth of hedge funds, there is still much that
?Created in July 2007 through the consolidation of NASD and the member regulation, enforcement and arbitration functions of the New York Stock Exchange, FINRA is dedicated to investor protection and market integrity through effective and efficient regulation and complementary compliance and technology-based services? (About FINRA (2007)).
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is unknown about these investments. As will be explained in further detail later, the hedge fund industry is not transparent, like stocks and mutual funds are. Any disclosures that individual hedge funds make regarding their operations are potentially self-serving and non-required; some hedge funds provide no information about themselves except recent performance and fees to their current investors. This makes using this information to attempt to understand an entire industry potentially tenuous. As such, instead of using the publicly available hedge fund data, this study will attempt to replicate at a basic level the returns a specific type of hedge fund might earn. The results of this replication will be compared to a replication of how a non-hedge fund investor would follow the same strategy. This will then allow a discussion of some of the motivations to invest in a hedge fund at all. Having a professional manage one's assets is clearly less time-consuming than doing it for oneself, so convenience is a clear motivator, though this does not distinguish hedge funds from other professionally managed investment options, such as mutual funds. Second, since most classes of hedge funds are available only to institutions and wealthy investors (there is a set of qualification standards that must be met by hedge fund investors, though these standards are much lower for investors in funds of hedge funds), there is a certain level of stature of being able to say that one's assets are tied up in hedge funds. If nothing else, it is a statement of one's financial status. How much of a statement it is can be questioned, but the prospect exists, nonetheless. The third motivator, the one that will be directly analyzed in this study, is the possibility of superior returns. Can a hedge fund offer a greater return on investment than an individual could obtain by investing in the financial markets without a ?middle man? to assist him? If not, the deficiency in hedge fund returns compared to
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personal asset management could be considered the cost of the convenience and stature of investing in hedge funds.
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III.Literature Review III. A. The Overreaction Hypothesis DT85 analyzed the difference in returns between prior long-term winners, those securities that experienced the greatest returns over the most recent three years, and prior long-term losers, those securities that experienced the least returns over the most recent three years. They found that the prior losers outperformed the prior winners by 24.6% over a subsequent three-year period. This paper will use that finding as inspiration to determine if an investor following a strategy to take advantage of this difference (by taking a long position in prior losers and a short position in prior winners) or investing in a hedge fund following such a strategy could earn excess returns. DT85's position was self-titled the ?overreaction hypothesis.? Their study was based upon the concept that in the long-run, securities will experience some form of mean reversion (the idea that there is some fundamental, or ?mean,? value that securities will return to if their prices shift too far from it). Thus, should a security experience returns in excess of its long-run expected average over a few years, the next few years should see returns below that average (and vice versa) so that overall, the security will return its fundamental value. While usually, this long-run expected average would be determined by using the CAPM or some multifactor model, DT85 simply compare a security's return in any given month to the market's return that month. They posit that by determining the winners and losers in this manner, they avoid any potential biases that would result from misspecification of the benchmark model (which is interesting in and of itself, as they note shortly before defining their model that such a benchmark is effectively the CAPM with ? = 0 and ? = 1). As such, while they describe their model as choosing the securities that performed best and worst relative to the market, their selection criteria is equivalent to choosing the securities with the best and worst raw returns.
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Note that since this study is concerned with using the results of DT85 to form a profitable investment strategy, it is sufficient that this selection strategy works; it is not necessary in this study to determine if their choice of selection criteria could be improved by, for example, using a better specified model. Once the stocks have been chosen for inclusion into the winner and loser portfolios, DT85's testing procedure effectively amounts to looking at equal-weighted portfolios of past winners or past losers each month that get rebalanced to equal weighting at the beginning of each month over the life of the portfolios (their procedure also accounts for stocks that are removed from either portfolio due to being delisted from the CRSP database from which they draw their return information). As mentioned earlier, DT85 found a 24.6% difference in the monthly rebalanced returns of equal-weighted portfolios of past losers over past winners (where losers averaged 19.6% more than the market and winners averaged 5.0% less than the market). While this result comes from choosing winners and losers based on three years of past returns and then holding those stocks for another three years, their results were robust to two- and five-year formation and testing periods as well, though the results at the two-year level were statistically insignificant.3 The asymmetry of these results is also interesting, as it suggests that prior pessimism is responded to in greater measure than prior optimism. Some of the issues raised earlier regarding the different costs of establishing long positions as opposed to establishing short positions may be partially at play here. Also, poor performance by a company's stock could lead to internal changes that are intended to result in improved performance. One may also want to consider investor psychology at work here. Even the occurrence of such a change may be enough to improve investors' confidence in that particular security. Also, shoppers of all varieties like a bargain, and a
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The difference between the loser and winner portfolios was also negative and significant when using one-year formation and testing periods, which would be in line with much of the literature on momentum in returns, but that is not a focus in this paper. 11
security that has experienced three years of relatively poor performance may very well be considered a bargain. Similarly, the psychological effects of poor stock performance can be devastating, and the investment community has historically been rather unforgiving to any entity that might be viewed as rocking the boat when the sailing is smooth (whether that smooth sailing is a myth or real). A few other interesting patterns appeared in DT85's results that this study will watch out for, as they could potentially affect investment decisions. These results include the impact of January returns on the overall results (17.7% of the losers' 19.6% excess returns occurred in the three Januaries of the testing period; the after-effects of tax-loss selling in December has been posited as a potential cause of this clustering of excess returns) and the slow build to the overreaction effects (only 5.4% of the 24.6% difference occurs in the first year after portfolio formation, but then 12.7%, or more than half of it, occurs in the second year). While this was merely mentioned in DT85, this second point can have very interesting implications for investors who may want to exploit when the majority of the overreaction effects occur. As should be expected if DT85's overreaction hypothesis is true, when the number of stocks allowed in the loser and winner portfolios expands, the magnitude of the overreaction declines (as more stocks are allowed in that were less extreme losers and winners). Also, as the formation period is extended, the magnitude of overreaction in the testing period grows. This implies that stocks that had longer periods of extreme performance will have a greater subsequent turnaround. Also, DT85 find the winner stocks to be riskier than the loser stocks when the portfolios are formed (prior 60-month CAPM betas of 1.369 and 1.026, respectively). While this differential riskiness may not carry over to the testing period, it is at least interesting to note that initially, the loser
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portfolio, from which the majority of the overreaction effect comes, is the safer portfolio relative to the overall market. There are issues in DT85's analysis that raise some concerns, though, when trying to extend their results to a study that is relevant for actual investors. Their decision to use monthly data instead of daily data was driven by a desire ?to avoid certain measurement problems that have received much attention in the literature,? including, but not limited to, ?the ?bid-ask' effect and the consequences of infrequent trading? (p. 799). This of course limits the researcher to make all purchases on the first trading day of the month and all sales on the last trading day of the month, which is rather unrealistic in comparison to how investors act. However, hedge funds seem to determine their net asset values for the purposes of investors buying and selling based on the share prices of their holdings as of the close of trading on the last trading day of the month, so this concern may not have as large of an overall effect as one might instinctually consider (Chan et. al. (2006)). These effects aside, DT85's concerns with the spread and low volumes will need to be accounted for in the model used later in this paper. They also required seven years of data to be available in the CRSP database prior to the portfolio formation. For one thing, many investors may not be concerned with a stock having quite so large a history available in order to consider it as an investment opportunity (on either the short or the long side). For another thing, when coupled with the fact that DT85 focused only on NYSE-traded securities, the combined effects of these two filters is to bias their analysis to select only large and established firms. For their purposes, this was acceptable, as they state that one popular critique of overreaction at the time of their study was that overreaction effects were predominantly small-firm effects. Thus, based on the literature at the time, they would have been biasing their results against finding overreaction effects. However, for an investor looking
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to maximize their returns, they would want to consider as much of the population of investable assets as possible. Plus, if this prior contention is true, and small firms would experience overreaction to a greater extent than large firms, then investors would be doing themselves a disservice not to consider small firms for inclusion in either portfolio. DT85's choice of formation months leaves much to be desired from a practical aspect as well. Their choice to start every portfolio in January was admittedly arbitrary, so they also performed tests on portfolios that start at the beginning of June (also arbitrarily chosen). To make this analysis more realistic, it will not focus on any specific formation date. On top of that, DT85 tested their portfolio in nonoverlapping periods, which would be analogous to an investor purchasing a stock and then deciding at that point in time to neither sell that security nor purchase another security for a preset period of time. While this decision may make sense from a statistical standpoint, it again makes no sense from the standpoint of an investor interested in maximizing his returns. Hedge funds will again be able to lessen the impact of this issue (though not entirely) due to lockup requirements that prevent their investors from withdrawing their funds for a predetermined time frame, though these lockup periods can vary across different hedge funds and also tend not to be three years long, the horizon used in DT85 (Liang (1999)). As described earlier, DT85 found evidence that a majority of their abnormal returns came during the three Januaries of the testing period. It also appeared that the lowest abnormal returns were realized during the three Decembers of the testing period. Tax-loss selling is proposed as a possible candidate to explain this phenomenon. Tam (1998) describes this concept as follows. ?Tax-loss selling essentially involves shedding the shares of a fund that has lost a lot of money since you bought it. (Even if a fund is down for the year, you can't take a tax loss unless the shares are below the price you paid.) By selling, you realize a loss that can then be used to offset
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any capital gains you have earned in another part of your portfolio [including potentially those in previous or future years]. The result: the capital-gains tax burden you anticipated is tempered.? What ends up happening, then, is that large institutional investors who can take great advantage of capital losses (in other words, those with a tax burden) sell off the securities in their portfolios that give them great losses, generally a few days or weeks before the end of the tax year. The market's sudden loss of equity causes a drop in that specific stock's price, leading to the tempering of abnormal returns in December. The strong January returns would then come about as the investors who sold securities in December return those securities to their portfolios, since there is no indication those investors wanted those securities out of their portfolios permanently (they simply wanted the tax benefits of selling at a loss). It would be reasonable to assume that since these securities have fallen in price that they would be considered underpriced, so those funds would try to repurchase them as soon as possible in the new tax year before the perceived underpricing was eliminated. Thus, those same securities that experienced a decline in their prices in December would see a subsequent increase in their prices in January. Chan (1986) analyzed tax-loss selling as a possible explanation of this seasonality. As a direct argument against the tax-loss selling argument, he points out that, ?Even if the year-end trading, for whatever reasons, is unusually heavy, one crucial assumption needed for the tax-loss selling hypothesis to explain the high January returns is that such selling exerts downward price pressure. If the year-end trading is purely caused by tax considerations, rational tax-loss sellers could repurchase stocks sold (by others) for tax reasons at the same time. Then the trading is not expected to depress stock prices.? That would imply that the funds that would intend to
repurchase in January the shares they sold in December should not see the benefits of buying underpriced securities, so they may look for other underpriced securities of characteristics
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similar to the shares they sold off. As such, DT85 should not have seen their January effect as a result of rational tax-loss selling. Empirically, Chan (1986) shows that the difference between the mean January effect of a short-term loss and the mean January effect of a long-term loss (this difference was seen as a proxy for the effect of tax-loss selling) is statistically insignificant in all but the smallest stocks, for which this difference is only marginally significant for the smallest decile of stocks available on the CRSP tapes at the time. Since the author does not specify that his study was limited to NYSE stocks on the CRSP tapes, it makes sense to conclude that the only subset of stocks for which the author possibly finds a significant tax-loss selling effect were a proportionately insignificant component of DT85's study. DeBondt and Thaler (1987) followed up their prior study on overreaction with an analysis of the effects of size and market-to-book ratios on overreaction. Forming their
portfolios in the odd years from 1969 to 1979, and using sixty-month periods as the prior formation periods and subsequent testing periods (note the departure from using non-overlapping periods in their previous study), they sorted the stocks in their study into quintiles ranked by cumulative abnormal return (their primary return metric from their previous study), market value of equity, market-to-book equity ratio, and assets. Using the five-year cumulative abnormal return, they find evidence of return reversals when sorting stocks based on previous cumulative abnormal returns (as would be predicted by DT85) and the market-to-book ratio and evidence of momentum in stocks sorted by assets. There is also a pronounced ?frown ? pattern in the cumulative abnormal returns of the market value of equity quintiles followed by decreasing cumulative abnormal returns of those quintiles in the testing period, providing weak evidence for momentum there as well. While the authors' intent may have been to search for the source of the overreaction they found in their previous study, their finding that is more pertinent to this study
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is the collective pattern of the testing period cumulative abnormal returns of each set of quintiles. In all four sorting mechanisms, they found decreasing cumulative abnormal returns from the first quintile to the fifth quintile. However, sorting by prior cumulative abnormal returns actually produced a lower difference in subsequent cumulative abnormal returns between the first and fifth quintiles (36.3%) than sorting by the market value of equity (50.8%), the market-to-book ratio (42.0%), or assets (38.7%). This leads to the possibility that the loser and winner portfolios are providing their returns based not as much on reverting to some long-term mean but on some characteristics of the stocks that happen to fall into those portfolios that grant a risk premium for size and/or value to investors in those stocks. This possibility will be tested later in this study. Conrad and Kaul (1993) introduced the possibility that DT85's results are biased. They explain that the abnormal return as a measure of excess returns contains within it an upward bias that is proportionate with the number of holding periods (in the case of DT85, each month is one holding period) of returns being measured and that removing this bias from DT85's calculations should eliminate any overreaction that exists. Due to bid-ask biases, they argue that the bias in cumulative abnormal returns is higher in low-priced stocks than in high-priced stocks.4 Since the loser portfolio is generally comprised of more low-priced stocks than the winner portfolio, DT85's combined portfolio includes an upward bias (loser bias > winner bias, so portfolio bias = loser bias - winner bias > 0). This conclusion comes from the findings of Bhardwaj and Brooks (1992), whose analysis of the January anomaly led them to the conclusion that the bid-ask bias on low-priced stocks averages between 0.80% and 1.42% in the first five trading days in January. For holding periods of less than one year (such as the one-month holding periods which determine DT85's cumulative abnormal returns), this bias tends to cause the returns on low-
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Decimalization of exchange-listed prices should reduce this difference if the spreads of the low-priced stocks that get included in the loser portfolios were generally at the minimum tick size. 17
priced NYSE stocks to be overestimated by 0.8% to 1.0%. This finding is in addition to the general idea that there is an upward bid-ask bias in the returns of low-priced stocks in general. To counter this bias, Conrad and Kaul (1993) follow a DT85-inspired method of determining the extent of overreaction through 1988 (using 35 securities in each portfolio and 36-month non-overlapping formation and testing periods, though they include NYSE and AMEX stocks, whereas DT85 included NYSE stocks only), comparing DT85's cumulative abnormal return on these portfolios with their average holding period abnormal return. While the
cumulative abnormal return would contain the effect of biases from thirty-six holding periods (one for each month), Conrad and Kaul (1993) calculate their returns based on the entire 36month span as one holding period. Consistent with DT85, they find that cumulative abnormal returns of the loser portfolio exceed those of the winner portfolio by 37.5%. They also find that the average holding period abnormal return of the loser portfolio exceeds that of the winner portfolio over the three-year testing portfolio by 27.1%. While this alone would seem to support their argument that DT85's results are the product of biases inherent in using cumulative abnormal returns, the average holding period abnormal return also has a marginally larger standard error (15.7% vs. 15.3%), reducing the statistical significance of their results. While Conrad and Kaul (1993) do not report p-values in their study to allow for a direct comparison of this significance, they use twenty testing periods in both of their analyses, so a t-distribution with nineteen degrees of freedom and a one-tailed test would result in p-values of 0.0120 for the cumulative abnormal return method and 0.0503 for the average holding period abnormal return method. Thus, they found an average bias of 10.4% over a 36-month testing period, and that bias may have been the source of the significance of their results.
18
While this argument might seem sufficient to refute any need to analyze DT85 further, Loughran and Ritter (1996) question Conrad and Kaul's (1993) results. They base their concern regarding this study on three points.5 While they do not dispute Conrad and Kaul's (1993) argument regarding bid-ask biases being magnified by cumulative abnormal returns, they counter that cumulative abnormal returns do not get the benefit of compounding returns over the entire testing period. Assuming DT85 is true, not accounting for the compounding of returns would bias Conrad and Kaul (1993) towards being able to claim a strong impact of bid-ask biases on DT85's results. When Loughran and Ritter (1996) compare the effects of using cumulative abnormal returns as the selection criteria with the effects of using buy-and-hold returns (analogous to Conrad and Kaul's (1993) average holding period abnormal returns), they find that buy-and-hold returns provide a greater segregation of securities relative to price, market capitalization, prior returns, and test period returns. Additionally, for each selection criteria, there is little difference between the testing period returns calculated using cumulative abnormal returns and those calculated using buy-and-hold returns. Second, Conrad and Kaul (1993) use CS-TS regressions to further explain their results beyond what I mentioned above, but Loughran and Ritter (1996) point out that this prevents them from being able to isolate time-series mean reversion patterns from the cross-sectional patterns they claim to find. Finally, they point out that Conrad and Kaul (1993) introduced a survivorship bias in their results by requiring all stocks included in their winner and loser portfolios to have return information throughout the entire subsequent testing period. If price is a risk proxy, then low-priced losers will be at a higher risk of being delisted than high-priced winners, but those stocks that are delisted would not be included in their portfolios. Since one of
5
Loughran and Ritter (1996) actually make four major points, but the second of the four points is not a refutation of Conrad and Kaul (1993), so I have excluded it from mention here. 19
Conrad and Kaul's (1993) hypotheses was that loser stocks would have higher returns than winner stocks due to the different prices of the stocks included in the portfolio, removing delisted stocks would bias their study in favor of coming to this very conclusion. Loughran and Ritter (1996) address both these issues through three stages of regressions. First, they perform a pooled CS-TS regression of test period returns on the logs of price, market capitalization, and prior returns with only survivors. They then repeat this procedure with non-survivors included in the population of potential loser and winner stocks to account for survivorship bias. This resulted in a lower economic and statistical significance for price and prior returns, greater economic and statistical significance for market capitalization, and adjusted R2 falling by approximately one third (10.6% to 6.8%). With survivorship bias accounted for, they then convert their pooled CSTS regression to a time series of cross-sectional regressions, reporting the means of the crosssectional regression coefficients. This adjustment resulted in eliminating the significance of price and market capitalization, magnifying the economic impact of prior returns while reducing its statistical significance, and virtually no effect on R2 (fell from 6.8% to 6.5%). Removing market capitalization (since its log is a linear combination of the log of price, which is another independent variable in their regressions, and the log of shares outstanding) as a variable in their regressions had no substantive effect on their results: prior returns were still the only significant determinant of test period returns. On another note, Dissanaike (1996) warns against extrapolating too much from the results of DT85 in relation to the implications of the behavior of mean reversion. One noticeable result of DT85 is that the cumulative abnormal returns of the loser portfolios (19.6%) exceeded the absolute cumulative abnormal returns of the winner portfolios (5.0%). While he argues that while this information is very useful for an investor looking to earn returns in excess of the
20
market, this asymmetry in test-period returns does not allow us to draw any conclusions about the reversals themselves. As a simple introductory example, he points out that two securities (or portfolios of securities) with the same value at the beginning of the formation period (which he calls the rank period) that earn equal returns in opposite directions during the formation period (creating winner and loser portfolios) but then revert halfway back to their original values during the test period would exhibit asymmetric returns in the test period, even though the compounded returns over both periods would still be equal in magnitude. He creates winner and loser portfolios out of the top and bottom deciles of returns from a four-year formation period then tracks the difference in returns at the 12-, 24-, 30-, 36-, 42-, and 48-month points of the testing period. Consistent with DT85, he finds that during the test period, the losers significantly outperform the winners at each of these points, the losers outperform the market, the winners underperform the market, and except at the 12-month point, the magnitude of the loser excess returns exceeds that of the winner excess returns. However, he also creates a reversal metric (labeled the portfolio reversal coefficient) that measures, for losers (winners), the proportion of the value lost (earned) during the formation period relative to the market that was recovered (given back) during the test period relative to the market. He finds that at each of the
checkpoints mentioned above, not only does the winner portfolio experience a greater reversal than the loser portfolio, but also that the disparity between the winner reversal and loser reversal increases at each subsequent checkpoint. By the end of the 48-month test period, his winner portfolios have given back 56.1% of their gains relative to the market during the formation period, but his loser portfolio only recovered 18.0% of the value it had lost relative to the market during the formation period.
21
III. B. Regulations that Prevent Unconstrained Investment This section will describe the regulations that apply to the general investment community. While DT85 looked simply for a difference in the levels of returns of two types of stocks, the intent of this paper is to attempt to directly exploit that difference. In order to do so, the regulations that prevent unconstrained short selling of equities must be applied to any model simulating this attempt must be understood. Regulation T states that, ?Its principal purpose is to regulate extensions of credit by brokers and dealers; it also covers related transactions within the Board's authority under the Act. It imposes, among other obligations, initial margin requirements and payment rules on certain securities transactions? (§220.1(a)). In addition, it ?provides a margin account and four special purpose accounts in which to record all financial relations between a customer and a creditor. Any transaction not specifically permitted in a special purpose account shall be
recorded in a margin account? (§220.1(b)(1)). As this paper will focus solely on purchases and short sales of tradable equity securities, the key minimum initial margin requirements to be concerned with are the fifty percent margin requirement for margin equity securities and the one hundred fifty percent margin requirement for short sales of nonexempted securities as described in section 12 of this regulation. The one hundred fifty percent requirement has the effect of forcing the investor to post the proceeds of the short sale in the margin account and then provide an additional fifty percent of this value as a form of collateral on this loan. As such, any further discussion of the required margin on short sales will assume the proceeds of the sale are already considered as part of the margin account, and any references to required margin on short sales will only describe the excess above these proceeds. Thus, I can, for simplicity's sake, refer to the fifty percent margin requirement on purchases and short sales going forward with the direct
22
implication that this fifty percent is in addition to the proceeds of the short sale that are automatically going to be posted in the margin account. It is also significant to note that the four special purpose accounts described above (and explained in detail in sections 5 through 8 of Regulation T) will have no direct effect on this study. The optional special memorandum account is a mirror to the margin account, whereby a credit to this account is to be matched up with a debit to the margin account. This account may contain dividends, interest, cash (including that deposited to meet a margin call), proceeds of sales of securities (short or liquidated), and transferred margin excess (§220.5). Effectively, the balance of this account could be the value of the equity held in the margin account. The good faith account is used for transactions involving exempt securities, non-equity securities, money market mutual funds, and exempt securities mutual funds. Required margin for these types of assets can be determined by the creditor on a case-by-case basis, as long as it meets the stipulations of a regulatory authority relevant to the asset type (§220.12). The broker-dealer credit account is a special account designed to facilitate liquidity among creditors and other broker-dealers (§220.7). The cash account is the location where a creditor can engage in basic transactions (non-short) on securities or other assets (including the issuance and exercise of options) of their customers, assuming there is a sufficient cash balance to complete said transactions (§220.8). Regulation U, on the other hand, states that its purpose is to impose ?credit restrictions upon persons other than brokers or dealers (hereinafter lenders) that extend credit for the purpose of buying or carrying margin stock if the credit is secured directly or indirectly by margin stock. Lenders include ?banks' ? [and] may not extend more than the maximum loan value of the collateral securing such credit?? (§221.1(b)(1)), which, for margin stock, ?is fifty percent of its
23
current market value? (§221.7(a)). The regulation allows only a plan-lender (a corporation extending credit to purchase specifically its own margin stock or that of its subsidiaries and affiliates) to exceed these limits (§221.3(a)(1) and §221.4(a)(1)), an exception that is not pertinent for this study. Note that while this regulation also discusses good faith lending (though to a lesser extent than in Regulation T), there is no provision in Regulation U pertaining to the short sale of securities. Its focus is solely on borrowing funds to purchase and hold stock. Regulation X effectively bars American investors from circumventing Regulations T and U by obtaining credit from foreign entities that would not be subject to Regulations T and U. Specifically, any United States person (?a person which is organized or exists under the laws of any State or, in the case of a natural person, a citizen or resident of the United States; a domestic estate; or a trust in which one or more of the foregoing persons has a cumulative direct or indirect beneficial interest in excess of 50 per centum of the value of the trust? (§224.2(a))) or foreign person controlled by a United States person (?any noncorporate entity in which United States persons directly or indirectly have more than a 50 per centum beneficial interest, and any corporation in which one or more United States persons, directly or indirectly, own stock possessing more than 50 per centum of the total combined voting power of all classes of stock entitled to vote, or more than 50 per centum of the total value of shares of all classes of stock? (§224.2(c))) who obtains credit within the United States to purchase or carry any securities or who obtains credit outside the United States to purchase or carry United States securities is subject to the aforementioned regulations, even if ?the borrower willfully causes the credit to be extended in contravention of Regulations T or U? (§224.1(b)(1)). While the aforementioned regulations establish minimum requirements for investors to follow, the exchanges that facilitate investment transactions establish a slightly higher level of
24
restriction on margin investment. For the purposes of this study, the margin regulations set forth by NYSE and FINRA are functionally equivalent, so the following rules are taken from the FINRA regulation, specifically, Rule 2520 from NASD's Rules of the Association. Paragraph (b) on initial margin states, ?For the purpose of effecting new securitie s transactions and commitments, the customer shall be required to deposit margin in cash and/or securities in the account which shall be at least the greater of: (1) the amount specified in Regulation T, or Rules 400 through 406 under the Act?; or (2) the amount specified in paragraph (c)(3) of this Rule [which is $5.00 per share, to be discussed in the next paragraph]; or (3) such greater amount as NASD may from time to time require for specific securities; or (4) equity of at least $2,000 except that cash need not be deposited in excess of the cost of any security purchased ?.? Subparagraphs (2), (3), and (4) provide an additional cushion above what is required by Regulation T for the special case of low-priced securities and securities the governing body deems especially volatile. Whereas Regulations T, U, and X focus solely on the initial margin that must be provided, the exchange regulations also deal with maintenance margin. Paragraph (c) of
FINRA's Rule 2520 states, ?The margin which must be maintained in all accounts of customers, except for cash accounts subject to other provisions of this rule, shall be as follows: (1) 25 percent of the current market value of all securities, except for securities futures contracts, ?long' in the account; plus (2) $2.50 per share or 100 percent of the current market value, whichever amount is greater, of each stock ?short' in the account selling at less than $5.00 per share; plus (3) $5.00 per share or 30 percent of the current market value, whichever amount is greater, of each stock ?short' in the account selling at $5.00 per share or above?.? This is the first level of regulation that describes a fundamental difference in treatment between long and short holdings
25
by an investor (recall that despite different descriptions, Regulation T set initial margin requirements of fifty percent of the value of either a long or short transaction). Other conditions of Rule 2520 allow member firms to ?(1) review limits and types of credit extended to all customers; (2) formulate their own margin requirements; and (3) review the need for instituting higher margin requirements, mark-to-markets and collateral deposits than are required by this paragraph for individual securities or customer accounts? (§2520(d)). The main effect of this component of the regulation is to allow member firms to create a buffer between when their customers will receive a margin call from them and when they would face a margin call of their own. Observing just a few firms' margin disclosures indicates that a five percent cushion above the FINRA requirements (thirty percent maintenance margin for long holdings and thirty-five percent for short holdings) is common. III. C. Hedge Funds Unlike commonly traded investment opportunities such as stocks and mutual funds, there are no available databases of the entire universe of hedge funds. Since hedge funds are not currently required to fully disclose their activities to the Securities and Exchange Commission (SEC), the only way to understand how these funds operate is through private investigation or through the self-disclosure that hedge funds provide to private databases established for the purpose of hedge funds desiring to lure investors. As such, even information about the basic operations of hedge funds will come from prior research on these two sources of information. III. C. 1. Regulations
Hedge funds are not all subject to the short selling restrictions and minimum disclosure requirements (among other regulations) of the SEC. This is due in part to two main exceptions to the Investment Company Act of 1940 of which hedge funds tend to take advantage (Wallace
26
(1999)). Section 3(c)(1) of this Act grants an exemption to investment companies owned by no more than 100 investors. This cap has also recently been expanded to grant this exception to funds with fewer than 500 U.S. investors. Section 3(c)(7) of this Act will grant an exception to hedge funds who only offer their shares to qualified purchasers. While there are several criteria that can deem an entity as a qualified purchaser, all such criteria fall under one of three general categories: high income, high net worth, knowledgeable investor. Variations within these
categories are based on whether the investor is an individual, a married couple, a family business, or an institution.6 For the purposes of this paper, the most important result of these exemptions is the ability to engage in short selling as part of an investing strategy. Section 12(a) of this Act states, ?It shall be unlawful for any registered investment company, in contravention of such rules and regulations or orders as the Commission may prescribe as necessary or appropriate in the public interest or for the protection of investors (1) to purchase any security on margin, except such short-term credits as are necessary for the clearance of transactions?or (3) to effect a short sale of any security, except in connection with an underwriting in which such registered company is a participant.? Application of Section 12(a) to a company then clearly prevents that company from attempting to profit via short selling, effectively removing the ability to employ strategies such as the one this study focuses on. Thus, funds that desire to use short selling as part of their strategies must then remain under the 500-investor limit and must only offer their shares to qualified purchasers. As mutual funds tend not to do so, investors looking for vehicles engaging in strategies similar to this study's focus must turn to hedge funds and their higher fee structures as described in the next section.
6
In light of the proliferation of offshore hedge funds, these rules have been interpreted to consider only U.S. investors, with no limit on the number or qualifications of non-U.S. investors for offshore hedge funds wishing to sell their securities in the United States. 27
III. C. 2.
Operating Characteristics
In order to properly model a hedge fund in this study, it is first necessary to understand the basic operations of hedge funds in general (and these characteristics will be included in the model used in this study). Several of these are summarized in Pearl (2006) for the population of analyzable hedge funds (i.e.: those listed in available databases). The most commonly used operating characteristics are the investment management fee and the incentive allocation (or performance fee). The investment management fee is the fee extracted by hedge fund managers for their actual services, and the majority of these fees fall between one and two percent of the net asset value of the fund.7 As its names suggest, the incentive allocation is the ?pay-forperformance? portion of the fees the hedge fund manager can extract, and the majority of funds extract twenty percent of the realized and unrealized gains of the fund over the course of a certain period (generally one quarter or one year). For individual funds, these fees tend to be stable over time (Liang (2001)). While these fees are commonly mentioned by researchers, Pearl (2006) also mentions expense charge offs. Depending on how liberally a fund defines items that can be charged off, he suggests that for a well-run fund, these should be less than one hundred basis points per year.8 In addition to these fees, many funds also incorporate a lockup period that restricts investors in the fund from withdrawing their money for a certain period of time after their initial investment. The purpose of this period is to give the manager ample opportunity to exercise his strategy without fear that early poor performance will result in premature withdrawals. Liang (1999) points out that hedge funds with longer lockup periods tend to experience better performance.
7
Chan et al (2006) note than many hedge funds mark their portfolios to market at the end of the month to strike a net asset value at which investors can buy into or cash out of the fund. 8 Note that this is the same demarcation point the mutual fund industry tends to advertise as the difference between funds with ?good? expense ratios and ?bad? expense ratios. 28
To protect the investors, many funds also covenant themselves with hurdle rates and high-water marks. A hurdle rate is a minimum return the fund must achieve in order for the manager to receive the performance fee. While every fund has a hurdle rate of at least zero (as there must be some positive returns for the manager to extract a percentage of), it is also conceivable that funds may apply hurdle rates equal to a risk-free return or inflation metric. In addition to providing increased protection for investors, positive hurdle rates can also double as a signal of quality to investors who want to be certain that the individuals in charge of their funds will not receive bonuses for providing returns inferior to those which the investor could have costlessly pursued elsewhere or that do not even compensate for increases in the cost of living. Also, a high-water mark provision forces a manager to recover all losses (relative to the hurdle rate) before extracting any performance fees. For example, assume a hedge fund with a hurdle rate equal to some risk-free return ends up losing twenty percent of its value over the course of a year. For this manager to earn any performance fees at the end of the next year, his fund would have to post a twenty-five percent gain (to get back to even from the beginning of the year just completed) plus last year's risk-free rate (to reach last year's hurdle) plus this year's risk-free rate (to reach this year's hurdle). III. C. 2. a. Hedge Funds vs. Mutual Funds
Since investors who would desire to profit from exploiting return differences such as those described in DT85 but who have neither the time, inclination, nor ability to do so directly through personally managing their own accounts do not have the option to follow the more familiar mutual fund route (for reasons described in Section III. B. 1. of this paper), this brief section will highlight the difference in the fee structures of hedge funds and mutual funds.
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Collins (2007) describes how the Investment Company Institute (ICI)9 measures mutual fund fees and expenses. ?Mutual fund investors incur two primary kinds of fees and expenses when investing in mutual funds: sales loads and ongoing expenses. Sales loads are one-time fees that investors pay either at the time of purchase (front loads) or, in some cases, when shares are redeemed (back-end loads). Ongoing expenses are paid from fund assets and investors thus pay these expenses indirectly. Ongoing fund expenses cover portfolio management, fund
administration, shareholder services, distribution charges known as 12b-1 fees, and other operating costs.? He notes that these fees averaged 107 basis points in 2006, including 19 basis points from load fees and 88 basis points from the total expense ratio. While these figures are down from previous years (from a recent peak of 124, 25, and 99 basis points, respectively, in 2001), they still imply a lower cost structure to mutual fund investors than to hedge fund investors. If we consider the mutual fund expense ratio and hedge fund expense charge offs to balance each other (as both are approximately one hundred basis points on average), then the difference comes down to comparing mutual funds' load fees of approximately 19 basis points against hedge funds' one to two percent investment management fees. So, without even
considering the incentive allocation fee that is only applicable when the hedge fund provides gains for its investors, the analyses of Pearl (2006) and Collins (2007) indicate that hedge funds are, indeed, more expensive assets in which to invest. However, since mutual funds cannot offer investors the opportunity to benefit from investment strategies involving short selling, investors who desire to benefit from such strategies must be willing to pay these higher fees if they are not willing or able to follow the strategies on their own.
9
On their website, the ICI describes itself as ?the national association of U.S. investment companies, including mutual funds, closed-end funds, exchange-traded funds (ETFs), and unit investment trusts (UITs)? (About the Investment Company Institute (2007)). 30
III. C. 3.
Hedge Fund Styles
One of the issues with attempting to understand the source of hedge fund returns is that fund exposures to common risk factors varies greatly based on the investment style of the fund manager. The different hedge fund databases apply different labels and definitions to similar styles, so I will focus on the eight style definitions as put forth by the SEC in Staff Report (2003).10 The style relevant to this paper is the market trend style, which will be described first and in its own section. III. C. 3. a. Market Trend
Market trend strategies, also referred to as directional or tactical strategies, attempt to exploit broad market trends in some investable asset. Macro funds invest in various currencies based on their perceptions of the macroeconomic fundamentals of various countries. These funds usually do not hedge their investments. Long/short funds search for pricing anomalies to exploit, taking a long position in assets the manager believes to be undervalued and a short position in assets the manager believes to be overvalued. While not necessary to meet this definition, the assets on both the long and short side will almost always be the same general category of asset (e.g. all equities, all bonds, all currencies, etc.). Sector funds would be even more specific, focusing on a specific industry (e.g. long/short tech stocks) or a particular class of assets (e.g. long/short long-term government bonds). This categorization also does not assume anything about the relative sizes of the investments on the long side and short side, but those that place equal dollar weights on their long investment as their short investment would be referred to as market neutral or relative value funds.11 While not explicitly mentioned in the SEC report referenced above, some databases separate funds termed short selling funds as their own style
10 11
Unless otherwise specified, any specific information in this section comes from this document. This is the specific strategy that this paper will focus on. 31
instead of being a subclass of the long/short style. These funds focus on overvalued securities, taking only short positions in those securities they consider overvalued ?enough.? At most, the proceeds of these short sales would be invested in a risk-free asset. III. C. 3. b. Other Styles
Event-driven strategies look to profit from mispricings surrounding major market events. Distressed securities funds focus their attention on firms going through bankruptcy proceedings and/or reorganizations. Since outstanding securities of these firms tend to be rather illiquid (if not frozen), these funds often wait for new issuances out of these firms, taking long positions in the new securities of firms they believe will survive and, if allowed by regulations, short positions in the new securities of firms they believe will not survive. Risk/merger arbitrage funds look to profit from mispricings that result from firms going through a merger, acquisition, or leveraged buyout. If the fund believes the mispricing is large enough, it will take a long position in the firm being acquired and (if this is part of their desired strategy) a short position in the acquiring firm. Arbitrage strategies are similar to long/short strategies and in general can be considered as a possible sub-strategy for most other styles (with the previously noted general exception of the macro style). These strategies are similar to long/short in their search for pricing
discrepancies, but these discrepancies do not have to be the same category of asset. The key here is that the long asset and the short asset are very closely related to each other. Convertible arbitrage funds look for companies who have issued convertible securities (e.g. bonds, preferred stock, or warrants). They will invest in those convertible securities deemed to be undervalued relative to the company's common stock, in which they will then take a short position. Fixed income arbitrage funds search for price discrepancies in the bond market among securities with
32
similar or identical terms issued by the same borrower.
Statistical arbitrage funds use
mathematical models to locate pricing inefficiencies then invest accordingly under the belief that mean reversion will occur. If a hedge fund can be compared momentarily to a stock, then a fund of hedge funds (FOHF) would be analogous to a mutual fund. The FOHF manager looks to provide positive returns not by determining which investable assets are undervalued and overvalued, but by determining which other managers are the most adept at doing so. FOHFs thus provide a
diversification benefit for an entire class of investments that is not completely transparent to the investment community. In addition, the initial capital required to invest in an FOHF (ranging from $25,000 to $1 million) tends to be much less than that required to invest in the average hedge fund (ranging from $50,000 to $10 million), making this class of investments more accessible to the investment community. However, the cost of these benefits is the double layer of fees that investors in FOHFs face. For the hedge funds which the FOHF manager correctly determined would increase in value, the managers of those hedge funds will extract both their management fees and performance fees. If the FOHF manager picks enough correct funds and thus earns positive returns net of the hedge funds' fees, then he will also be able to extract management fees and performance fees before the investors see their returns. In a small bit of relief, the fees of FOHFs tend to be smaller than those observed in the overall hedge funds universe. Gregoriou and Rouah (2002) observe management fees on the high side at two percent with average performance fees at ten percent, usually with high-water mark and hurdle rate provisions. Bernstein (2002) reports management fees tending to range between 1% and 1.5% with performance fees between 5% and 10%.
33
III. C. 4.
A Focus on Market Neutral Hedge Funds
As mentioned earlier, a market neutral hedge fund places equal dollar weight on its portfolio of long investments as it does its portfolio of short investments. The intent here is not necessarily that the long portfolio would have a positive return while the short portfolio would have a negative return (although that would be the ideal). Instead, the long portfolio merely has to outperform the short portfolio by the amount of the costs of engaging in this strategy (including transactions costs and the interest on margin loans) and the management fees extracted from the fund for the market neutral manager to show a profit to his investors. Thus, a market neutral hedge fund manager merely has to discover a way to determine classes of stocks that should experience slightly different levels of performance from each other in the future in order to be successful. III. C. 5. Risk Exposures of Market Neutral Hedge Funds
When research on the performance of hedge funds started becoming more common approximately ten years ago, there seemed to be a belief that the traditional models of explaining returns, especially those applied to mutual funds, should suffice to provide adequate explanations, even if it was discovered that the sources of hedge fund returns were different than those observed for other classes of investments. As articles on the subject continued to be published, though, it was becoming more and more apparent that the traditional explanatory models were not explaining very much. This is especially true for the market neutral strategy that this study is focusing on, even though similar results would be found by exploring other strategies. Brown, Goetzmann, and Ibbotson (1999) point out that the market neutral style is the classic hedge fund style and was never intended to track broad indices. Liang (1999) says that the market neutral strategy is the only one to truly ?hedge? buy-and-hold market risk. In
34
Gregoriou and Rouah's (2002) study, they note that market neutral funds are designed to be neutral to first-order moments (actual market movements) but not second order moments (the volatility of market movements), even though their volatilities may still be low relative to other hedge fund styles.12 As such, there should not be much, if any, surprise when index-based and factor models fail to account for large portions of their returns. In spite of this, researchers have continued to look for ways to fit hedge fund returns into traditional models. Ackermann, McEnnally, and Ravenscraft (1999) note that market neutral funds have low average returns and standard deviations of returns relative to other hedge fund styles and to the S&P 500.13 They also note that Sharpe ratios for market neutral hedge funds tend to be high relative to other strategies, implying that despite having lower returns, market neutral hedge funds provide a superior risk-return tradeoff. Schneeweis, Kazemi, and Martin (2003) find that market neutral hedge funds have little to no exposure to equity, debt, volatility, credit spreads, or a term premium. Kouwenberg (2003) observes that relative to other hedge fund strategies, market neutral hedge funds have almost universally the smallest absolute correlation with various market (stock and bond) indices, option selling strategies, Fama-French factors (market excess return, size-based returns, book-to-market-based returns), and the analogous Carhart momentum factor (return differences between prior winners and prior losers). Agarwal and Naik (2004) conclude that, based on their negative factor loading on the momentum factor in their analysis, relative value funds are contrarian in nature. They explain the intuitiveness of this result by describing these funds as waiting for the prices of fundamentally similar stocks to
12 13
This is a measure of the importance of managerial skill in this hedge fund category. Earlier in the same paper, they find that market neutral hedge funds tend to have higher performance fees than other hedge fund styles. This could be a way to compensate the fund manager for the lower expected returns of this style. 35
diverge then purchasing the newly undervalued stocks (losers) and shorting the suddenly overvalued stocks (winners). Spurgin, Martin, and Schneeweis (2001) point out that the long/short equity style in general exhibits market neutrality when regressed against the market return and a quadratic term designed to estimate changes in correlation with the market return in periods of extreme market shifts (neither term is significant and R2 = 0.014). Ranaldo and Favre (2005) analyzed which form of the market model provides the most explanatory power for each hedge fund style: the traditional model with only a linear term, a model with a quadratic term to account for a coskewness premium (for securities whose return distributions are negatively skewed during positively skewed markets), or a model with a cubic term as well to account for a cokurtosis premium (for securities that are more likely to experience extreme returns when the market experiences extreme returns). For the equity market neutral strategy, they found the traditional model to be best. However, for the relative value strategy (which it can be argued some equity market neutral strategies fall under), the quadratic model provides the best fit, and this model indicates that such strategies require an estimated 2.60 - 2.80% premium for the coskewness they exhibit. III. C. 5. a. Return Persistence
It has been argued that factor-based models like the ones used later in this study have difficulty separating return premia from managerial skill, so some researchers have attempted to look for persistence in hedge fund returns as a way of determining managerial skill. Brown, Goetzmann, and Ibbotson (1999) search for risk-adjusted return persistence in offshore hedge funds and are unable to locate any when accounting for style category and managerial skill. Agarwal and Naik (2000b) find little evidence of return persistence across hedge fund strategies
36
beyond two periods and for longer than quarterly periods (i.e. on a month-to-month or quarter-toquarter basis, but no further). Additionally, where persistence can be found, there is greater evidence of it in hedge fund losers (relative to the median return) than in winners. In contrast to these results, Amenc, El Bied, and Martellini (2003) apply the Hurst exponent (an econometric measure of persistence in time series data comparing its range to the number of periods being analyzed) to their analysis and are able to locate monthly return persistence (note that most other studies tend to focus on quarterly or yearly return persistence, only, though). III. C. 5. b. Non-Normality of Returns
While there has not been a direct study that focuses on the distribution of returns for long/short hedge funds, several authors have shown that hedge fund returns in general are not normally distributed. Since metrics such as Jensen's alpha and Sharpe ratios are based on the assumption that returns are normally distributed, the need to account for the third and possibly the fourth moments of hedge fund returns (skewness and kurtosis) is considered by several authors, including Amenc, Martellini, and Vaissié (2003) and Mackey (2006). In reporting the non-normality of hedge fund returns, Mackey (2006) specifically points out that after sorting several individual hedge funds by their alphas as he calculated them, he finds that most of the variation in alpha (85%), excess return (73%), and risk premium (61%) is concentrated in the tails of the alpha-ranked distribution.14 Anecdotally, only 37.95% of the total variation is found in the tails of a normally distributed random variable, and only 48.8% of the total variation is found in the tails of a uniformly distributed random variable. This indicates that hedge fund returns may be either highly skewed or possibly bimodal towards the tails.
14
These tails are defined as the top ten percent and bottom ten percent combined of individual hedge funds after sorting by alpha. 37
When de Beus, Bressers, and de Graaf (2003) simulate hedge fund performance by using a normal inverse Gaussian distribution and then form a portfolio of traditional and alternative investments, they first optimize their portfolio mix by incorrectly assuming hedge fund returns are normal. This ?optimal? portfolio exhibits value-at-risk (VaR) that is fifty percent greater than expected and expected shortfall that is sixty percent greater than expected if hedge fund returns were normally distributed. When subsequently optimizing the portfolio mix using the ?true? distribution, the portfolio mix changes substantially, reducing the optimal weight in alternative investments from sixty-five percent under the incorrect normality assumption to only fifteen percent under the correct assumption. Amin and Kat (2003) attempt to create a metric to compare hedge fund returns with the S&P 500 without relying on this assumption and subsequently find that hedge funds do not compensate investors for their risk as well as the S&P 500. Unfortunately, their metric assumes that the hedge fund benchmark should have a payoff function that is a monotonic nondecreasing function of the market index, which is a questionable assumption; since hedge funds exhibit near-zero correlation with various market indices, it seems odd to create a benchmark that likely has a strong positive correlation with the market index. While they attempt to find an alternative way to explain hedge fund betas, Kouwenberg (2003) points out that the non-normality of hedge fund returns does not impact alpha significantly. III. C. 5. c. Absolute Versus Relative Return Targets
Most common investment tools are analyzed based on a relative return framework. Individual stocks are considered to do well if they outperform their industry average. Mutual funds are considered to do well if they outperform the market or some specific large segment of the market. Thus, even if a stock or mutual fund lost some of its value over a certain period, this
38
would not be considered poor performance if the benchmark against which it is being compared lost even more value (in terms of returns). This is not true for hedge funds. In fact, one of the diversification benefits that hedge funds claim to offer is their ability to provide positive returns across all market conditions. This is why a hedge fund is said to have an absolute return target, as opposed to a relative return target. In spite of near-zero correlation with the S&P 500, for example, Amenc, Martellini, and Vaissié (2003) found market neutral returns to be consistent across the different types of markets (bull, bear, and steady). Capocci, Corhay, and Hübner (2005) go further by pointing out that the market neutral strategy is the only one to show consistent abnormal positive performance during both bullish and bearish periods. Fung and Hsieh (1997) attempt to expand Sharpe's (1992) model for hedge fund managers who have more absolute return targets by adding trading strategy and leverage determinants to the asset return determinant. In this article, their systems/trend following
strategy15 has a very low R2 and is not related to any of nine standard asset classes. Graphing this strategy's returns against the market shows that it acts more like a straddle (long a put and a call) than anything else. In contrast, their 2004 paper shows that seven asset-based style risk factors (including market risk and small-cap/large-cap return differences) provide good predictors for the overall hedge fund industry in an arbitrage pricing theory framework with R2 values generally above 0.5. The additional factors would need to be included when focusing on specific hedge fund styles. III. C. 5. d. The Role of Leverage
As pointed out in the section on regulations, hedge funds have a much greater access to leverage than do traditional investment vehicles due to their ability to take short positions in
15
Fung and Hsieh (1997) do not explicitly look at an equity market neutral strategy, but the systems/trend following strategy described in their paper is the closest match to the market neutral style. 39
securities as part of their strategies, even though Regulations T and U still apply to hedge funds attempting to gain leverage through margin (Nadel (1998)). In the much publicized 1998
collapse of Long Term Capital Management, it was noted that the fund had reached leverage ratios of as much as 100-to-1. Clearly, it is crucial to understand, then, the potential impact leverage may have on hedge fund performance. Kao (2002) summarizes this issue by pointing out that it has been difficult to determine empirically the link between leverage and hedge fund performance. As expected, increased leverage would have a negative impact on survival metrics (Gregoriou (2002)); the leverage magnifies the extent to which any downward movement in the unlevered investment affects the levered investment. Fung, Xu, and Yau (2002), in their analysis of global hedge funds, note that leverage magnifies Sharpe ratios and Jensen's alpha, but not excess returns nor beta. While a levered hedge fund can face effectively unlimited possibility of bankruptcy (especially if the leverage is being utilized to take short positions in some asset), there is only limited benefit to using leverage. There seems to be a firm belief among hedge funds themselves that they will become inefficient if they reach a certain size, because the sizes of their potential trades may eclipse the market's capacity for supply or demand, thus limiting their liquidity. Leveraging the investment in a hedge fund can bring the fund closer to that inefficient point (depending on the size of the fund and the instruments being traded). This is possibly one of the reasons that hedge funds remove themselves from databases once they reach a certain size (which varies by the fund). In the same vein, Goetzmann et al (2003) argue that there is only a finite amount of arbitrage profits available in the economy at any point in time, so the benefits of leverage are limited to those profits that have not yet been captured.
40
III. C. 5. e.
Dynamic Versus Passive Strategies
Another factor plaguing researchers' attempts to model hedge fund returns is that traditional models assume that investments are purely passive buy-and-hold strategies or at most systematically rebalanced (equal-weighted benchmarks mimic this). Hedge fund managers, however, follow what would be considered dynamic trading strategies, potentially jumping in and out of investments whenever the need arises to protect their position. This is why Fung and Hsieh (1997) attempt to add three dynamic trading strategy factors to a more traditional assetbased factor model. If beta is considered to be an asset's exposure to traditional risk factors and alpha the return component derived from managerial skill, there is an unexplained middle ground that Fung and Hsieh (1997) begin to touch upon. Jaeger and Wagner (2005) refer to this middle ground as ?alternative beta,? whereas Leibowitz (2005) calls it ?allocation alpha.? In either case, there is a concept that some component of a hedge fund's return is purely a function of properly following a specific hedge fund strategy. Over time, this may become a more important
component of hedge fund returns to determine. If there is, in fact, only a finite amount of arbitrage profits, then hedge fund alphas will decline as more money chases them (Jaeger and Wagner (2005)). They also point out that the average alpha will decline as more hedge fund managers enter the market, eroding the overall average skill level of all hedge fund managers (assuming the earliest entrants to this industry contained a high concentration of the most capable managers, which is not necessarily true, especially in the long run where brand new entrants to the job market could be very highly skilled relative to existing fund managers).
41
III. C. 5. f.
Biases in Databases
One of the major problems with studying hedge funds historically lies with the data itself. Since the main role of the most commonly used hedge fund databases has been to signal an openness for new investment (in other words, advertise), no single database has really been considered the best database of funds. Since funds choose the databases in which they want to be included, and there is no requirement that prohibits funds from going into one and only one database, the samples that make up each database tend to be vastly different. As such, using database-generated indices of fund returns as benchmarks (as is popular in equity research that benchmarks against the CRSP equal-weighted and value-weighted indices) can create results highly dependent on the database being used. For the market neutral strategy, indices from various databases vary by as much as five percent (Amenc, Martellini, and Vaissié (2003)). Fung and Hsieh (2002b) break down the biases generated by this situation into two categories. Natural biases are those ?that are consequences of sampling from an unobservable universe of hedge funds,? and spurious biases are ?those that arise from the way data vendors collect hedge fund information.? Natural biases, such as survivorship bias, are difficult if not impossible to rectify, but they are also common across different types of investment assets. Spurious biases, such as self-selection and instant history biases, are specific to the hedge fund industry, but are generally correctable through careful data manipulation. III. C. 5. f. 1) Survivorship Bias Survivorship bias in hedge fund databases is similar to the survivorship bias that plagues some more commonly used databases of financial information. In addition, since inclusion in these databases is voluntary, hedge funds no longer in operation for any reason may be thrown out of databases in which they were previously included. Liang (2001) estimates this bias to be
42
approximately 2.43% per annum. Others have put this bias at approximately three percent per annum (Brown, Goetzmann, and Ibbotson (1999); Fung and Hsieh (2000)). Unfortunately, these estimates are not analogous to the measurements of survivorship bias in other segments of the investment industry, which compare the average return of all of a particular type of investment asset over a time period to the average return of the members of that asset type still in operation at the end of the same period. Since the entire universe of hedge funds is unobservable, this calculation is impossible. In addition, the reliability of estimators of this bias for the hedge funs industry degrade as one tries to look further back in time, since hedge fund databases did not become very heavily populated until the mid-1990s (Fung and Hsieh (2002b)). III. C. 5. f. 2) Self-Selection Bias As mentioned earlier, hedge funds are not required to report their results to any database, and those that do are using the database as a means of advertising that they are accepting additional investment funds. The most logical reason a fund would not report its results is that its performance has not been good enough to expect that it would draw in any additional investors. The less obvious reason that has been touted as a reason to not report a fund's results to any database (or to choose to pull out of reporting to any database) is that some hedge funds stop reporting their results once they reach a certain size (Goetzmann et al (2003)). This implies that hedge fund managers believe there is some finite optimal level of assets to manage, as mentioned in the above section on leverage. These two factors make the net effect of this bias indeterminate. III. C. 5. f. 3) Instant History Bias The nature of the self-selection bias leads to yet another bias, the instant history bias. While hedge funds can decide when they want to consider reporting their results to a database,
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commercial hedge fund databases do not generally allow new hedge funds to just begin reporting their information. Usually, they must have approximately twelve months of prior results to report. As such, hedge funds with poor performance over their first few months may choose not to report in any database. Those that do decide to report in one or more databases will have thus likely had strong prior performance, and this past performance is automatically included in the database, thus creating an ?instant history? that will almost always report positive results. III. C. 6. Alternative Risk Measures
Since traditional return models tend to experience difficulty in explaining the sources of hedge fund returns, researchers have had to look to different factors and different performance metrics to help explain what would otherwise appear to be strong, significant alphas. Amenc, El Bied, and Martellini (2003) find that market neutral hedge funds have statistically significant exposures to oil prices (a proxy for the short term business cycle) and changes in three-month T-bill rates (a proxy for changes in expectations of future economic activity). In other words, their results indicate that market neutral hedge funds are exposed to risks related to actual and expected future economic activity. Even though this model (like so many others) had a very low R2 value, it provided a very strong predictability for the direction of the returns on a market neutral hedge fund. While equal- and value-weighted indices of individual hedge funds might be a sensible benchmark to evaluate a fund's performance (similar to how CRSP indices are used), Fung and Hsieh (2002b) suggest using funds of funds as appropriate benchmarks. While funds of funds do have an additional layer of fees than other hedge funds, using the performance of funds of funds eliminates or reduces the impact of the survivorship, self-selection, and instant history biases described above.
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Agarwal and Naik (2004) suggest conditional value-at-risk (CVaR), the expected value of the returns in the lowest tail of the distribution of returns, as a better estimate of hedge fund risk than variance. They support their contention by also noting that CVaR improves as an estimator over variance as volatility declines (which would be relevant for hedge funds that target and are able to claim lower volatilities than the market). According to Chan, Getmansky, Haas, and Lo (2006), market neutral hedge funds obtain higher expected returns during distressed periods, implying that returns generated by this strategy may come from volatility. This conclusion is further supported as they point out the recent struggles of this strategy as a result of recent (relative to their study) large fund inflows (thus increasing the sizes of these funds and bringing them closer to the aforementioned inefficient point) and changes in equity markets designed to reduce volatility and/or increase investor confidence, such as the decimalization of exchange-listed prices, the use of electronic communication networks that enhance communication between brokers and investors, the increased use of automated trading systems, and the fair disclosure provisions of Regulation FD. While associating declining performance with large inflows is not a surprise (as discussed above in the section on self-selection bias in databases), the other four items listed should all result in lower volatilities. This supports the use of an index such as VIX in a model attempting to explain market neutral strategy returns (in a factor-based regression, the difference between the average return on VIX call options, which profit from increased volatility, and VIX put options, which profit from decreased volatility, may be appropriate). Recalling Fung and Hsieh's (1997) contention that this style acts as a straddle on the market return further supports this inclusion. With many different possibilities for the ?right? model, none of which truly seem to do a great job of capturing hedge fund return variation, it would appear that any discussion of how
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well a hedge fund performs would be heavily influenced by which model is being applied to explain that performance. Fortunately for investors who desire to place their money in a hedge fund, while different models will clearly result in different calculated values of alphas, Alexander and Dimitriu (2005b) show that the ranks of individual fund alphas relative to each other are mostly consistent across different models. In other words, while the various models may agree on which fund managers are providing the most value added to investments in their funds, there is great discrepancy across models as to precisely how much value is being added (or destroyed) by the managers.
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IV. Hypotheses and Model Development In order to come up with a proper basis for comparing the profitability of personal management of assets relative to hedge fund management of assets, this study will simulate the portfolios that would be formed by following the advice implied by DT85 and holding them for three-year periods under the two possible investment options discussed in Part III of this paper: using the services of a broker-dealer (and facing the institutional constraints subsequently imposed on margin investors and short sellers) and using a hedge fund manager who will provide convenience for the investor who desires to profit from this strategy but who will charge additional fees for this convenience. IV. A. Hypotheses to Test The first test that will need to be performed is to check that the strategy implied by DT85 still is viable in the years after it was announced. In its purest form, with no frictions, there is little to suggest that the phenomenon that was studied in DT85 could not still exist. H1a: Stocks that were the most extreme poor performers (losers) over a three-year period should outperform stocks that were the most extreme good performers (winners) over the subsequent three-year period.
To test this hypothesis, I will replicate the DT85 model as closely as possible and test the difference between the returns of the loser and winner portfolios. This hypothesis will be supported if the three-year returns on the loser portfolio exceed the three-year returns on the winner portfolio by a statistically significant amount. I will also test this hypothesis against relaxed assumptions relative to DT85, such as the inclusion of non-NYSE stocks and requiring fewer years of prior data to exist on included stocks. Additionally, the nature of the stocks studied suggests that the return difference between these two categories of stocks may simply be based on compensation for different risk factors. Fama and French (1996), sorting NYSE stocks on deciles of prior returns, note that when they
47
regressed future returns of each decile in their three-factor model (Fama and French (1993)), the factor loadings on size and book-to-market were both significant at the extremes and declined while moving from the lowest prior return decile to the highest prior return decile. The factor loading on the market premium exhibited a slight smile pattern across deciles with little difference (likely not significant based on an observation of the magnitude of the difference, though this was not tested in the original paper) between the market risk factor loadings of the lowest and highest deciles. Thus, it can be expected that the returns on a portfolio consisting of long positions of previous losers and short positions of previous winners should be affected by the size and book-to-market risk adjustments exhibited by the included stocks. H1b: The factor loadings on size and book-to-market of a portfolio long in prior loser stocks and short in prior winner stocks should both be positive, while the factor loading on market returns should not be significantly different than zero.
Similarly, Carhart (1997) developed a risk factor to account for persistence in stock returns (momentum). Since DT85 is based on reversals in stock returns, the opposite effect should be observed. H1c: The momentum factor loading of the same portfolio should be negative.
Using the same methodologies that will form the returns tested in the first hypothesis, these two hypotheses will be supported based on the coefficients that result from regressing the differences in returns described earlier in a market model, capital asset pricing model, three-factor model, and three-factor model with momentum. In all four models, the market risk factor should be near zero. In both three-factor models, the size and book-to-market coefficients should be positive. In the momentum model, the momentum coefficient should be negative. Also, while not a formally-tested hypothesis, it would be beneficial to this study if all the alphas of these models are positive and significant, indicating that there is potentially some risk-adjusted excess return to following this strategy.
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Once this is shown to be a viable strategy, the focus will shift to using this strategy as a means of obtaining abnormal returns on an investment. This will allow a direct comparison of the two methods of investing detailed in this paper, personal/direct management of one's own investment and investment in a hedge fund. In either case, since both methods entail some form of cost or constraint, the returns on either strategy should be less than the difference between the returns of loser and winner stocks. This comparison, of course, needs to take into consideration the use of leverage in both strategies. H2a: After adjusting for leverage, the returns on the DT85 contrarian strategy through personal asset management should be less than the difference between the returns of DT85's loser stocks and DT85's winner stocks. After adjusting for leverage, the returns on the DT85 contrarian strategy through hedge fund investment should be less than the difference between the returns of DT85's loser stocks and DT85's winner stocks.
H3a:
Here, I will simply look for the raw returns from personal asset management to be significantly less than the returns calculated in testing H1a and for the raw returns from hedge fund investment to be significantly less than the returns calculated in testing H1a. Also, the restrictions imposed on investors attempting to employ leverage and engage in short selling are designed to lessen the risks associated with utilizing such investment tools. H2b: In absolute value terms, each risk factor loading from following the DT85 contrarian strategy through personal asset management should be less than the same loadings of the return differences analyzed in H1b and H1c. In absolute value terms, each risk factor loading from following the DT85 contrarian strategy through hedge fund investment should be less than the same loadings of the return differences analyzed in H1b and H1c.
H3b:
Two conclusions are wrapped up in this hypothesis. The crucial conclusion is that the absolute values of the slope coefficients of the various regressions should be significantly less in both the personal asset management and hedge fund investment cases than in the initial return difference case. The less crucial conclusion is that the signs of each risk factor should be the same across
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all three cases, though this point becomes even less important if a particular risk factor is not statistically significant.
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V. Data and Results V. A. Data Collection Most data for this study were obtained from databases provided by the Wharton Research Data Services (WRDS). Monthly and daily stock returns (and other stock information) from January 1979 through December 2006 came from the Center for Research in Security Prices (CRSP) Stock Monthly and Daily files, respectively. The January 1986 through December 2006 values for the independent variables used in the factor regressions came from Kenneth French's Data Library web site at Dartmouth. Separate from WRDS, interest rate information was
obtained from the Federal Reserve Economic Data (FRED) database maintained by the Federal Reserve Bank of St. Louis, and hedge fund index information was obtained from Hedge Fund Research, Inc. (HFR). V. B. DT85 Cumulative Abnormal Returns The initial step in testing the above hypotheses is to verify that the results described in DT85 still apply to investors who may have attempted to take advantage of the anomaly since it was published. As the initial study was published in the July 1985 issue of The Journal of Finance, the first portfolio (chronologically) to be studied will be formed at the beginning of January 1986; this is to hopefully allow the mechanics of market efficiency more than enough time to exert their influences as a result of newly published information. Consistent with DT85, for a stock to be potentially included in a portfolio, it must have seven years of continuous information available prior to the formation date (January 1979 through December 1985 for the first portfolio). Any security that does not have this information available is removed from the pool of potential stocks to include. Also, only stocks priced at no less than five dollars on the formation date and traded on the NYSE are included initially in this study. Once these filters
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have been applied, the returns of the stocks still in the pool are compounded over the previous three years (January 1983 through December 1985 for the first portfolio) and ranked according to these compounded returns.16 The thirty-five stocks with the highest such returns will be placed in the winner portfolio, and the thirty-five stocks with the lowest such returns will be placed in the loser portfolio. Then, for each month of the three-year testing period (January 1986 through December 1988 for the first portfolio), each stock's abnormal return is calculated relative to the market ( ) and summed up over the entire 36-month testing period to come up ). To avoid survivorship bias
with each stock's cumulative abnormal return (
at this point, any stock that is delisted before the end of the testing period is assumed to have zero return from that time forward. This is the equivalent of closing out one's position in a security at the end of the last month for which information about it is available and then doing nothing with the proceeds. While this may not be realistic (the proceeds from the sale of stock would at least be invested at a riskless rate), this should bias the results against finding a positive return differential, as extreme poor performers (loser stocks) are more likely candidates for delisting than extreme good performers (winner stocks). The average cumulative abnormal return is then computed for the portfolios of loser and winner stocks ( where X represents the loser (L) or winner (W) stocks and n = the number of stocks in each group). The difference between this figure for the loser portfolio and for the winner portfolio is the main test statistic used in DT85 ( ). If this study were to use ,
non-overlapping three-year periods, there would only be seven observations of DACAR to analyze (for the portfolios beginning in January of the following years: 1986, 1989, 1992, 1995,
16
This is a deviation from DT85, which ranked stocks by cumulative abnormal returns, but which is being done for consistency with later hypothesis tests that will use buy-and-hold (compounded) returns to both choose securities for the portfolios and to measure their results. 52
1998, 2001, and 2004). So, to have more data to analyze, DACAR is calculated for each of 217 portfolios beginning each month from January 1986 through January 2004. While this also deviates from DT85, it is not unprecedented in the literature focusing on DT85 to move away from non-overlapping testing periods (including DeBondt and Thaler (1987), their own followup to their original study). Initial results of this analysis indicate that the DT85-based approach to obtaining arbitrage profits has been arbitraged away. In the 217 testing periods, loser portfolios
underperformed the market by 3.57% over a 36-month period while winner portfolios underperformed the market by 3.59% over the same period, for a DACAR of 0.02% (p = 0.9932), ranging from a minimum of -83.51% to a maximum of 121.83%. While this might seem sufficient to refute the possibility of using DT85's overreaction hypothesis as a stock selection filter, the point of this paper is not simply to replicate DT85, but to assess its feasibility in a somewhat realistic investment environment. As such, it would make sense to expand the
population of stocks available for the loser and winner portfolios to include stocks traded on AMEX and NASDAQ as well. Doing so provides results along the same lines of DT85. Losers outperform the market by an average of 17.22%, and winners underperform the market by and average of 11.38%. DACAR then averages 28.60% (p < 0.0001), ranging from -56.77% to 259.92%. Given the difference between these results, it is tempting to consider that when AMEX and NASDAQ stocks became candidates for inclusion in the portfolios, they did so to the near complete exclusion of NYSE stocks from these portfolios. As such, this analysis also looked at the results of only incorporating AMEX and NASDAQ stocks through the initial filter. The assumption is, of course, that if there is little difference between these figures and the figures that
53
include all three exchanges, then NYSE stocks were effectively excluded from the loser and winner portfolios. The results do not bear this out. Losers outperformed the market by 28.21%, and winners underperformed the market by 10.29% for a mean DACAR of 38.49% (p < 0.0001) that ranges from -46.13% to 254.86%. Also, it may not make sense to require seven years of returns to exist prior to formation for a stock to be a candidate for either portfolio. Thus, a five-year cutoff was arbitrarily chosen to determine the pool of available stocks. While tests were not specifically performed to verify this, the performance of the various portfolios relative to the market tended to be magnified as a result of this adjustment: underperformers did even worse relative to the market, outperformers did better. For example, when all three exchanges are included, the loser portfolio outperformed the market by 23.75%, winners underperformed the market by 11.10%, and DACAR increased to 34.85% (p < 0.0001) while ranging from -64.01% to 223.92%. Table 1 summarizes these results. Overall, it would appear that the first hypothesis earlier is supported enough to continue with this study. While the original DT85 approach to comparing returns no longer results in a significant difference between the performance of prior losers and prior winners, the inclusion of stocks from AMEX and NASDAQ allows one to discover such a difference. V. C. DT85 Buy-and-Hold Returns While the previous analysis shows how the loser and winner portfolios perform relative to the market on average each month, it is more important for this study to observe how an investment made in the loser portfolio and held for thirty-six months compares to an investment made in the winner portfolio and held for thirty-six months. Table 2 shows that the amount by which the 36-month return on the loser portfolio exceeds the 36-month return on the winner portfolio is qualitatively similar to the DACARs of the previous section. There is no evidence of
54
a difference when only NYSE stocks are considered but strong evidence for a difference when stocks from AMEX and NASDAQ are incorporated into the analysis. With only NYSE stocks, the loser portfolio underperformed the winner portfolio by 1.75% (p = 0.5931) when seven years of prior data were required and by 4.87% (p = 0.1439) when only five years of prior data were required. When all three exchanges were included, the losers outperformed the winners by 37.93% (p < 0.0001) and 48.11% (p < 0.0001), respectively. Loser portfolios formed from only AMEX and NASDAQ stocks outperformed winners by 56.99% (p < 0.0001) and 66.54% (p < 0.0001), respectively. These figures again support the first hypothesis. These results were then tested to determine if the return differentials were generated by some uncertain anomaly or as premia for some risk factors. Three traditional models; the market model, CAPM, and the Fama-French three factor model; and a fourth model that adds a momentum factor to the Fama-French three factor model (Carhart (1997)) were used as explained below. Market model: CAPM: Three-factor model: Momentum model: where = the return generated by portfolio X in month t = the market return in month t = the risk-free rate of return in month t = the Fama-French size factor (small minus big) in month t = the Fama-French book-to-market factor (high minus low) in month t = the Carhart momentum factor (up minus down) in month t
55
For each of the 217 testing periods within a given parameter set (exchanges and years of prior information), the return differentials were divided up into their 36 months, resulting in 7,812 monthly return observations for each regression. The coefficients in each regression represent the sensitivity of the returns to the specific risk factors, and the intercept in each regression represents the unexplained (possibly anomalous) return per month. All the regression results are contained in Table 3. As expected, the return differentials were positively related to the size and book-to-market premia (all with p < 0.0001). The size factor was greatest when only NYSE stocks were included17 (ranging from 0.6499 to 0.7599), declining when AMEX and NASDAQ stocks were included (0.3230 to 0.3494), and declining again when NYSE stocks were removed (0.2655 to 0.2838). Also, decreasing the prior return requirement from seven years to five years increased the size factor loading in five out of six regressions, the exception being the momentum model without NYSE stocks, where the factor decreased from 0.2698 to 0.2655. For the book-to-market factor, the all-exchange regressions (0.5670 to 0.6418) have a greater value in three out of four cases than the NYSE-only regressions (0.5434 to 0.6241), and the non-NYSE book-to-market coefficients are universally lower than the rest (0.4384 to 0.4847). Reducing the data requirement increases this factor in the NYSE-only regressions but decreases it in the regressions that include AMEX and NASDAQ stocks (alone or all-inclusive). However, the rest of the results do not appear to line up with the expectations on the market and momentum factors as described in the second and third hypotheses above. Relative to the market risk factor, the expectation was that market factor loadings would not be significantly different than zero. Even if all twenty-four market factor loadings were statistically significant, this part of the second hypothesis could still be supported if the coefficients were
17
Even though there is no statistical evidence for any difference between the loser and winner returns when only NYSE stocks were included in the selection process, those returns are still analyzed due to their relationship with DT85. 56
economically insignificant or evenly distributed above and below zero. Instead, all twenty-four market factor loadings are negative with p < 0.0001. In absolute terms, the NYSE-only
coefficients were the smallest (-0.2171 to -0.3845), followed by the non-NYSE coefficients (0.3650 to -0.5940), followed by the largest such figures in the all-inclusive regressions (-0.4221 to -0.7261). Reducing prior data requirements increased the magnitude of this factor in all cases, with changes ranging from 0.0470 to 0.1290. Also, the momentum factor does not align with the predictions mentioned earlier. While the NYSE-only return differences experienced a negative momentum factor loading in both the five-year (-0.1495, p < 0.0001) and seven-year (-0.0719, p < 0.0001) data requirements, the inclusion of AMEX and NASDAQ stocks changes this coefficient to a positive or insignificant value, 0.1473 (p < 0.0001) and 0.0620 (p = 0.0059) for the all-inclusive cases and 0.1517 (p < 0.0001) and 0.0110 (p = 0.6061) when only AMEX and NASDAQ stocks are included. Note that this effect is also magnified when the data requirement is reduced from seven to five years. Before analyzing these coefficients more succinctly, note the promising results of the intercepts as they relate to moving forward to the next section, where these results form the justification for the investing strategy to be followed later. In all sixteen regressions that
included AMEX and NASDAQ stocks, the intercepts were positive and significant. The smallest and least significant of these intercepts was for the momentum regression when all exchanges are included and seven years of prior data are required: = 0.00372 and p = 0.0006, implying an
annual excess return of approximately 4.464%, or 13.392% over the entire three-year period. When looking at NYSE-only return differences, six of the eight regressions had negative intercepts; only the market model intercepts were positive (0.00323, p = 0.0001 for the sevenyear requirement; 0.00343, p = 0.0003 for the five-year requirement).
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It should also not be too surprising to note, based on the discussion earlier in section III. C. 5. of this paper, that the adjusted R2 values of these models are relatively low, ranging from 3.61% to 13.82%. Whether these returns are better explained by some of the alternative models described in that section is beyond the scope of this study. V. C. 1. Unexpected Positive Momentum Coefficients The especially surprising point about the positive coefficients to momentum is the nature of the momentum independent variable (UMD). Carhart (1997) defines this factor as ?the equalweight average of firms with the highest 30 percent eleven-month returns lagged one month minus the equal-weight average of firms with the lowest 30 percent eleven-month returns lagged one month. The portfolios include all NYSE, AMEX, and NASDAQ stocks and are re-formed monthly.? The similarity between this factor and the selection criteria for the portfolios tested in this paper is relatively clear. Since the UMD factor subtracts the returns of prior losers from the returns of prior winners, it should be inversely related to the return differences calculated above. To investigate this odd result, I performed the same regressions on the loser and winner portfolios separately. The results of these regressions are found in Tables 4a - c. Here, a possible explanation for the positive momentum factor loadings can be found. First, in all six cases, the momentum factor loadings on both the loser and winner portfolios are negative, ranging from -0.3569 to -0.2328 for the loser portfolios and from -0.4025 to -0.2039 for the winner portfolios, all with p < 0.0001. In the two NYSE-only cases, the factor loadings on the losers are greater than the factor loadings on the winners. In the other four cases, which all include AMEX and NASDAQ stocks, the factor loadings on the losers are all less than the factor loadings on the winners. So, while the positive coefficients on the momentum factor in the return difference regressions may result in rejection of the third hypothesis as stated above,
58
the results of the separate winner and loser regressions support the idea that there is a significant reversal component to the returns generated by both the loser and winner portfolios. For NYSE stocks, the reversal component is stronger in the losers than in the winners. For AMEX and NASDAQ stocks, the reversal component is stronger in the winners than in the losers, and that effect also dominates when combined with NYSE stocks, resulting in the positive momentum coefficient in the return difference regressions. It is also interesting to observe the breakdown of the excess returns as represented by the intercepts. In twenty of the twenty-four winner regressions, the intercept is negative and
significant. In the other four regressions, which are the momentum regressions with AMEX and NASDAQ stocks, the intercept is positive yet insignificant. On the other hand, in all sixteen loser regressions that include AMEX and NASDAQ stocks, the intercept is positive and significant; in the eight NYSE-only regressions, the intercept is either negative, insignificant, or both. Also, as a follow-up to the brief mention of the low adjusted R2 values, this breakdown also gives a strong impression that much of the inability to use these factor models to explain the variability in the return differences results from the low explanatory power of the various factor models to explain the returns to the loser portfolios (adjusted R2 ranging from 8.59% to 37.55%), as the winner portfolios tend to fit these models well (51.28% to 76.50%). V. D. Personal Asset Management As required by Regulation T, for every dollar an investor wishes to sell a security short, he will be required to post at least half that amount in cash as collateral with his broker. The sum of these two amounts (initial securities sold short + cash deposit) is called the investor's credit
59
balance (CR)18 and can earn interest. The current value of the securities sold short at any point in time is called the short market value (SMV). The difference between the two amounts is the investor's equity (EQ = CR - SMV). The investor could also take a long position in securities and use margin to leverage his position. According again to Regulation T, for every dollar of securities the investor wants to purchase, he would have to post at least half that amount in cash. The broker will loan the remaining amount that the investor does not provide to him; the amount of this loan is the investor's debit balance (DR). The current value of the securities purchased in this manner is called the long market value (LMV). The difference between the two amounts is the investor's equity (EQ = LMV - DR).19 The investor in this paper is taking both a long and short position in securities. In such a case, the two scenarios just presented are analyzed in tandem with each other. In other words, the two equity values are added together (EQ = LMV DR + CR - SMV).20 This equity value is adjusted whenever the broker marks-to-market. As an example, assume the investor has $100,000 that he would like to invest, he would like to both maximize his investment through using as much margin as Regulation T allows, and he would like to have his initial investment split equally among long and short positions. On the long side, he posts $50,000, borrows $50,000 (DR), and purchases $100,000 in securities (LMV). On the short side, he posts the other $50,000 (cash deposit) and is allowed to take short positions in $100,000 (SMV) worth of securities (thus, CR = $50,000 + $100,000 = $150,000). His initial equity would then be $100,000 - $50,000 + $150,000 - $100,000 = $100,000. At the first marking-to-market, two things occur immediately. First, the LMV and SMV are adjusted to reflect changes that occurred in the market values of the securities. If the securities held long
18
The terms introduced in this section are described in greater detail in the Securities Training Corp.'s study guide for the Series 7 exam. 19 Note that in both cases, the initial equity equals the investor's cash deposit. 20 LMV represents the value of the equal-weighted portfolio comprising the 3035 loser securities, and SMV represents the value of the equal-weighted portfolio comprising the 3035 winner securities. 60
declined in value by an average of 10% and the securities held short rose in value by an average of 20%, then the investor would have LMV = $90,000 and SMV = $120,000. Second, since the debit balance represents a loan, interest owed will accrue on that loan, thus increasing the debit balance. For simplicity's sake, temporarily assume the broker-dealer applies a monthly markingto-market and that the interest applied to the loan is 12% per annum (or 1% per month). The new debit balance would then be $50,500. Also, the credit balance could be invested in a money market fund if the broker-dealer provides such an option for the investor. Again for the sake of simplicity, I will temporarily assume this option is not available in working through this example (though it will certainly be considered as an option during the simulation). The new value of the investor's equity can now be determined: EQ = $90,000 - $50,500 + $150,000 - $120,000 = $69,500. In reality, the interest rate applied to debit balances each month varies, and is based off of what is known as the broker loan rate, which is the interest rate banks charge brokers to borrow funds. Brokers then generally charge investors a premium on the broker loan rate as interest on the debit balances in their margin accounts (a 3% premium is used in this analysis). Since the broker loan rate can vary depending on the broker (just as interest rates vary from one investor to another), it is estimated for the purposes of this analysis as that month's prime interest rate. Once all marking-to-market has been completed, the FINRA margin requirements must be satisfied. The requirement is that equity must be maintained at a minimum level of 25% of the LMV and 30% of the SMV. 21 The margin requirement could then be defined as REQ = 0.25 * LMV + 0.30 * SMV. In the example above, the investor's margin requirement after the first
21
Different brokers; such as E*Trade, Bank of America, UBS Paine Webber, and several others; were contacted to determine what margin requirements are actually imposed on investors. Although the federal minimum requirements of 25% and 30% are used in this example, brokers usually use requirements of 30% on long positions and 35% on short positions to protect themselves from the risk associated with providing margin. 61
marking-to-market would have been REQ = 0.25 ($90,000) + 0.30 ($120,000) = $22,500 + $36,000 = $58,500. Since EQ > REQ ($69,500 > $58,500), there would be no margin call imposed on the investor this period. Several months later, the new positions the investor faces may be as follows: LMV= $140,000, SMV = $160,000, DR = $56,000, CR = $150,000. In this case, EQ = $140,000 - $56,000 + $150,000 - $160,000 = $74,000 and REQ = 0.25 ($140,000) + 0.30 ($160,000) = $35,000 + $48,000 = $83,000. Since EQ < REQ, the investor would now receive a margin call. He would be forced to adjust his positions so that his equity would be at least equal to his margin requirement. One possibility would be to give the investor unlimited cash to deposit, but this option becomes uninteresting rather quickly, as it reduces to DeBondt and Thaler (1985) with the inclusion only of interest payments on the credit and debit balances. However, with unlimited cash, a profit maximizer would very likely pay off his loan immediately as well, which further reduces the problem to simply DeBondt and Thaler (1985), so we do not give the investor the ability to simply deposit cash. He decided at the outset that his initial deposit was all he was willing to deposit for this account. Whether this is because he needs the rest of his cash to pay his day-to-day living expenses or because he is simply stubborn does not matter. This gives the investor two options. He can sell off some of his long position, the proceeds of which would either be used to pay off some of his loan (thus reducing DR by the same amount) or go into his cash account (thus increasing CR by the same amount). Otherwise, he can close out some of his short position. Since this is equivalent to purchasing the securities in his short portfolio, the funds would either be obtained from the credits he has on hand with the broker (thus reducing CR by the same amount) or by borrowing additional funds from the broker (thus increasing DR by the same amount). Note how all these options result in no change to the
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investor's equity, but reduce the margin requirement he faces (since in either scenario, either LMV or SMV would decrease). This leads to two more decisions for the investor: which positions should he change and by how much. A real investor could analyze all the securities in his portfolios and then decide which specific positions he would like to liquidate/close out. The investor in this paper will follow a much simpler decision-making process.22 First, he will always make the minimum change necessary to meet the margin requirements. Then, when changing his portfolios, he will first analyze how his long and short positions are performing against each other. If his short position is outperforming his long position (SMV > LMV), he will close out his short position by the amount of the adjustment necessary to lower the margin requirement to his equity value as long as this will not lower his short position to below his long position in hopes of cutting future losses due to future gains in the short positions. If his long position is outperforming his short position (LMV > SMV) by a sufficient amount, he will liquidate his long position by the amount of the adjustment necessary to lower the margin requirement to his equity value as long as this will not lower his long position to below his short position (this has the effect of ?locking in? some of his gains). If this adjustment would make the position that was greater cross below the lesser position, he would adjust both positions by whichever amount would be necessary to both lower the margin requirement to his equity value and to set his long and short positions equal to each other (thus ?locking in? all gains or losses so far from the difference in portfolio returns). Whether DR or CR is adjusted is also based on the investor's preferences. If he decides to sell some of his long position, he would prefer to pay off his debt (thus reducing his future interest payments) above increasing his interest-earning balances (since the interest rate on the debit
22
The effect of this process will be to bias results of analyses in favor of efficiency ar35 loser securities, and SMV represents the value of the equal-weighted portfolio comprising the 35 maximization. 63
balance will tend to be greater than the interest rate on the credit balance). If he decides to close out some of his short position, he would prefer to obtain the funds to do so by using his interestearning balances above acquiring more debt with the broker (thus increasing his future interest payments). So, a reduction in LMV due to a margin call is accompanied by an equal reduction in DR and a reduction in SMV due to a margin call is accompanied by an equal reduction in CR. However, if the investor is actually earning greater returns on his credit balance than he is paying on his debit balance, then these conclusions would be reversed (increase CR when reducing LMV and increase DR when reducing SMV). The amount to change the portfolio mix by is simple in the first two scenarios. If the investor desires to reduce his short position, he would close out REQ EQ of his short position 0.30 (reducing both SMV and CR by this amount) as long as this does not reduce his short position below his long position. If he desires to reduce his long position, he would liquidate REQ EQ 0.25 of his long position (reducing both LMV and DR by this amount) as long as this does not reduce his long position below his short position. In the third scenario, recall that the equity value will remain unchanged after the adjustments have been made. Since he is readjusting his long and short positions to the same values, the new margin requirement after adjustments would be 0.25 * LMVpost-adj + 0.30 * SMVpost-adj. This amount also equals the equity though, since he is setting his portfolio up so that the requirement falls to exactly the equity value. Thus, LMVpost-adj = SMVpost-adj = EQ . It then becomes clear that the investor would liquidate his long position 0.55 (reducing LMV and DR) by LMV
EQ and close out his short position (reducing SMV and 0.55
64
CR) by SMV
EQ . Applying these rules to the example above, equity is $9,000 less than the 0.55
margin requirement ($74,000 vs. $83,000), and the short positions are outperforming the long positions ($160,000 vs. $140,000). Thus, the investor would initially want to close out $9,000 0.30 = $30,000 of his short positions. But this adjustment would lower his short position below his long position. This will cause the investor to instead adjust both his long and short positions to the same value, $74,000 = $134,545.45. The sale of some of his long positions will allow him 0.55 to pay off $140,000 - $134,545.45 = $5,454.55 of his debt. Closing out some of his short positions will use $160,000 - $134,545.45 = $25,454.55 of his credits with the broker. After this adjustment, his portfolio would have the following positions: LMV = $134,545.45, SMV = $134,545.45, DR = $50,545.45, CR = $124,545.45. Now, EQ = $134,545.45 - $50,545.45 + $134,545.45 - $124,545.45 = $74,000 and REQ = 0.25 ($134,545.45) + 0.30 ($134,545.45) = $33,636.36 + $40,363.64 = $74,000. Two other constraints must be imposed as well. First, none of the four portions of equity (LMV, SMV, DR, CR) can be negative. This may cause the investor to increase CR if he completely pays off his loan or to increase DR if he has no more credits with which to close out his short position. Second, if equity ever falls below zero, the investor cannot lower his margin requirement to equal his equity (since LMV and SMV cannot fall below zero), so if this circumstance ever occurred, he would completely liquidate this account. He will do the same if equity reaches zero exactly, since it defeats his purpose to lower his margin requirement to zero (possible only by setting LMV = SMV = 0) and then continue to allow his equity to erode as interest accumulates on his debit balance. On a complete liquidation, the investor most likely had to post additional funds that he did not intend to use at the outset. To represent the
65
(opportunity) cost of these additional funds, this amount is adjusted each month through the end of the testing period to accrue interest at the risk-free rate (i.e.: 3-month T-bill rate) in which he could have otherwise invested. V. D. 1. Results of Personal Asset Management To test H2 and H3, I am first going to focus solely on the scenario where only five years of prior data are required and where stocks can be chosen from NYSE, AMEX, and NASDAQ (thus providing the greatest population of stocks of the six scenarios analyzed earlier). Using the same selection criteria as was used to test the first set of hypotheses, I use the method described in the previous section with the following additional assumptions: Portfolios are formed on the first trading day of each month to allow for comparability with results from other sections. To lessen the problem of thinly traded stocks mentioned briefly during the literature review, stocks whose bid-ask spread is at least five percent of the open price on the portfolio formation date are removed from the population of selectable stocks. Balances are marked to market at the end of each trading day for the purpose of determining margin calls. Maintenance margin rates are set at 30% for long holdings (the loser portfolio) and 35% for short holdings (the winner portfolio). When a margin call is made, long (short) positions are sold (closed) to maintain the same weights in each security as there was after the marking-to-market but prior to the margin call. While not realistic (it would require the sale/purchase of fractional shares of stocks), it provides a middle ground between what actually are the best and worst possible margin call strategies.
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Dividends received from long holdings are added to the credit balance, and dividends paid to short holdings are subtracted from the credit balance. The credit balance is assumed to be invested in a money market account that earns a riskless rate of return (assumed to be the three-month T-bill return). The debit balance is a loan that accrues interest at a rate three percentage points above the prime rate of interest. No matter how well or how poorly the investment is performing, the investor will not withdraw his funds until the end of the three-year test period. Figure 1a presents a flowchart describing the algorithm used in this simulation. Table 5 details the results of following this strategy. The personal asset management strategy averaged a 51.44% return (p < 0.0001) over the 217 three-year testing periods studied, ranging from -40.83% to 187.36%. While this exceeds the 48.11% return differences observed in the DT85-based analysis, it is not by a significant amount (p-value of difference = 0.4934), and the unlevered value of the return from this strategy (25.72%)23 is less than the DT85 return differences (p-value of difference < 0.0001). This lines up with the expectations of H2a. Table 6 provides the results of running the factor regressions on the personal asset management results, including the breakdowns by loser and winner portfolios. Focusing on the overall results first, most of the expectations for the coefficients discussed for DT85 (insignificant market factor, positive size and book-to-market factors, and negative momentum factor) are met in the personal asset management strategy.24 In the market model and CAPM regressions, the loading on the market return (or excess market return) is positive and insignificant in both cases, 0.0181 (p = 0.2599) and 0.0224 (p = 0.1629). The adjusted R2 of
Since the maximum leverage allowed by Regulation T, 50%, was used, allowing the investor to ?double ? their investment, the unlevered returns in all cases are determined simply by halving the levered returns. 24 Unless stated otherwise, all coefficients from this table had p < 0.0001.
23
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both models is only 0.02%. In the three-factor and momentum regressions, the excess market return factor became positive and statistically significant (0.1801 and 0.1421, respectively), and both the size (0.4877 and 0.5075) and book-to-market (0.6289 and 0.5948) factors are positive and significant; the momentum factor is negative and significant (-0.1646). Also, while greater than the other two models, the adjusted R2 values of these two models are still relatively small at 9.80% and 11.25%, respectively. Finally, all four intercepts are positive and significant:
0.01201, 0.00832, 0.00469, and 0.00645, respectively. This last intercept (from the momentum model) implies an annual excess return of approximately 7.74% for the astute investor, or 23.22% over the entire three-year period. Breaking down this regression into its component loser and winner portfolios finds substantively similar results to what were shown in the DT85 loser/winner regressions. The intercepts are positive and significant for the loser portfolios and negative or insignificant for the winner portfolio. The (excess) market return factor loadings are positive and significant for all the loser and winner portfolios, and the magnitude is greater for the winners than the losers (though this difference is only 0.0237 in the three-factor model and 0.0202 in the momentum model). The loadings on the size factor are positive and significant for the losers and winners in both models in which it is included, and the loading has a greater magnitude on the losers than on the winners. The book-to-market loadings are positive and significant for the loser portfolios and negative and significant for the winner portfolios. One difference from the DT85 case is looking at the momentum factor. It is negative and significant for both the loser and winner portfolios, with the value being greater for the winners (though only by 0.0151), as opposed to the value for the loser being greater in the DT85 case. The regressions on the separate loser and winner portfolios have greater explanatory power as measured by adjusted R2 than the combined
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portfolio.
The main difference between this case and the DT85 case, though, is that the
explanatory power of these models on the loser portfolios is approximately 30% higher in all four models under personal asset management than their DT85 counterparts. V. E. Additional Hedge Fund Expenses As mentioned earlier, an investor who would like to take advantage of the profit potential of this strategy but has neither the time, inclination, nor ability to do so directly through personally managing his own account can invest in a hedge fund that follows a strategy similar to their desired strategy. This investor would then face not only the margin regulations described earlier but also the fees that hedge funds assess. Figure 1b presents a flowchart describing the algorithm used in this simulation and includes the following additional assumptions: Management and performance fees are assessed at the end of each calendar quarter and at the end of the three-year test period (if it does not already fall on the end of a quarter). These fees result in a reduction of the credit balance in the investor's account with the hedge fund. The management fee is one percent of the average daily balance of the assets under management of the investor's account since the previous fee assessment. Assets under management are calculated as the sum of the long holdings and the credit balance of the account after each day's marking-to-market and after any margin call has been resolved. The performance fee is twenty percent of the equity balance above the high watermark. If equity on the fee assessment date is above the high watermark, it becomes the new high watermark.
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No hurdle rate is applied to the high watermark. This will create more fees for the hedge fund to extract and bias the results of the simulation against being profitable for the investor. Table 5 also details the results of following this approach, which averaged 32.54% net of fees over the 217 three-year testing periods (p < 0.0001), ranging from -45.44% to 140.56%. The management fee averaged 8.17% per three-year period, ranging from 4.87% to 10.82%; and the performance fee averaged 9.76% per three-year period, ranging from 0% to 33.75%. Even including the benefits of leverage in these results, the investor in the hedge fund earns significantly less than the pure DT85 return difference (p-value of difference < 0.0001), which is in line with the expectations of H3a. Table 7 provides the results of running the factor regressions on the hedge fund results, including the breakdowns by loser and winner portfolios, and the results are similar to the personal asset management results (the next section will compare these two approaches in further detail).25 In the market model and CAPM model, the (excess) market return factors are 0.0342 (p = 0.0398) and 0.0387 (p = 0.0203), respectively. The market factor is positive and significant in the three-factor and momentum models as well, at 0.1985 and 0.1521. The size (0.4984 and 0.5226) and book-to-market (0.6391 and 0.5976) are positive and significant, and the momentum factor is negative and significant (-0.2006). These results all line up with the expectations of performing these regressions on the DT85 return differences as described in H1b and H1c. The adjusted R2 values for the market and CAPM models are extremely small at 0.04% and 0.06%, while the explanatory power of the three-factor model is 9.48% and that of the momentum model is 11.52%. All four intercepts are positive, at 0.00837, 0.00475, 0.00106, and 0.00320, For the
respectively, with only the three-factor intercept being insignificant (p = 0.1391).
25
Unless stated otherwise, results in this section are also assumed to have p-values < 0.0001. 70
momentum model, the intercept indicates a risk-adjusted return of 3.84% per year, or 11.52% over a three-year period. V. F. Changes in Risk Comparing the momentum regression results of this strategy with that of the DT85 return differences indicates that, in line with the expectations of H2b and H3b, the imposition of institutional constraints does indeed lessen the investor's exposure to the various risk factors analyzed. However, maximizing leverage like the investor in this study brings some of that risk back. Table 8 compares the momentum regression coefficients between the DT85 return
differences and both the levered and unlevered personal asset management and hedge fund approaches. The momentum model was reanalyzed by combining the two results datasets being compared and creating a dummy variable equal to 1 if the observation was from the DT85 return difference and 0 if it was from the personal asset management approach or hedge fund approach (each comparison performed separately). The comparison results are the coefficients for the dummy variable and the four interaction terms between the dummy and the four factors. Focusing on the unlevered results first, notice that applying institutional constraints alone had a significant impact on not only the investor's risk exposures, but also his ability to earn abnormal returns. For the personal asset management approach, exposure to market- and momentumbased risk has been reversed but reduced in absolute value terms (by 86.64% and 55.87%), exposure to size- and book-to-market-based risk has been reduced (23.49% and 50.23%), and risk-adjusted returns have been reduced by 41.67% (from 0.552% per month to 0.322% per month). For the hedge fund approach, the changes in risk are similar: reversals and reductions of market- and momentum-based risk (85.68% and 31.91%) and reductions in size- and book-tomarket-based risk (21.20% and 50.00%) accompanied by the loss of 71.01% of risk-adjusted
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returns (from 0.552% per month to 0.160% per month).
Incorporating leverage, however,
appears to eliminate most of the risk reductions and may have even made the strategy riskier than the pure return differences suggested. Compared to the DT85 return differences, there is no statistical change in either book-to-market-based risk (p-value of changes = 0.9530 for personal asset management and 0.9998 for hedge fund investment) or the ability to extract abnormal returns (p-value of changes = 0.4760 and 0.0561). The exposure to size-based risk increases (53.05% and 57.60%), as does the absolute exposure to momentum-based risk (11.74% and 36.18%). Only the market-based exposure is still reduced, though its reduction (73.26% and 71.38%) is less than in the unlevered situation. Table 8 also compares the results of the momentum model regressions from the personal asset management and hedge fund approaches using the same dummy variable method described above (dummy = 1 for personal asset management and 0 for hedge fund). While none of the changes to the risk factor loadings are statistically significant (p-values of 0.6953, 0.6083, 0.9390, and 0.0861), it is interesting to note that all four factor loadings have greater absolute values when using the hedge fund approach. However, the risk-adjusted return falls significantly when shifting from the personal asset management approach to the hedge fund approach. The unlevered 0.00325 decrease in the intercept indicates the loss of 3.90% risk-adjusted return per year, or 11.70% over three years. V. G. Other Results Two other points that were discussed earlier in this paper were the concept of arbitrage and the January effect. While the results gathered above indicate that the return differences discovered in DT85 have not on average been arbitraged away over the 1986 - 2006 period studied in this paper, the effects may have slowly been arbitraged away. If so, then the positive
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returns found would have been the result of high returns early in the period analyzed that would have declined to some equilibrium level at some point along the way. Figure 2 shows the average monthly return of each of the 217 portfolios. For both the personal asset management and hedge fund approaches, it appears that the average returns rise for approximately the first 67 portfolios (formed January 1986 - July 1991), follow a ?smile? pattern through the next 112 portfolios (August 1991 - November 2000), then decline for the remaining 38 portfolios (December 2000 - January 2004). Figure 3 shows the model regressions on the 217 portfolios. values of performing momentum
For both approaches, while there seems to be
fluctuations up and down for the first 96 portfolios (January 1986 - December 1993) that make it difficult to discern a pattern visually, the values decline on average for the remainder of the
portfolios (January 1994 - January 2004), indicating that the ability of this strategy to provide returns beyond the risk premia for the investor has diminished or possibly even disappeared. Figure 4 shows the average returns in each calendar month for both approaches. This figure clearly indicates there was a January effect during the period analyzed in this study. Returns in January following the personal asset management approach averaged 6.09%, over 2.5 times as much as the next highest month (February, 2.23%); the hedge fund approach was comparable, with a January average of 6.36% compared to February's 2.29%. This does not seem to be the result of tax-loss selling, though, as both the loser and winner portfolios experience positive and significant returns in both November (2.57% and 2.47% for personal asset management, 2.49% and 2.39% for hedge funds, all p < 0.0001) and December (2.08% and 1.39%, 1.91% and 1.27%, all p < 0.0001). Figure 5 presents the values of performing
momentum model regressions on each month (651 observations in each regression). There seems to be a January effect in the intercepts as well, as the value for January (0.03593 for
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personal asset management and 0.03745 for hedge funds) is more than three times the next highest value (February, 0.01148 and 0.01196). This, however, seems to be driven by the loser portfolio (0.03564 and 0.03462 in January), as the portfolios all have absolute values less than 0.01. Finally, since the hedge fund approach did result in positive values, it would be values for each month in the winner
interesting to see if some hedge funds are actually applying this strategy in practice. To look at this, I first took the average monthly return results from the hedge fund simulation for all months in which there were 36 months of simulation results. I then used these averages as independent variables in various factor regressions on HFRI and HFRX indices designed to track the performance of funds that follow equity-based strategies (e.g.: equity market neutral, equity hedge, and equity non-hedge). In none of these regressions was the factor based on the
simulation in this paper significant, whether it was the only factor in the model or whether it was included with the four factors from the momentum model used in earlier analyses. Thus, this study cannot provide evidence that the strategy described herein is actually followed by existing hedge funds. However, this non-result could simply be caused by the use of indices as
dependent variables that incorporate many approaches to equity investment even within the same category, so this also does not provide evidence that there are no hedge funds that follow this strategy.
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VI. Conclusion and Directions for Future Research This study revisited the overreaction hypothesis studied by DeBondt and Thaler (1985). In their original paper, they found that stocks that performed the poorest over the previous three years could outperform stocks that performed the best over the previous three years by an average of 24.6%, as measured by subsequent three-year cumulative abnormal returns. While subsequent studies debated the source of this return differential, Fama and French (1996) seemed to be able to account for this (and other anomalies) using risk factor analysis, resulting in little subsequent research that directly focused on the findings of DT85. However, by using a
different sampling technique (sorting stocks by deciles) than DT85 used (top/bottom 35 stocks), Fama and French (1996) did not fully explain if those same risk factors are the source of the return differential among the most extreme prior performers. As such, this paper replicated the DT85 study by forming portfolios following their method with starting months from January 1986 through January 2004. Using the same filters as DT85, the prior losers only outperformed the prior winners by 0.02% over the subsequent three years, indicating that whatever results DT85 found, they did not exist any longer. However, DT85 only observed NYSE stocks. The inclusion of AMEX and NASDAQ stocks resulted in a cumulative abnormal return differential of 28.60%; this difference increased to 34.85% when the requirement of preexisting data was reduced from seven years to five years. Qualitatively similar results were found when the analysis shifted from looking at cumulative abnormal returns to looking at buy-and-hold returns. The buy-and-hold returns were then analyzed to determine if, in the spirit of Fama and French (1996), the return differences can be accounted for by differences in risk. While it was found that all six buy-and-hold return results faced significant exposure to market, size, book-to-
75
market, and momentum-based risk, the explanatory power of models incorporating these factors was relatively low (maximum 13.82%), and there still existed significant risk-adjusted returns as determined by the intercept of the regressions (maximum when all four factors are included was 0.824% per month). Additionally, while the factor regressions on the positive return differences (those that included AMEX and NASDAQ stocks) yielded the expected results for the size and book-to-market factor loadings, the momentum factor loading was positive, indicating a tendency towards return continuation instead of reversal. Breaking down the factor analysis to be run on the two sets of stocks (losers and winners) separately showed that both losers and winners experienced reversals in their returns, as indicated by significant negative momentum factor loadings, and that these reversals are stronger in the winners than the losers. These results provide the justification for determining whether a private investor could earn positive risk-adjusted returns by following a contrarian strategy based on the DT85 loser/winner portfolio selection criteria. The simulations performed in this study indicate that there are profits available to those investors willing to pursue this strategy. The investor willing to manage his own account and maximize his leverage within the legal limits established by Regulation T could earn an average 51.44% return over a three-year period, with only 28.22% being compensation for risk and the other 23.22% considered abnormal return. The investor who, on the other hand, invests in a hypothetical hedge fund following this strategy because he could not or desires not to follow this strategy on his own would earn an average 32.54% return over a three-year period, with only 21.02% being compensation for risk and the other 11.52% considered abnormal return while compensating the hedge fund manager with 17.92% of the initial investment in the form of management and performance fees. While the institutional constraints in place designed to protect investors who engage in the type of short selling required
76
to implement this strategy succeed in reducing the investor's general exposure to various risk factors, the legal use of maximum leverage actually eliminates most of the risk-reducing benefits of these constraints without providing compensation in the form of additional returns (either on a raw or risk-adjusted basis). Additional analyses indicate that the effects discovered by DT85 have not been arbitraged away over time and that there appears to be a January effect that is not the result of tax-loss selling that may be impacting the results. The average monthly returns to following this strategy only began to steadily decline during the last few years analyzed, approximately fifteen years after DT85 was published. Average returns in January are over 2.5 times as much as the returns in any other month, and November and December returns do not show declines that would indicate investors are selling poor performers to realize losses. Finally, there is no indication from any results in this study of the extent to which this strategy is followed in practice. One acknowledged area for improvement in this simulation is the manner in which the investor manages his account. This investor (or hedge fund manager) makes his investment decision once at the formation of the portfolio and then does not take any other action to change the relative positions within his long and short portfolios. A more active investor may be able to make decisions regarding his margin calls in order to offset some losses that the less active investor would face. For example, an active investor may decide to close out some of his short position when he expects a margin call instead of selling off some of his long position, as the broker does for the investor in this analysis, if he believes that some stocks he is holding short will make large gains in the future. More simply, instead of selling off owned stocks on a proportional basis, the active investor would be able to pick and choose which stocks to sell off (or cover) to avoid a margin call. Also, the costs of engaging in various purchases and sales
77
were not incorporated in this study. By making all transactions at the relevant open or close prices, transactions costs were ignored. Once the simulation is updated to allow the
selling/closure of specific positions when a margin call is received, a simple way to incorporate transaction costs would be to make all purchases at the ask price and all sales at the bid price as reported in the database on the date of each transaction. This would also expand the population of securities available for investment, as it would then account for much of the costs of buying and selling thinly-traded stocks, which was the motivation for filtering out low-priced and highspread securities on the portfolio formation date. On a different path, running this simulation on an expanded parameter set should create a more robust set of results to analyze (e.g.: different hurdle rates to set the high watermark and different interest rates on margin debt).
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Table 1: Cumulative Abnormal Return Differentials The following table provides information on the 36-month average cumulative abnormal returns (ACAR) of the loser and winner portfolios and the amount by which ACARL exceeded ACARW under two sets of parameters: exchanges allowed and years of data prior to the formation date required. In all cases, n = 217 36-month testing period returns; p-values of mean returns are in parentheses.
Exchanges NYSE 5 Formation Years Return DACAR ACARL ACARW DACAR ACARL ACARW DACAR ACARL ACARW DACAR ACARL ACARW DACAR ACARL ACARW DACAR ACARL ACARW Mean -1.23% (0.6552) -5.68% (0.0734) -4.45% (0.0027) 0.02% (0.9932) -3.57% (0.2266) -3.59% (0.0165) 34.85% (<0.0001) 23.75% (<0.0001) -11.10% (<0.0001) 28.60% (<0.0001) 17.22% (<0.0001) -11.38% (<0.0001) 45.06% (<0.0001) 32.82% (<0.0001) -12.24% (<0.0001) 38.49% (<0.0001) 28.21% (<0.0001) -10.29% (<0.0001) Minimum -82.06% -92.40% -69.97% -83.51% -88.09% -57.96% -64.01% -69.06% -77.95% -56.77% -84.38% -98.18% -48.89% -58.67% -88.91% -46.13% -82.86% -97.29% Maximum 159.75% 163.48% 53.75% 121.83% 127.10% 57.14% 223.92% 205.27% 63.89% 259.92% 221.94% 60.17% 292.44% 255.41% 69.06% 254.86% 207.74% 66.66%
7
NYSE/AMEX/ NASDAQ
5
7
AMEX/NASDAQ
5
7
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Table 2: Buy-and-Hold Return Differentials The following table provides information on the amount by which the 36-month return on a portfolio of prior losers exceeded the 36-month return on a portfolio of prior winners under two sets of parameters: exchanges allowed and years of data prior to the formation date required. In all cases, n = 217 36-month testing period returns; p-values of mean returns are in parentheses.
Exchanges NYSE NYSE/AMEX/NASDAQ AMEX/NASDAQ Formation Years 5 7 5 7 5 7 Mean -4.87% (0.1439) -1.75% (0.5931) 48.11% (<0.0001) 37.93% (<0.0001) 66.54% (<0.0001) 56.99% (<0.0001) Minimum -90.43% -84.21% -40.17% -83.68% -41.27% -69.41% Maximum 321.80% 260.47% 654.33% 371.48% 662.33% 532.02%
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Table 3: Regression Results on Buy-and-Hold Return Differentials The following table provides the regression coefficients from analyzing the returns described in Table 2: market risk factor loading, = the size factor loading, = the book-to-market factor loading, and loading. In all cases, n = 7,812 monthly returns; p-values of regression coefficients are in parentheses.
Exchanges NYSE Formation Years 5 (mkt model) 0.00343 (0.0003) -0.00175 (0.0592) 0.00538 (<0.0001 )0.00378 (<0.0001 ) 0.00323 (0.0001) 0.00175 (0.0345) 0.00499 (<0.0001 )0.00423 (<0.0001 ) 0.01681 (<0.0001) 0.01036 (<0.0001) 0.00709 (<0.0001) 0.00552 (<0.0001) 0.01407 (<0.0001) 0.00800 (<0.0001) 0.00438 (<0.0001) 0.00372 (0.0006) -0.3845 (<0.0001) -0.3789 (<0.0001) -0.2641 (<0.0001) -0.2986 (<0.0001) -0.3289 (<0.0001) -0.3221 (<0.0001) -0.2171 (<0.0001) -0.2337 (<0.0001) -0.7261 (<0.0001) -0.7222 (<0.0001) -0.5654 (<0.0001) -0.5314 (<0.0001) -0.6244 (<0.0001) -0.6195 (<0.0001) -0.4364 (<0.0001) -0.4221 (<0.0001) 0.3305 (<0.0001) 0.3230 (<0.0001) 0.6289 (<0.0001) 0.6418 (<0.0001) 0.3494 (<0.0001) 0.3316 (<0.0001) 0.5670 (<0.0001) 0.5976 (<0.0001) 0.6499 (<0.0001) 0.6586 (<0.0001) 0.5584 (<0.0001) 0.5434 (<0.0001) 0.7419 (<0.0001) 0.7599 (<0.0001) 0.6241 (<0.0001) 0.5931 (<0.0001) (other models)
= the intercept, = the = the momentum factor
Adj. R2 4.07% 3.95% 13.16% -0.1495 (<0.0001) 13.82% 3.78% 3.61% 12.61% -0.0719 (<0.0001) 12.81% 10.36% 10.24% 12.89% 0.1473 (<0.0001) 13.35% 8.12% 7.98% 11.20% 0.0620 (0.0059) 11.29%
7
NYSE/AMEX/ NASDAQ
5
7
88
Exchanges AMEX/NASDAQ
Formation Years 5
(mkt model) 0.01835 (<0.0001) 0.01239 (<0.0001) 0.00986 (<0.0001) 0.00824 (<0.0001) 0.01570 (<0.0001) 0.01005 (<0.0001) 0.00727 (<0.0001) 0.00720 (<0.0001) -0.5940 (<0.0001)
(other models)
Adj. R2 7.73%
-0.5895 (<0.0001) -0.4705 (<0.0001) -0.4355 (<0.0001) -0.5105 (<0.0001) -0.5052 (<0.0001) -0.3676 (<0.0001) -0.3650 (<0.0001)
7.60% 0.2838 (<0.0001) 0.2655 (<0.0001) 0.4384 (<0.0001) 0.4698 (<0.0001) 9.42% 0.1517 (<0.0001) 9.96% 6.19% 6.05% 0.2712 (<0.0001) 0.2698 (<0.0001) 0.4824 (<0.0001) 0.4847 (<0.0001) 8.27% 0.0110 (0.6061) 8.27%
7
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Table 4: Regression Results on Buy-and-Hold Return Differentials and Loser and Winner Portfolios The following tables expand the results explained in Table 3 by running the loser and winner portfolios that formed the differences through the same regressions: = the intercept, = the market risk factor loading, = the size factor loading, = the book-to-market factor loading, and = the momentum factor loading. In all cases, n = 7,812 monthly returns; p-values of regression coefficients are in parentheses.
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Table 4a: NYSE Stocks
Formation Years 5 Portfolio Difference Loser Winner Difference Loser Winner Difference Loser Winner Difference Loser Winner 7 Difference Loser Winner Difference Loser Winner Difference Loser Winner Difference Loser Winner 0.00343 (0.0003) 0.00113 (0.2230) -0.00230 (<0.0001 )0.00175 (0.0592) 0.00007 (0.9471) -0.00191 (<0.0001) -0.00538 (<0.0001) -0.00501 (<0.0001) -0.00343 (<0.0001) -0.00378 (<0.0001) -0.00121 (0.1520) 0.00120 (0.0004) 0.00323 (0.0001) 0.00136 (0.0942) 0.00187 (<0.0001) -0.00175 (0.0345) 0.00042 (0.6008) 0.00155 (<0.0001) -0.00499 (<0.0001) -0.00427 (<0.0001) -0.00307 (<0.0001) -0.00423 (<0.0001) -0.00135 (0.0680) 0.00089 (0.0067) (mkt model) -0.3845 (<0.0001) 0.7240 (<0.0001) 1.1085 (<0.0001) (other models) Adj. R2 4.07% 13.45% 70.58% -0.3789 (<0.0001) 0.7311 (<0.0001) 1.1108 (<0.0001) -0.2641 (<0.0001) 0.8946 (<0.0001) 1.1619 (<0.0001) -0.2986 (<0.0001) 0.8121 (<0.0001) 1.1134 (<0.0001) -0.3289 (<0.0001) 0.7600 (<0.0001) 1.0889 (<0.0001) -0.3221 (<0.0001) 0.7682 (<0.0001) 1.0911 (<0.0001) -0.2171 (<0.0001) 0.9229 (<0.0001) 1.1432 (<0.0001) -0.2337 (<0.0001) 0.8595 (<0.0001) 1.0960 (<0.0001) 3.95% 13.67% 70.69% 0.7419 (<0.0001) 1.0236 (<0.0001) 0.2931 (<0.0001) 0.7599 (<0.0001) 1.0667 (<0.0001) 0.3184 (<0.0001) 0.6241 (<0.0001) 0.8745 (<0.0001) 0.2617 (<0.0001) 0.5931 (<0.0001) 0.8005 (<0.0001) 0.2193 (<0.0001) 13.16% 30.06% 73.76% -0.1495 (<0.0001) -0.3569 (<0.0001) -0.2094 (<0.0001) 13.82% 33.58% 76.47% 3.78% 18.18% 70.67% 3.61% 18.49% 70.77% 0.6499 (<0.0001) 0.9239 (<0.0001) 0.2854 (<0.0001) 0.6586 (<0.0001) 0.9570 (<0.0001) 0.3100 (<0.0001) 0.5584 (<0.0001) 0.8081 (<0.0001) 0.2611 (<0.0001) 0.5434 (<0.0001) 0.7514 (<0.0001) 0.2189 (<0.0001) 12.61% 35.02% 73.83% -0.0719 (<0.0001) -0.2738 (<0.0001) -0.2039 (<0.0001) 12.81% 37.55% 76.50%
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Table 4b: NYSE/AMEX/NASDAQ Stocks
Formation Years 5 Portfolio Difference Loser Winner Difference Loser Winner Difference Loser Winner Difference Loser Winner 7 Difference Loser Winner Difference Loser Winner Difference Loser Winner Difference Loser Winner 0.01681 (<0.0001) 0.01010 (<0.0001) -0.00671 (<0.0001) 0.01036 (<0.0001) 0.00874 (<0.0001) -0.00535 (<0.0001) 0.00709 (<0.0001) 0.00719 (<0.0001) -0.00369 (<0.0001) 0.00552 (<0.0001) 0.00989 (<0.0001) 0.00060 (0.2393) 0.01407 (<0.0001) 0.00814 (<0.0001) -0.00593 (<0.0001) 0.00800 (<0.0001) 0.00683 (<0.0001) -0.00489 (<0.0001) 0.00438 (<0.0001) 0.00427 (<0.0001) -0.00390 (<0.0001) 0.00372 (0.0006) 0.00753 (<0.0001) 0.00005 (0.9230) (mkt model) -0.7261 (<0.0001) 0.6431 (<0.0001) 1.3692 (<0.0001) (other models) Adj. R2 10.36% 8.59% 54.10% -0.7222 (<0.0001) 0.6490 (<0.0001) 1.3720 (<0.0001) -0.5654 (<0.0001) 0.5769 (<0.0001) 1.1456 (<0.0001) -0.5314 (<0.0001) 0.5184 (<0.0001) 1.0525 (<0.0001) -0.6244 (<0.0001) 0.6575 (<0.0001) 1.2819 (<0.0001) -0.6195 (<0.0001) 0.6640 (<0.0001) 1.2843 (<0.0001) -0.4364 (<0.0001) 0.6655 (<0.0001) 1.1052 (<0.0001) -0.4221 (<0.0001) 0.5949 (<0.0001) 1.0197 (<0.0001) 10.24% 8.73% 54.23% 0.3494 (<0.0001) 1.0441 (<0.0001) 0.7060 (<0.0001) 0.3316 (<0.0001) 1.0746 (<0.0001) 0.7546 (<0.0001) 0.5670 (<0.0001) 0.2565 (<0.0001) -0.2992 (<0.0001) 0.5976 (<0.0001) 0.2040 (<0.0001) -0.3826 (<0.0001) 12.89% 21.84% 67.39% 0.1473 (<0.0001) -0.2531 (<0.0001) -0.4025 (<0.0001) 13.35% 23.28% 72.43% 8.12% 9.05% 54.68% 7.98% 9.21% 54.80% 0.3305 (<0.0001) 1.0024 (<0.0001) 0.6833 (<0.0001) 0.3230 (<0.0001) 1.0393 (<0.0001) 0.7279 (<0.0001) 0.6289 (<0.0001) 0.4344 (<0.0001) -0.1831 (<0.0001) 0.6418 (<0.0001) 0.3711 (<0.0001) -0.2598 (<0.0001) 11.20% 20.88% 67.27% 0.0620 (0.0059) 0.3057 (<0.0001) -0.3697 (<0.0001) 11.29% 22.98% 72.17%
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Table 4c: AMEX/NASDAQ Stocks
Formation Years 5 Portfolio Difference Loser Winner Difference Loser Winner Difference Loser Winner Difference Loser Winner 7 Difference Loser Winner Difference Loser Winner Difference Loser Winner Difference Loser Winner 0.01835 (<0.0001) 0.01206 (<0.0001) -0.00629 (<0.0001) 0.01239 (<0.0001) 0.01090 (<0.0001) -0.00521 (<0.0001) 0.00986 (<0.0001) 0.01025 (<0.0001) -0.00340 (<0.0001) 0.00824 (<0.0001) 0.01273 (<0.0001) 0.00072 (0.1583) 0.01570 (<0.0001) 0.01071 (<0.0001) -0.00499 (<0.0001) 0.01005 (<0.0001) 0.00958 (<0.0001) -0.00420 (<0.0001) 0.00727 (<0.0001) 0.00813 (<0.0001) -0.00293 (<0.0001) 0.00720 (<0.0001) 0.01148 (<0.0001) 0.00056 (0.2476) (mkt model) -0.5940 (<0.0001) 0.7006 (<0.0001) 1.2946 (<0.0001) (other models) Adj. R2 7.73% 10.51% 51.28% -0.5895 (<0.0001) 0.7073 (<0.0001) 1.2976 (<0.0001) -0.4705 (<0.0001) 0.5873 (<0.0001) 1.0611 (<0.0001) -0.4355 (<0.0001) 0.5335 (<0.0001) 0.9717 (<0.0001) -0.5105 (<0.0001) 0.7068 (<0.0001) 1.2172 (<0.0001) -0.5052 (<0.0001) 0.7134 (<0.0001) 1.2200 (<0.0001) -0.3676 (<0.0001) 0.6508 (<0.0001) 1.0216 (<0.0001) -0.3650 (<0.0001) 0.5783 (<0.0001) 0.9461 (<0.0001) 7.60% 10.68% 51.43% 0.2838 (<0.0001) 0.9799 (<0.0001) 0.7075 (<0.0001) 0.2655 (<0.0001) 1.0080 (<0.0001) 0.7542 (<0.0001) 0.4384 (<0.0001) 0.1015 (0.0043) 0.3255 (<0.0001) 0.4698 (<0.0001) 0.0532 (0.1341) 0.4057 (<0.0001) 9.42% 23.38% 65.88% 0.1517 (<0.0001) -0.2328 (<0.0001) -0.3866 (<0.0001) 9.96% 24.63% 70.81% 6.19% 11.07% 51.89% 6.05% 11.26% 52.02% 0.2712 (<0.0001) 0.9506 (<0.0001) 0.6909 (<0.0001) 0.2698 (<0.0001) 0.9885 (<0.0001) 0.7303 (<0.0001) 0.4824 (<0.0001) 0.2401 (<0.0001) -0.2310 (<0.0001) 0.4847 (<0.0001) 0.1750 (<0.0001) -0.2987 (<0.0001) 8.27% 22.84% 66.19% 0.0110 (0.6061) 0.3137 (<0.0001) -0.3268 (<0.0001) 8.27% 25.18% 70.22%
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Table 5: Comparison of 36-Month Testing Period Returns This table presents the returns that would be expected by an investor following the personal asset management and hedge fund approaches to following the DT85-based strategy allowing all exchanges and requiring five years of prior data and compares them with each other and with the DT85 return differences detailed in Table 2. In all cases, n = 217 36-month testing period returns; p-values of mean returns and of comparisons are in parentheses.
Approach (<0.0001) Personal Asset Management (Unlevered) Hedge Fund, net of fees (Unlevered) Management Fees Performance Fees Comparison DT85 - Pers. Asset Mgmt. DT85 - Pers. Asset Mgmt. (Unlevered) DT85 - Hedge Fund DT85 - Hedge Fund (Unlevered) Pers. Asset Mgmt. - Hedge Fund Pers. Asset Mgmt. - Hedge Fund (Both Unlevered) Mean Minimum -40.17% 51.44% (<0.0001) 25.72% (<0.0001) 32.54% (<0.0001) 16.27% (<0.0001) 8.17% (<0.0001) 9.76% (<0.0001) Mean -3.33% (0.4934) 22.39% (<0.0001) 15.57% (0.0011) 31.84% (<0.0001) 18.90% (<0.0001) 9.45% (<0.0001) Maximum DT85 654.33% -40.83% -20.42% -45.44% -22.72% 4.87% 0.00% 48.11% 187.36% 93.68% 140.56% 70 .28 % 10.82% 33.75% Maximum 563.21% 608.77% 588.63% 621.48% 4 7 .10 %23 .55%
Minimum -198.54% -116.58% 161.91% -99.96% 4.60% 2.30%
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Table 6: Regression Results on Personal Asset Management Returns and Loser and Winner Portfolios The following table provides the regression coefficients from analyzing the returns from following the personal asset management approach: = the intercept, = the market risk factor loading, = the size factor loading, = the book-to-market factor loading, and = the momentum factor loading. Loser and winner portfolios were run through the same regressions. In all cases, n = 7,812 monthly returns; p-values of regression coefficients are in parentheses.
(mkt Portfolio Total Loser Winner Total Loser Winner Total Loser Winner Total Loser Winner 0.01201 (<0.0001) 0.00727 (<0.0001) -0.00524 (<0.0001) 0.00832 (<0.0001) 0.00760 (<0.0001) -0.00418 (<0.0001) 0.00469 (<0.0001) 0.00460 (<0.0001) -0.00381 (<0.0001) 0.00645 (<0.0001) 0.00787 (<0.0001) -0.00038 (0.4404) 0.0181 (0.2599) 1.0987 (<0.0001) 1.2911 (<0.0001) 0.0224 (0.1629) 1.1042 (<0.0001) 1.2937 (<0.0001) 0.1801 (<0.0001) 1.1441 (<0.0001) 1.1678 (<0.0001) 0.1421 (<0.0001) 1.0733 (<0.0001) 1.0935 (<0.0001) (other Adj. R2 model) models) 0.02% 42.58% 57.09% 0 .02 % 42.84% 57.22% 0.4877 (<0.0001) 0.9468 (<0.0001) 0.6104 (<0.0001) 0.5075 (<0.0001) 0.9838 (<0.0001) 0.6492 (<0.0001) 0.6289 (<0.0001) 0.5126 (<0.0001) -0.0728 (0.0001) 0.5948 (<0.0001) 0.4491 (<0.0001) -0.1394 (<0.0001) 9.80% 60.35% 66.34% -0.1646 (<0.0001) -0.3063 (<0.0001) -0.3214 (<0.0001) 11.25% 63.91% 70.15%
95
Table 7: Regression Results on Hedge Fund Investment Returns and Loser and Winner Portfolios The following table provides the regression coefficients from analyzing the returns from following the hedge fund investment approach: = the intercept, = the market risk factor loading, = the size factor loading, = the book-to-market factor loading, and = the momentum factor loading. Loser and winner portfolios were run through the same regressions. In all cases, n = 7,812 monthly returns; p-values of regression coefficients are in parentheses.
(mkt Portfolio Total Loser Winner Total Loser Winner Total Loser Winner Total Loser Winner 0.00837 (<0.0001) 0.00637 (<0.0001) -0.00615 (<0.0001) 0.00475 (<0.0001) 0.00667 (<0.0001) -0.00511 (<0.0001) 0.00106 (0.1391) 0.00362 (<0.0001) -0.00476 (<0.0001) 0.00320 (<0.0001) 0.00695 (<0.0001) -0.00128 (0.0099) 0.0342 (0.0398) 1.0877 (<0.0001) 1.2824 (<0.0001) 0.0387 (0.0203) 1.0931 (<0.0001) 1.2851 (<0.0001) 0.1985 (<0.0001) 1.1371 (<0.0001) 1.1606 (<0.0001) 0.1521 (<0.0001) 1.0649 (<0.0001) 1.0853 (<0.0001) (other Adj. R2 model) models) 0.04% 41.13% 56.11% 0.06% 41.39% 56.25% 0.4984 (<0.0001) 0.9417 (<0.0001) 0.6078 (<0.0001) 0.5226 (<0.0001) 0.9794 (<0.0001) 0.6471 (<0.0001) 0.6391 (<0.0001) 0.5212 (<0.0001) -0.0701 (0.0002) 0.5976 (<0.0001) 0.4564 (<0.0001) -0.1376 (<0.0001) 9.48% 58.48% 65.22% -0.2006 (<0.0001) -0.3123 (<0.0001) -0.3255 (<0.0001) 11.52% 62.12% 69.11%
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Table 8: Momentum Regression Results for All Approaches The following table compares the regression coefficients from analyzing the returns from following the three approaches studies in this paper: = the intercept, = the market risk factor loading, = the size factor loading, = the book-to-market factor loading, and = the momentum factor loading. In all cases, n = 7,812 monthly returns for strategy regressions and 15,632 for comparative regressions; p-values of regression coefficients are in parentheses.
Portfolio DT85 Personal Asset Management (Unlevered) Personal Asset Management Hedge Fund (Unlevered) Hedge Fund Comparison DT85 - P.A.M. (Unlevered) DT85 - P.A.M. DT85 - H.F. (Unlevered) DT85 - H.F. P.A.M. - H.F. (Both Unlevered) P.A.M. - H.F. 0.00552 (<0.0001) 0.00322 (<0.0001) 0.00645 (<0.0001) 0.00160 (<0.0001) 0.00320 (<0.0001) 0.00230 (<0.0001) -0.00093 (0.4760) 0.00392 (<0.0001) 0.00232 (0.0561) 0.00163 (0.0012) 0.00325 (<0.0001) -0.5314 (<0.0001) 0.0710 (<0.0001) 0.1421 (<0.0001) 0.0761 (<0.0001) 0.1521 (<0.0001) -0.6024 (<0.0001) -0.6735 (<0.0001) -0.6074 (<0.0001) -0.6835 (<0.0001) -0.0050 (0.6953) -0.0100 (0.6953) 0.3316 (<0.0001) 0.2538 (<0.0001) 0.5075 (<0.0001) 0.2613 (<0.0001) 0.5226 (<0.0001) 0.0779 (0.0206) -0.1759 (<0.0001) 0.0703 (0.0145) -0.1910 (<0.0001) -0.0075 (0.6083) -0.0151 (0.6083) 0.5976 (<0.0001) 0.2974 (<0.0001) 0.5948 (<0.0001) 0.2988 (<0.0001) 0.5976 (<0.0001) 0.3002 (<0.0001) 0.0028 (0.9530) 0.2988 (<0.0001) 0.0000 (0.9998) -0.0014 (0.9390) -0.0028 (0.9390) 0.1473 (<0.0001) -0.0823 (<0.0001) -0.1646 (<0.0001) -0.1003 (<0.0001) -0.2006 (<0.0001) 0.2296 (<0.0001) 0.3119 (<0.0001) 0.2476 (<0.0001) 0.3479 (<0.0001) 0.0180 (0.0861) 0.0360 (0.0861)
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Figure 1a: Personal Asset Management Simulation Flowchart
Determine stocks to include in wi n n e r a n d l o se r portfolios
Ma r k l o n g a n d short positions to ma r k e t a t e n d o f day
Adjust credit balance for d i vi d e n d s r e ce i ve d and/or paid
Accrue interest to cr e d i t a n d d e b i t balances
Will LMV fall below SMV if it is only account changed?
No
Re d u c e L MV by shortfall/ 0.30
Yes
Yes
Calculate maintenance margin requirement
Is equity> requirement?
No
Is LMV > SMV?
Reduce both LMV and SMV to EQ/ 0.65
Adjust debit and cr e d i t b a l a n ce s a ccord ing ly
Yes
No
Yes
No Go to next day Is this the last day of the three-year test period?
Will SMV fall below L MV i f i t i s o n l y a c c o u n t changed? No
Reduce SMV by shortfall/ 0.35
Yes
End simulation
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Figure 1b: Hedge Fund Simulation Flowchart
Determine stocks to include in wi n n e r a n d l o se r portfolios
Ma r k l o n g a n d short positions to ma r k e t a t e n d o f day
Adjust credit balance for d i vi d e n d s r e ce i ve d and/or paid
Accrue interest to cr e d i t a n d d e b i t b a lances
Will LMV fall below SMV if it is only account cha nge d?
No
Re d u c e L MV by shortfall/ 0.30
Yes
Yes
Calculate maintenance mar gin r eq ui reme nt
Is equity> requirement?
No
Is LMV > SMV?
Reduce both LMV and SMV to EQ/ 0.65
Adjust debit and cr e d i t b a l a n ce s a ccord ing ly
Go to next day
Yes
No
Yes
No No Is this the last day of the three-year test p eri od? Yes End simulation Yes No Assess hedge fund fees Is this the last day of the three-year test p eri od? Assess hedge fund fees Yes Is this the last day of a quarter? Will SMV fall below L MV i f i t i s o n l y a c c o u n t cha nge d? Reduce SMV by shortfall/ 0.35
No
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Figure 2: Average Monthly Returns for Each 36-Month Testing Period
3.5%
3.0%
2.5%
2.0%
1.5%
1.0%
0.5%
0.0%
Jan 1986
Jan 1987
Jan 1988
Jan 1989
Jan 1990
Jan 1991
Jan 1992
Jan 1993
Jan 1994
Jan 1995
Jan 1996
Jan 1997
Jan 1998
Jan 1999
Jan 2000
Jan 2001
Jan 2002
Jan 2003
-0.5%
-1.0%
-1.5%
-2.0%
Formation Month Personal Asset Management Hedge Fund
100
Jan 2004
Figure 3: Momentum Model Intercepts for Each 36-Month Testing Period
3.5%
3.0%
2.5%
2.0%
1.5%
1.0%
0.5%
0.0%
Jan 1986
Jan 1987
Jan 1988
Jan 1989
Jan 1990
Jan 1991
Jan 1992
Jan 1993
Jan 1994
Jan 1995
Jan 1996
Jan 1997
Jan 1998
Jan 1999
Jan 2000
Jan 2001
Jan 2002
Jan 2003
-0.5%
-1.0%
-1.5%
-2.0%
-2.5% Formation Month Personal Asset Management Hedge Fund
101
Jan 2004
Figure 4: Average Monthly Returns for Each Calendar Month
6.5% 6.0% 5.5% 5.0% 4.5% 4.0% 3.5% 3.0% 2.5% 2.0% 1.5% 1.0% 0.5% 0.0% January -0.5% -1.0% -1.5% -2.0% Personal Asset Management Hedge Fund February March April May June July August September October November December
102
Figure 5: Momentum Model Intercepts for Each Calendar Month
4.0%
3.5%
3.0%
2.5%
2.0%
1.5%
1.0%
0.5%
0.0% January -0.5% February March April May June July August September October November December
-1.0% Personal Asset Management Hedge Fund
103
doc_256102345.docx
In finance, an investment strategy is a set of rules, behaviors or procedures, designed to guide an investor's selection of an investment portfolio. Usually the strategy will be designed around the investor's risk-return tradeoff: some investors will prefer to maximize expected returns by investing in risky assets, others will prefer to minimize risk, but most will select a strategy somewhere in between.
Financial Study on A Simulation And Analysis of The Overreaction Hypothesis Market Anomaly As An Investment Strategy For Individual And Hedge Fund Investors
TABLE OF CONTENTS LIST OF TABLES AND FIGURES ABSTRACT I. II. Introduction Surrounding Issues II. A. II. B. Market Efficiency Long-Term Overreaction Institutional Constraints to Short Selling vii viii 1 3 3 6 7 7 10 10 22 26 26 28 29 31 31 32
II. B. 1. II. C. III.
Hedge Funds Literature Review The Overreaction Hypothesis Regulations that Prevent Unconstrained Investment Hedge Funds Regulations Operating Characteristics
III. A. III. B. III. C.
III. C. 1. III. C. 2.
III. C. 2. a. Hedge Funds vs. Mutual Funds III. C. 3. Hedge Fund Styles
III. C. 3. a. Market Trend III. C. 3. b. Other Styles
iv
III. C. 4. III. C. 5.
A Focus on Market Neutral Hedge Funds Risk Exposures of Market Neutral Hedge Funds
34 34 36 37 38 39 41 42 42 43 43 44 47 47 51 51 51 54 58 59
III. C. 5. a. Return Persistence III. C. 5. b. Non-Normality of Returns III. C. 5. c. Absolute Versus Relative Return Targets III. C. 5. d. The Role of Leverage III. C. 5. e. Dynamic Versus Passive Strategies III. C. 5. f. Biases in Databases III. C. 5. f. 1) Survivorship Bias III. C. 5. f. 2) Self-Selection Bias III. C. 5. f. 3) Instant History Bias III. C. 6. IV. Alternative Risk Measures
Hypotheses and Model Development
IV. A. Hypotheses to Test V. Data and Results V. A. V. B. V. C. Data Collection DT85 Cumulative Abnormal Returns DT85 Buy-and-Hold Returns Unexpected Positive Momentum Coefficients
V. C. 1. V. D.
Personal Asset Management
v
V. D. 1. V. E. V. F. V. G. VI.
Results of Personal Asset Management
66 69 71 72 75 79
Additional Hedge Fund Expenses Changes in Risk Other Results Conclusion and Directions for Future Research
BIBLIOGRAPHY
vi
LIST OF TABLES AND FIGURES Table 1: Cumulative Abnormal Return Differentials Table 2: Buy-and-Hold Return Differentials Table 3: Regression Results on Buy-and-Hold Return Differentials Table 4: Regression Results on Buy-and-Hold Return Differentials and Loser and Winner Portfolios Table 4a: NYSE Stocks Table 4b: NYSE/AMEX/NASDAQ Stocks Table 4c: AMEX/NASDAQ Stocks Table 5: Comparison of 36-Month Testing Period Returns Table 6: Regression Results on Personal Asset Management Returns and Loser and Winner Portfolios Table 7: Regression Results on Hedge Fund Investment Returns and Loser and Winner Portfolios Table 8: Momentum Regression Results for All Approaches Figure 1a: Personal Asset Management Simulation Flowchart Figure 1b: Hedge Fund Simulation Flowchart Figure 2: Average Monthly Returns for Each 36-Month Testing Period Figure 3: Momentum Model Intercepts for Each 36-Month Testing Period Figure 4: Average Monthly Returns for Each Calendar Month Figure 5: Momentum Model Intercepts for Each Calendar Month
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86 87 88
90 91 92 93 94
95
96 97 98 99 100 101 102 103
ABSTRACT This study revisited the overreaction hypothesis studied by DeBondt and Thaler (1985) to determine its suitability as a strategy for private investment. Using their same filters from January 1986 through January 2004, prior NYSE losers only outperformed prior NYSE winners by 0.02% over the subsequent three years. The inclusion of AMEX and NASDAQ stocks resulted in a cumulative abnormal return differential of 28.60%; this difference increased to 34.85% when the requirement of preexisting data was reduced from seven years to five years. Qualitatively similar results were found when the analysis shifted from looking at cumulative abnormal returns to looking at buy-and-hold returns. While the buy-and-hold return results faced significant exposure to market, size, book-tomarket, and momentum-based risk, the explanatory power of models incorporating these factors was relatively low (maximum 13.82%), and there still existed significant risk-adjusted returns as determined by the intercept of the regressions of up to 0.824% per month. Additionally,
breaking down the factor analysis to be run on the losers and winners separately showed that both losers and winners experienced reversals in their returns and that these reversals were stronger in the winners than the losers. An investor looking to exploit these return differences could earn up to 51.44% over a three-year period, 23.22% of which would be considered risk-adjusted return, by using the maximum amount of leverage allowed by Regulation T. If this investor desires to instead invest in a hypothetical hedge fund following this same strategy, he could still earn 32.54% over three years, 11.52% of which would be risk-adjusted, while the hedge fund manager extracts 17.92% of the initial investment over the same three-year period in the form of management and performance fees. While the institutional constraints in place designed to protect investors who
viii
engage in the type of short selling required to implement this strategy succeed in reducing the investor's general exposure to various risk factors, the legal use of maximum leverage actually eliminates most of the risk-reducing benefits of these constraints without providing compensation in the form of additional returns (either on a raw or risk-adjusted basis). Even though the initial study was published in 1985, there is little evidence that arbitrageurs have reduced the difference in the returns between prior losers and winners. There also appears to be a pronounced January effect in the returns to investing by this strategy. Finally, there is no indication of the extent to which this strategy is followed in practice.
ix
I. Introduction This dissertation will analyze the possibility of taking advantage of a controversial statistical anomaly in an investment strategy that is subject to the constraints that actual investors must face. The overreaction hypothesis was explained in detail by DeBondt and Thaler (1985, henceforth DT85) as return reversals experienced by the stocks with the most extreme returns over a three- to five-year period. While the original article's results were scrutinized by
researchers, this study intends to focus on whether this phenomenon still exists in the time period since the publication of their findings and whether it can be applied in a profitable manner. This study is feasible in spite of previous refutations of DT85 because (1) direct refutations of DT85 were themselves scrutinized, leaving the general issue open-ended, (2) the necessity of prior refutations to focus on time frames heavily overlapping the original article's study neglects the issue of whether investors using this hypothesis since its publication could have profited from it, and (3) research that was well-designed to analyze DT85 (e.g. Fama and French (1996)) analyzed the entire pool of stocks looking for general patterns in returns and risk factors based on prior returns instead of looking for those patterns in the specific securities that would have been chosen by the DT85 filter. I will test my hypotheses that DT85 will work for investors since its publication, first by replicating the DT85 results in the years since the original article came out. I will then adjust this filter and the testing metric to more realistically reflect long-term investors' buy-and-hold strategies. Once this adjustment shows that the overreaction hypothesis still holds the potential to be used by investors to earn profits, I will apply the DT85 filter to two possible investing scenarios that could take advantage of it: personally investing and managing one's own assets through a broker and investing one's assets in a hedge fund that follows a similar strategy. Due
1
to some of the objections raised by researchers towards the original article (such as in the aforementioned Fama and French (1996) article), I will not only look for profits from raw returns but also for profits from risk-adjusted returns. The remainder of this paper is structured as follows. Part II will briefly introduce the main issues that this study confronts. Part III will detail some of the major regulations that will need to be taken into consideration in the models developed later. It will also overview a significant portion of the overreaction literature that relates to hedge funds, focusing at certain points on the class of hedge funds most relevant to the models being used in this study, and the overreaction hypothesis, which will be the basis for the investment strategy used in those models. Part IV explains the hypotheses that will be tested. Part V details data collection and the results of tests of the hypotheses. Part VI concludes and details potential next steps in this line of research.
2
II. Surrounding Issues II. A. Market Efficiency Market efficiency is a core concept in financial research and practice. In its present form, it implies an inability to profit on a risk-adjusted basis from predictions of future asset prices based on current knowledge. Should any anomalies (underpriced or overpriced assets) arise, market forces would work swiftly to offset these deviations. If an asset is underpriced, potential buyers would be quick to enter the market and force the price up to fair value. Similarly, overpriced assets would see a large quantity of long and short sellers in the market. However, while anyone can make an offer to purchase an underpriced asset, there are limitations to market participants' ability to make an offer to sell. Whereas the owners of an overpriced asset can simply offer the item for sale at the market price, not everyone who notices and wants to take advantage of the overpricing may own the asset. While such individuals have the option to take a short position in the asset, there are restrictions on their ability to do so. They, or their broker, must be able to find one or more current owners willing to lend their asset to the individual who feels it is overpriced for the purpose of selling it. Since they are selling another person's property, they are also liable to purchase the asset at the market price should it be recalled by the original owner for any reason (such as an increase in its price to a point where the owner wants to liquidate their position in the asset), thus prematurely closing out their short position. Note that while the use of street name securities in such transactions often makes premature closeout unlikely, it is still a potential restriction to be considered. In addition to the raw mechanics that restrict investors' ability to engage in short sales, there are other institutional constraints that make short selling a costly endeavor. For example, the short seller must post some collateral in addition to the proceeds of the short sale, preventing him from using those funds for some other
3
potentially profitable opportunity, whereas the long seller simply needs to make an offer to sell what they already own. So, while a long seller gains the use of all the post-commission proceeds of the sale, a short seller would be able to use only a portion of those proceeds once they are netted out against the lost availability of the collateral posted. And while it is true that an investor with bearish sentiment towards an asset has other ways to exercise his belief that do not come with the same level of additional restrictions, any such choice is counterbalanced by an equally viable route for a bullish investor, assuming these alternative choices are available for that particular asset. For example, put and call options balance each other out, and they are not publicly traded for many listed securities. Overall, the problem this creates is that there is a potential extra level of expenses for investors who choose to exercise their bearish sentiment regarding an asset than for those exercising a bullish sentiment. Efficiency proponents would argue that economic agents will only look to take advantage of asset mispricing as long as the level of the mispricing (and thus the potential gains to be made) is greater than the costs involved with establishing their desired positions in the asset. As such, ceteris paribus, there should be a smaller pool of investors who can exercise bearish sentiments than of those who can exercise bullish sentiments. Thus, market overpricings would exist in greater quantities and magnitudes and with greater persistence than market underpricings. This, however, also creates an opportunity for astute investors to search for ways to exploit market mispricings at lower costs, thus taking advantage of opportunities that others are not able to and reaping potentially large profits. To this end, the hedge fund industry seems to have reduced the discrepancy between the costs of exercising bullish sentiment and exercising bearish sentiment. Hedge fund managers are able to avoid some of the institutional restrictions
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on short selling that mutual funds face by keeping their number of investors, assets under management, and beneficial ownership of individual securities within specified limits. This in itself creates a different set of restrictions on these economic agents, but their continued existence implies that these restrictions are worth it for the profits they will generate as a result of adhering to these restrictions. Ultimately, hedge funds can exist for the same reason most businesses exist: because they are profitable for those who run them. While some of these profits come from their relaxed restrictions relative to mutual funds, hedge funds, like mutual funds, are also able to extract profits by charging fees to those who invest in them (the difference between the fee structures of hedge funds and mutual funds will be described in Part III of this paper). This then creates a dilemma for the individual who wants to invest but cannot establish his own hedge fund. Assuming this person is a wise investor who sees a mispricing he wants to exploit for arbitrage profits, he has two choices. He can take his concept to the markets on his own and establish the proper long and short positions he desires, incurring all the costs and being subject to all the restrictions applicable to such a strategy. On the other hand, he could search for a hedge fund that employs a strategy similar to what he sees as potentially profitable and that is accepting new investors, saving himself the time going forward that he would otherwise require to maintain his arbitrage position and some of the costs of transacting in the markets, but incurring the additional fees that the hedge fund manager will extract from his investment and not being able to follow his intended strategy as precisely as he would desire. Part of this paper will look at the return difference between these two options.
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II. B. Long-Term Overreaction The work in this paper will be based on the results of DT85, which revealed a pattern in some long-term investments. They observed evidence that in the long-run, securities with extreme positive or negative returns over a period of a few years (three or five in their study) tend to reverse direction for a similar period of time. This creates an easily observable
opportunity for astute investors to exploit in the search for increased returns. DT85 also found a few patterns within this general pattern. Since the focus of this paper is on a realistic investor's opportunities to profit, I will also discuss and explore those patterns in terms of their applicability and potential profitability over and above the profitability provided by the general pattern itself, if any. The first avenue I will explore will be to attempt to replicate DT85's findings in the years since the publication of their work. If proponents of market efficiency are correct, then the announcement of such an inefficiency would lead arbitrageurs to work to profit from it. Investors would search for the securities that performed the poorest over the previous three years1 (losers) to purchase. They would also sell off or establish short positions in any securities that performed the best over the previous three years (winners). That should then result in the inefficiency being eliminated relatively quickly. Another possibility includes a ?slow burn? of the inefficiency, where it exists early on while investors determine the best way to exploit it, and their aptitude at doing so increases over time. Here, the magnitude of the difference between the returns of the losers and winners should decline over time to some equilibrium difference. Otherwise, the inefficiency may be robust to any efforts to arbitrage it away, and its magnitude may fluctuate over time but never really diminish by a significant amount. As long as the
1
Three years was the primary time frame on which DT85 focused. 6
inefficiency of DT85's original model still exists, the next step will be to change the setup of the model to make it more relevant for investors. II. B. 1. Institutional Constraints to Short Selling While pure efficiency theory would suggest the inefficiencies would be eliminated once they are publicized, the existence of various forms of transactions costs, as mentioned earlier, would prevent this inefficiency from being fully arbitraged away. The Federal Reserve's
Regulations T and U are the two main institutional constraints that create these costs that are imposed on investors who desire to engage in borrowing to help finance stock purchases. These regulations set the limits on the amount of leverage investors can utilize to finance securities transactions. Additionally, the Financial Industry Regulatory Authority (FINRA)2 establishes requirements that exceed those laid out by Regulations T and U. Whereas Regulations T and U focus on the activities of the financial intermediaries (broker-dealers in the case of Regulation T and other lenders in the case of Regulation U) in their dealings with investors, the FINRA regulations focus on the investors who utilize these intermediaries' services and allow the relevant intermediaries to establish margin requirements in excess of the FINRA minimum standards. II. C. Hedge Funds Over the past several years, the hedge fund industry has grown from being a tiny piece of the investment community to a significant factor that has grabbed the attention of investors and regulators alike. While the academic community has done its part to attempt to explain the underlying factors that have led to the success and growth of hedge funds, there is still much that
?Created in July 2007 through the consolidation of NASD and the member regulation, enforcement and arbitration functions of the New York Stock Exchange, FINRA is dedicated to investor protection and market integrity through effective and efficient regulation and complementary compliance and technology-based services? (About FINRA (2007)).
2
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is unknown about these investments. As will be explained in further detail later, the hedge fund industry is not transparent, like stocks and mutual funds are. Any disclosures that individual hedge funds make regarding their operations are potentially self-serving and non-required; some hedge funds provide no information about themselves except recent performance and fees to their current investors. This makes using this information to attempt to understand an entire industry potentially tenuous. As such, instead of using the publicly available hedge fund data, this study will attempt to replicate at a basic level the returns a specific type of hedge fund might earn. The results of this replication will be compared to a replication of how a non-hedge fund investor would follow the same strategy. This will then allow a discussion of some of the motivations to invest in a hedge fund at all. Having a professional manage one's assets is clearly less time-consuming than doing it for oneself, so convenience is a clear motivator, though this does not distinguish hedge funds from other professionally managed investment options, such as mutual funds. Second, since most classes of hedge funds are available only to institutions and wealthy investors (there is a set of qualification standards that must be met by hedge fund investors, though these standards are much lower for investors in funds of hedge funds), there is a certain level of stature of being able to say that one's assets are tied up in hedge funds. If nothing else, it is a statement of one's financial status. How much of a statement it is can be questioned, but the prospect exists, nonetheless. The third motivator, the one that will be directly analyzed in this study, is the possibility of superior returns. Can a hedge fund offer a greater return on investment than an individual could obtain by investing in the financial markets without a ?middle man? to assist him? If not, the deficiency in hedge fund returns compared to
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personal asset management could be considered the cost of the convenience and stature of investing in hedge funds.
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III.Literature Review III. A. The Overreaction Hypothesis DT85 analyzed the difference in returns between prior long-term winners, those securities that experienced the greatest returns over the most recent three years, and prior long-term losers, those securities that experienced the least returns over the most recent three years. They found that the prior losers outperformed the prior winners by 24.6% over a subsequent three-year period. This paper will use that finding as inspiration to determine if an investor following a strategy to take advantage of this difference (by taking a long position in prior losers and a short position in prior winners) or investing in a hedge fund following such a strategy could earn excess returns. DT85's position was self-titled the ?overreaction hypothesis.? Their study was based upon the concept that in the long-run, securities will experience some form of mean reversion (the idea that there is some fundamental, or ?mean,? value that securities will return to if their prices shift too far from it). Thus, should a security experience returns in excess of its long-run expected average over a few years, the next few years should see returns below that average (and vice versa) so that overall, the security will return its fundamental value. While usually, this long-run expected average would be determined by using the CAPM or some multifactor model, DT85 simply compare a security's return in any given month to the market's return that month. They posit that by determining the winners and losers in this manner, they avoid any potential biases that would result from misspecification of the benchmark model (which is interesting in and of itself, as they note shortly before defining their model that such a benchmark is effectively the CAPM with ? = 0 and ? = 1). As such, while they describe their model as choosing the securities that performed best and worst relative to the market, their selection criteria is equivalent to choosing the securities with the best and worst raw returns.
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Note that since this study is concerned with using the results of DT85 to form a profitable investment strategy, it is sufficient that this selection strategy works; it is not necessary in this study to determine if their choice of selection criteria could be improved by, for example, using a better specified model. Once the stocks have been chosen for inclusion into the winner and loser portfolios, DT85's testing procedure effectively amounts to looking at equal-weighted portfolios of past winners or past losers each month that get rebalanced to equal weighting at the beginning of each month over the life of the portfolios (their procedure also accounts for stocks that are removed from either portfolio due to being delisted from the CRSP database from which they draw their return information). As mentioned earlier, DT85 found a 24.6% difference in the monthly rebalanced returns of equal-weighted portfolios of past losers over past winners (where losers averaged 19.6% more than the market and winners averaged 5.0% less than the market). While this result comes from choosing winners and losers based on three years of past returns and then holding those stocks for another three years, their results were robust to two- and five-year formation and testing periods as well, though the results at the two-year level were statistically insignificant.3 The asymmetry of these results is also interesting, as it suggests that prior pessimism is responded to in greater measure than prior optimism. Some of the issues raised earlier regarding the different costs of establishing long positions as opposed to establishing short positions may be partially at play here. Also, poor performance by a company's stock could lead to internal changes that are intended to result in improved performance. One may also want to consider investor psychology at work here. Even the occurrence of such a change may be enough to improve investors' confidence in that particular security. Also, shoppers of all varieties like a bargain, and a
3
The difference between the loser and winner portfolios was also negative and significant when using one-year formation and testing periods, which would be in line with much of the literature on momentum in returns, but that is not a focus in this paper. 11
security that has experienced three years of relatively poor performance may very well be considered a bargain. Similarly, the psychological effects of poor stock performance can be devastating, and the investment community has historically been rather unforgiving to any entity that might be viewed as rocking the boat when the sailing is smooth (whether that smooth sailing is a myth or real). A few other interesting patterns appeared in DT85's results that this study will watch out for, as they could potentially affect investment decisions. These results include the impact of January returns on the overall results (17.7% of the losers' 19.6% excess returns occurred in the three Januaries of the testing period; the after-effects of tax-loss selling in December has been posited as a potential cause of this clustering of excess returns) and the slow build to the overreaction effects (only 5.4% of the 24.6% difference occurs in the first year after portfolio formation, but then 12.7%, or more than half of it, occurs in the second year). While this was merely mentioned in DT85, this second point can have very interesting implications for investors who may want to exploit when the majority of the overreaction effects occur. As should be expected if DT85's overreaction hypothesis is true, when the number of stocks allowed in the loser and winner portfolios expands, the magnitude of the overreaction declines (as more stocks are allowed in that were less extreme losers and winners). Also, as the formation period is extended, the magnitude of overreaction in the testing period grows. This implies that stocks that had longer periods of extreme performance will have a greater subsequent turnaround. Also, DT85 find the winner stocks to be riskier than the loser stocks when the portfolios are formed (prior 60-month CAPM betas of 1.369 and 1.026, respectively). While this differential riskiness may not carry over to the testing period, it is at least interesting to note that initially, the loser
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portfolio, from which the majority of the overreaction effect comes, is the safer portfolio relative to the overall market. There are issues in DT85's analysis that raise some concerns, though, when trying to extend their results to a study that is relevant for actual investors. Their decision to use monthly data instead of daily data was driven by a desire ?to avoid certain measurement problems that have received much attention in the literature,? including, but not limited to, ?the ?bid-ask' effect and the consequences of infrequent trading? (p. 799). This of course limits the researcher to make all purchases on the first trading day of the month and all sales on the last trading day of the month, which is rather unrealistic in comparison to how investors act. However, hedge funds seem to determine their net asset values for the purposes of investors buying and selling based on the share prices of their holdings as of the close of trading on the last trading day of the month, so this concern may not have as large of an overall effect as one might instinctually consider (Chan et. al. (2006)). These effects aside, DT85's concerns with the spread and low volumes will need to be accounted for in the model used later in this paper. They also required seven years of data to be available in the CRSP database prior to the portfolio formation. For one thing, many investors may not be concerned with a stock having quite so large a history available in order to consider it as an investment opportunity (on either the short or the long side). For another thing, when coupled with the fact that DT85 focused only on NYSE-traded securities, the combined effects of these two filters is to bias their analysis to select only large and established firms. For their purposes, this was acceptable, as they state that one popular critique of overreaction at the time of their study was that overreaction effects were predominantly small-firm effects. Thus, based on the literature at the time, they would have been biasing their results against finding overreaction effects. However, for an investor looking
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to maximize their returns, they would want to consider as much of the population of investable assets as possible. Plus, if this prior contention is true, and small firms would experience overreaction to a greater extent than large firms, then investors would be doing themselves a disservice not to consider small firms for inclusion in either portfolio. DT85's choice of formation months leaves much to be desired from a practical aspect as well. Their choice to start every portfolio in January was admittedly arbitrary, so they also performed tests on portfolios that start at the beginning of June (also arbitrarily chosen). To make this analysis more realistic, it will not focus on any specific formation date. On top of that, DT85 tested their portfolio in nonoverlapping periods, which would be analogous to an investor purchasing a stock and then deciding at that point in time to neither sell that security nor purchase another security for a preset period of time. While this decision may make sense from a statistical standpoint, it again makes no sense from the standpoint of an investor interested in maximizing his returns. Hedge funds will again be able to lessen the impact of this issue (though not entirely) due to lockup requirements that prevent their investors from withdrawing their funds for a predetermined time frame, though these lockup periods can vary across different hedge funds and also tend not to be three years long, the horizon used in DT85 (Liang (1999)). As described earlier, DT85 found evidence that a majority of their abnormal returns came during the three Januaries of the testing period. It also appeared that the lowest abnormal returns were realized during the three Decembers of the testing period. Tax-loss selling is proposed as a possible candidate to explain this phenomenon. Tam (1998) describes this concept as follows. ?Tax-loss selling essentially involves shedding the shares of a fund that has lost a lot of money since you bought it. (Even if a fund is down for the year, you can't take a tax loss unless the shares are below the price you paid.) By selling, you realize a loss that can then be used to offset
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any capital gains you have earned in another part of your portfolio [including potentially those in previous or future years]. The result: the capital-gains tax burden you anticipated is tempered.? What ends up happening, then, is that large institutional investors who can take great advantage of capital losses (in other words, those with a tax burden) sell off the securities in their portfolios that give them great losses, generally a few days or weeks before the end of the tax year. The market's sudden loss of equity causes a drop in that specific stock's price, leading to the tempering of abnormal returns in December. The strong January returns would then come about as the investors who sold securities in December return those securities to their portfolios, since there is no indication those investors wanted those securities out of their portfolios permanently (they simply wanted the tax benefits of selling at a loss). It would be reasonable to assume that since these securities have fallen in price that they would be considered underpriced, so those funds would try to repurchase them as soon as possible in the new tax year before the perceived underpricing was eliminated. Thus, those same securities that experienced a decline in their prices in December would see a subsequent increase in their prices in January. Chan (1986) analyzed tax-loss selling as a possible explanation of this seasonality. As a direct argument against the tax-loss selling argument, he points out that, ?Even if the year-end trading, for whatever reasons, is unusually heavy, one crucial assumption needed for the tax-loss selling hypothesis to explain the high January returns is that such selling exerts downward price pressure. If the year-end trading is purely caused by tax considerations, rational tax-loss sellers could repurchase stocks sold (by others) for tax reasons at the same time. Then the trading is not expected to depress stock prices.? That would imply that the funds that would intend to
repurchase in January the shares they sold in December should not see the benefits of buying underpriced securities, so they may look for other underpriced securities of characteristics
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similar to the shares they sold off. As such, DT85 should not have seen their January effect as a result of rational tax-loss selling. Empirically, Chan (1986) shows that the difference between the mean January effect of a short-term loss and the mean January effect of a long-term loss (this difference was seen as a proxy for the effect of tax-loss selling) is statistically insignificant in all but the smallest stocks, for which this difference is only marginally significant for the smallest decile of stocks available on the CRSP tapes at the time. Since the author does not specify that his study was limited to NYSE stocks on the CRSP tapes, it makes sense to conclude that the only subset of stocks for which the author possibly finds a significant tax-loss selling effect were a proportionately insignificant component of DT85's study. DeBondt and Thaler (1987) followed up their prior study on overreaction with an analysis of the effects of size and market-to-book ratios on overreaction. Forming their
portfolios in the odd years from 1969 to 1979, and using sixty-month periods as the prior formation periods and subsequent testing periods (note the departure from using non-overlapping periods in their previous study), they sorted the stocks in their study into quintiles ranked by cumulative abnormal return (their primary return metric from their previous study), market value of equity, market-to-book equity ratio, and assets. Using the five-year cumulative abnormal return, they find evidence of return reversals when sorting stocks based on previous cumulative abnormal returns (as would be predicted by DT85) and the market-to-book ratio and evidence of momentum in stocks sorted by assets. There is also a pronounced ?frown ? pattern in the cumulative abnormal returns of the market value of equity quintiles followed by decreasing cumulative abnormal returns of those quintiles in the testing period, providing weak evidence for momentum there as well. While the authors' intent may have been to search for the source of the overreaction they found in their previous study, their finding that is more pertinent to this study
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is the collective pattern of the testing period cumulative abnormal returns of each set of quintiles. In all four sorting mechanisms, they found decreasing cumulative abnormal returns from the first quintile to the fifth quintile. However, sorting by prior cumulative abnormal returns actually produced a lower difference in subsequent cumulative abnormal returns between the first and fifth quintiles (36.3%) than sorting by the market value of equity (50.8%), the market-to-book ratio (42.0%), or assets (38.7%). This leads to the possibility that the loser and winner portfolios are providing their returns based not as much on reverting to some long-term mean but on some characteristics of the stocks that happen to fall into those portfolios that grant a risk premium for size and/or value to investors in those stocks. This possibility will be tested later in this study. Conrad and Kaul (1993) introduced the possibility that DT85's results are biased. They explain that the abnormal return as a measure of excess returns contains within it an upward bias that is proportionate with the number of holding periods (in the case of DT85, each month is one holding period) of returns being measured and that removing this bias from DT85's calculations should eliminate any overreaction that exists. Due to bid-ask biases, they argue that the bias in cumulative abnormal returns is higher in low-priced stocks than in high-priced stocks.4 Since the loser portfolio is generally comprised of more low-priced stocks than the winner portfolio, DT85's combined portfolio includes an upward bias (loser bias > winner bias, so portfolio bias = loser bias - winner bias > 0). This conclusion comes from the findings of Bhardwaj and Brooks (1992), whose analysis of the January anomaly led them to the conclusion that the bid-ask bias on low-priced stocks averages between 0.80% and 1.42% in the first five trading days in January. For holding periods of less than one year (such as the one-month holding periods which determine DT85's cumulative abnormal returns), this bias tends to cause the returns on low-
4
Decimalization of exchange-listed prices should reduce this difference if the spreads of the low-priced stocks that get included in the loser portfolios were generally at the minimum tick size. 17
priced NYSE stocks to be overestimated by 0.8% to 1.0%. This finding is in addition to the general idea that there is an upward bid-ask bias in the returns of low-priced stocks in general. To counter this bias, Conrad and Kaul (1993) follow a DT85-inspired method of determining the extent of overreaction through 1988 (using 35 securities in each portfolio and 36-month non-overlapping formation and testing periods, though they include NYSE and AMEX stocks, whereas DT85 included NYSE stocks only), comparing DT85's cumulative abnormal return on these portfolios with their average holding period abnormal return. While the
cumulative abnormal return would contain the effect of biases from thirty-six holding periods (one for each month), Conrad and Kaul (1993) calculate their returns based on the entire 36month span as one holding period. Consistent with DT85, they find that cumulative abnormal returns of the loser portfolio exceed those of the winner portfolio by 37.5%. They also find that the average holding period abnormal return of the loser portfolio exceeds that of the winner portfolio over the three-year testing portfolio by 27.1%. While this alone would seem to support their argument that DT85's results are the product of biases inherent in using cumulative abnormal returns, the average holding period abnormal return also has a marginally larger standard error (15.7% vs. 15.3%), reducing the statistical significance of their results. While Conrad and Kaul (1993) do not report p-values in their study to allow for a direct comparison of this significance, they use twenty testing periods in both of their analyses, so a t-distribution with nineteen degrees of freedom and a one-tailed test would result in p-values of 0.0120 for the cumulative abnormal return method and 0.0503 for the average holding period abnormal return method. Thus, they found an average bias of 10.4% over a 36-month testing period, and that bias may have been the source of the significance of their results.
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While this argument might seem sufficient to refute any need to analyze DT85 further, Loughran and Ritter (1996) question Conrad and Kaul's (1993) results. They base their concern regarding this study on three points.5 While they do not dispute Conrad and Kaul's (1993) argument regarding bid-ask biases being magnified by cumulative abnormal returns, they counter that cumulative abnormal returns do not get the benefit of compounding returns over the entire testing period. Assuming DT85 is true, not accounting for the compounding of returns would bias Conrad and Kaul (1993) towards being able to claim a strong impact of bid-ask biases on DT85's results. When Loughran and Ritter (1996) compare the effects of using cumulative abnormal returns as the selection criteria with the effects of using buy-and-hold returns (analogous to Conrad and Kaul's (1993) average holding period abnormal returns), they find that buy-and-hold returns provide a greater segregation of securities relative to price, market capitalization, prior returns, and test period returns. Additionally, for each selection criteria, there is little difference between the testing period returns calculated using cumulative abnormal returns and those calculated using buy-and-hold returns. Second, Conrad and Kaul (1993) use CS-TS regressions to further explain their results beyond what I mentioned above, but Loughran and Ritter (1996) point out that this prevents them from being able to isolate time-series mean reversion patterns from the cross-sectional patterns they claim to find. Finally, they point out that Conrad and Kaul (1993) introduced a survivorship bias in their results by requiring all stocks included in their winner and loser portfolios to have return information throughout the entire subsequent testing period. If price is a risk proxy, then low-priced losers will be at a higher risk of being delisted than high-priced winners, but those stocks that are delisted would not be included in their portfolios. Since one of
5
Loughran and Ritter (1996) actually make four major points, but the second of the four points is not a refutation of Conrad and Kaul (1993), so I have excluded it from mention here. 19
Conrad and Kaul's (1993) hypotheses was that loser stocks would have higher returns than winner stocks due to the different prices of the stocks included in the portfolio, removing delisted stocks would bias their study in favor of coming to this very conclusion. Loughran and Ritter (1996) address both these issues through three stages of regressions. First, they perform a pooled CS-TS regression of test period returns on the logs of price, market capitalization, and prior returns with only survivors. They then repeat this procedure with non-survivors included in the population of potential loser and winner stocks to account for survivorship bias. This resulted in a lower economic and statistical significance for price and prior returns, greater economic and statistical significance for market capitalization, and adjusted R2 falling by approximately one third (10.6% to 6.8%). With survivorship bias accounted for, they then convert their pooled CSTS regression to a time series of cross-sectional regressions, reporting the means of the crosssectional regression coefficients. This adjustment resulted in eliminating the significance of price and market capitalization, magnifying the economic impact of prior returns while reducing its statistical significance, and virtually no effect on R2 (fell from 6.8% to 6.5%). Removing market capitalization (since its log is a linear combination of the log of price, which is another independent variable in their regressions, and the log of shares outstanding) as a variable in their regressions had no substantive effect on their results: prior returns were still the only significant determinant of test period returns. On another note, Dissanaike (1996) warns against extrapolating too much from the results of DT85 in relation to the implications of the behavior of mean reversion. One noticeable result of DT85 is that the cumulative abnormal returns of the loser portfolios (19.6%) exceeded the absolute cumulative abnormal returns of the winner portfolios (5.0%). While he argues that while this information is very useful for an investor looking to earn returns in excess of the
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market, this asymmetry in test-period returns does not allow us to draw any conclusions about the reversals themselves. As a simple introductory example, he points out that two securities (or portfolios of securities) with the same value at the beginning of the formation period (which he calls the rank period) that earn equal returns in opposite directions during the formation period (creating winner and loser portfolios) but then revert halfway back to their original values during the test period would exhibit asymmetric returns in the test period, even though the compounded returns over both periods would still be equal in magnitude. He creates winner and loser portfolios out of the top and bottom deciles of returns from a four-year formation period then tracks the difference in returns at the 12-, 24-, 30-, 36-, 42-, and 48-month points of the testing period. Consistent with DT85, he finds that during the test period, the losers significantly outperform the winners at each of these points, the losers outperform the market, the winners underperform the market, and except at the 12-month point, the magnitude of the loser excess returns exceeds that of the winner excess returns. However, he also creates a reversal metric (labeled the portfolio reversal coefficient) that measures, for losers (winners), the proportion of the value lost (earned) during the formation period relative to the market that was recovered (given back) during the test period relative to the market. He finds that at each of the
checkpoints mentioned above, not only does the winner portfolio experience a greater reversal than the loser portfolio, but also that the disparity between the winner reversal and loser reversal increases at each subsequent checkpoint. By the end of the 48-month test period, his winner portfolios have given back 56.1% of their gains relative to the market during the formation period, but his loser portfolio only recovered 18.0% of the value it had lost relative to the market during the formation period.
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III. B. Regulations that Prevent Unconstrained Investment This section will describe the regulations that apply to the general investment community. While DT85 looked simply for a difference in the levels of returns of two types of stocks, the intent of this paper is to attempt to directly exploit that difference. In order to do so, the regulations that prevent unconstrained short selling of equities must be applied to any model simulating this attempt must be understood. Regulation T states that, ?Its principal purpose is to regulate extensions of credit by brokers and dealers; it also covers related transactions within the Board's authority under the Act. It imposes, among other obligations, initial margin requirements and payment rules on certain securities transactions? (§220.1(a)). In addition, it ?provides a margin account and four special purpose accounts in which to record all financial relations between a customer and a creditor. Any transaction not specifically permitted in a special purpose account shall be
recorded in a margin account? (§220.1(b)(1)). As this paper will focus solely on purchases and short sales of tradable equity securities, the key minimum initial margin requirements to be concerned with are the fifty percent margin requirement for margin equity securities and the one hundred fifty percent margin requirement for short sales of nonexempted securities as described in section 12 of this regulation. The one hundred fifty percent requirement has the effect of forcing the investor to post the proceeds of the short sale in the margin account and then provide an additional fifty percent of this value as a form of collateral on this loan. As such, any further discussion of the required margin on short sales will assume the proceeds of the sale are already considered as part of the margin account, and any references to required margin on short sales will only describe the excess above these proceeds. Thus, I can, for simplicity's sake, refer to the fifty percent margin requirement on purchases and short sales going forward with the direct
22
implication that this fifty percent is in addition to the proceeds of the short sale that are automatically going to be posted in the margin account. It is also significant to note that the four special purpose accounts described above (and explained in detail in sections 5 through 8 of Regulation T) will have no direct effect on this study. The optional special memorandum account is a mirror to the margin account, whereby a credit to this account is to be matched up with a debit to the margin account. This account may contain dividends, interest, cash (including that deposited to meet a margin call), proceeds of sales of securities (short or liquidated), and transferred margin excess (§220.5). Effectively, the balance of this account could be the value of the equity held in the margin account. The good faith account is used for transactions involving exempt securities, non-equity securities, money market mutual funds, and exempt securities mutual funds. Required margin for these types of assets can be determined by the creditor on a case-by-case basis, as long as it meets the stipulations of a regulatory authority relevant to the asset type (§220.12). The broker-dealer credit account is a special account designed to facilitate liquidity among creditors and other broker-dealers (§220.7). The cash account is the location where a creditor can engage in basic transactions (non-short) on securities or other assets (including the issuance and exercise of options) of their customers, assuming there is a sufficient cash balance to complete said transactions (§220.8). Regulation U, on the other hand, states that its purpose is to impose ?credit restrictions upon persons other than brokers or dealers (hereinafter lenders) that extend credit for the purpose of buying or carrying margin stock if the credit is secured directly or indirectly by margin stock. Lenders include ?banks' ? [and] may not extend more than the maximum loan value of the collateral securing such credit?? (§221.1(b)(1)), which, for margin stock, ?is fifty percent of its
23
current market value? (§221.7(a)). The regulation allows only a plan-lender (a corporation extending credit to purchase specifically its own margin stock or that of its subsidiaries and affiliates) to exceed these limits (§221.3(a)(1) and §221.4(a)(1)), an exception that is not pertinent for this study. Note that while this regulation also discusses good faith lending (though to a lesser extent than in Regulation T), there is no provision in Regulation U pertaining to the short sale of securities. Its focus is solely on borrowing funds to purchase and hold stock. Regulation X effectively bars American investors from circumventing Regulations T and U by obtaining credit from foreign entities that would not be subject to Regulations T and U. Specifically, any United States person (?a person which is organized or exists under the laws of any State or, in the case of a natural person, a citizen or resident of the United States; a domestic estate; or a trust in which one or more of the foregoing persons has a cumulative direct or indirect beneficial interest in excess of 50 per centum of the value of the trust? (§224.2(a))) or foreign person controlled by a United States person (?any noncorporate entity in which United States persons directly or indirectly have more than a 50 per centum beneficial interest, and any corporation in which one or more United States persons, directly or indirectly, own stock possessing more than 50 per centum of the total combined voting power of all classes of stock entitled to vote, or more than 50 per centum of the total value of shares of all classes of stock? (§224.2(c))) who obtains credit within the United States to purchase or carry any securities or who obtains credit outside the United States to purchase or carry United States securities is subject to the aforementioned regulations, even if ?the borrower willfully causes the credit to be extended in contravention of Regulations T or U? (§224.1(b)(1)). While the aforementioned regulations establish minimum requirements for investors to follow, the exchanges that facilitate investment transactions establish a slightly higher level of
24
restriction on margin investment. For the purposes of this study, the margin regulations set forth by NYSE and FINRA are functionally equivalent, so the following rules are taken from the FINRA regulation, specifically, Rule 2520 from NASD's Rules of the Association. Paragraph (b) on initial margin states, ?For the purpose of effecting new securitie s transactions and commitments, the customer shall be required to deposit margin in cash and/or securities in the account which shall be at least the greater of: (1) the amount specified in Regulation T, or Rules 400 through 406 under the Act?; or (2) the amount specified in paragraph (c)(3) of this Rule [which is $5.00 per share, to be discussed in the next paragraph]; or (3) such greater amount as NASD may from time to time require for specific securities; or (4) equity of at least $2,000 except that cash need not be deposited in excess of the cost of any security purchased ?.? Subparagraphs (2), (3), and (4) provide an additional cushion above what is required by Regulation T for the special case of low-priced securities and securities the governing body deems especially volatile. Whereas Regulations T, U, and X focus solely on the initial margin that must be provided, the exchange regulations also deal with maintenance margin. Paragraph (c) of
FINRA's Rule 2520 states, ?The margin which must be maintained in all accounts of customers, except for cash accounts subject to other provisions of this rule, shall be as follows: (1) 25 percent of the current market value of all securities, except for securities futures contracts, ?long' in the account; plus (2) $2.50 per share or 100 percent of the current market value, whichever amount is greater, of each stock ?short' in the account selling at less than $5.00 per share; plus (3) $5.00 per share or 30 percent of the current market value, whichever amount is greater, of each stock ?short' in the account selling at $5.00 per share or above?.? This is the first level of regulation that describes a fundamental difference in treatment between long and short holdings
25
by an investor (recall that despite different descriptions, Regulation T set initial margin requirements of fifty percent of the value of either a long or short transaction). Other conditions of Rule 2520 allow member firms to ?(1) review limits and types of credit extended to all customers; (2) formulate their own margin requirements; and (3) review the need for instituting higher margin requirements, mark-to-markets and collateral deposits than are required by this paragraph for individual securities or customer accounts? (§2520(d)). The main effect of this component of the regulation is to allow member firms to create a buffer between when their customers will receive a margin call from them and when they would face a margin call of their own. Observing just a few firms' margin disclosures indicates that a five percent cushion above the FINRA requirements (thirty percent maintenance margin for long holdings and thirty-five percent for short holdings) is common. III. C. Hedge Funds Unlike commonly traded investment opportunities such as stocks and mutual funds, there are no available databases of the entire universe of hedge funds. Since hedge funds are not currently required to fully disclose their activities to the Securities and Exchange Commission (SEC), the only way to understand how these funds operate is through private investigation or through the self-disclosure that hedge funds provide to private databases established for the purpose of hedge funds desiring to lure investors. As such, even information about the basic operations of hedge funds will come from prior research on these two sources of information. III. C. 1. Regulations
Hedge funds are not all subject to the short selling restrictions and minimum disclosure requirements (among other regulations) of the SEC. This is due in part to two main exceptions to the Investment Company Act of 1940 of which hedge funds tend to take advantage (Wallace
26
(1999)). Section 3(c)(1) of this Act grants an exemption to investment companies owned by no more than 100 investors. This cap has also recently been expanded to grant this exception to funds with fewer than 500 U.S. investors. Section 3(c)(7) of this Act will grant an exception to hedge funds who only offer their shares to qualified purchasers. While there are several criteria that can deem an entity as a qualified purchaser, all such criteria fall under one of three general categories: high income, high net worth, knowledgeable investor. Variations within these
categories are based on whether the investor is an individual, a married couple, a family business, or an institution.6 For the purposes of this paper, the most important result of these exemptions is the ability to engage in short selling as part of an investing strategy. Section 12(a) of this Act states, ?It shall be unlawful for any registered investment company, in contravention of such rules and regulations or orders as the Commission may prescribe as necessary or appropriate in the public interest or for the protection of investors (1) to purchase any security on margin, except such short-term credits as are necessary for the clearance of transactions?or (3) to effect a short sale of any security, except in connection with an underwriting in which such registered company is a participant.? Application of Section 12(a) to a company then clearly prevents that company from attempting to profit via short selling, effectively removing the ability to employ strategies such as the one this study focuses on. Thus, funds that desire to use short selling as part of their strategies must then remain under the 500-investor limit and must only offer their shares to qualified purchasers. As mutual funds tend not to do so, investors looking for vehicles engaging in strategies similar to this study's focus must turn to hedge funds and their higher fee structures as described in the next section.
6
In light of the proliferation of offshore hedge funds, these rules have been interpreted to consider only U.S. investors, with no limit on the number or qualifications of non-U.S. investors for offshore hedge funds wishing to sell their securities in the United States. 27
III. C. 2.
Operating Characteristics
In order to properly model a hedge fund in this study, it is first necessary to understand the basic operations of hedge funds in general (and these characteristics will be included in the model used in this study). Several of these are summarized in Pearl (2006) for the population of analyzable hedge funds (i.e.: those listed in available databases). The most commonly used operating characteristics are the investment management fee and the incentive allocation (or performance fee). The investment management fee is the fee extracted by hedge fund managers for their actual services, and the majority of these fees fall between one and two percent of the net asset value of the fund.7 As its names suggest, the incentive allocation is the ?pay-forperformance? portion of the fees the hedge fund manager can extract, and the majority of funds extract twenty percent of the realized and unrealized gains of the fund over the course of a certain period (generally one quarter or one year). For individual funds, these fees tend to be stable over time (Liang (2001)). While these fees are commonly mentioned by researchers, Pearl (2006) also mentions expense charge offs. Depending on how liberally a fund defines items that can be charged off, he suggests that for a well-run fund, these should be less than one hundred basis points per year.8 In addition to these fees, many funds also incorporate a lockup period that restricts investors in the fund from withdrawing their money for a certain period of time after their initial investment. The purpose of this period is to give the manager ample opportunity to exercise his strategy without fear that early poor performance will result in premature withdrawals. Liang (1999) points out that hedge funds with longer lockup periods tend to experience better performance.
7
Chan et al (2006) note than many hedge funds mark their portfolios to market at the end of the month to strike a net asset value at which investors can buy into or cash out of the fund. 8 Note that this is the same demarcation point the mutual fund industry tends to advertise as the difference between funds with ?good? expense ratios and ?bad? expense ratios. 28
To protect the investors, many funds also covenant themselves with hurdle rates and high-water marks. A hurdle rate is a minimum return the fund must achieve in order for the manager to receive the performance fee. While every fund has a hurdle rate of at least zero (as there must be some positive returns for the manager to extract a percentage of), it is also conceivable that funds may apply hurdle rates equal to a risk-free return or inflation metric. In addition to providing increased protection for investors, positive hurdle rates can also double as a signal of quality to investors who want to be certain that the individuals in charge of their funds will not receive bonuses for providing returns inferior to those which the investor could have costlessly pursued elsewhere or that do not even compensate for increases in the cost of living. Also, a high-water mark provision forces a manager to recover all losses (relative to the hurdle rate) before extracting any performance fees. For example, assume a hedge fund with a hurdle rate equal to some risk-free return ends up losing twenty percent of its value over the course of a year. For this manager to earn any performance fees at the end of the next year, his fund would have to post a twenty-five percent gain (to get back to even from the beginning of the year just completed) plus last year's risk-free rate (to reach last year's hurdle) plus this year's risk-free rate (to reach this year's hurdle). III. C. 2. a. Hedge Funds vs. Mutual Funds
Since investors who would desire to profit from exploiting return differences such as those described in DT85 but who have neither the time, inclination, nor ability to do so directly through personally managing their own accounts do not have the option to follow the more familiar mutual fund route (for reasons described in Section III. B. 1. of this paper), this brief section will highlight the difference in the fee structures of hedge funds and mutual funds.
29
Collins (2007) describes how the Investment Company Institute (ICI)9 measures mutual fund fees and expenses. ?Mutual fund investors incur two primary kinds of fees and expenses when investing in mutual funds: sales loads and ongoing expenses. Sales loads are one-time fees that investors pay either at the time of purchase (front loads) or, in some cases, when shares are redeemed (back-end loads). Ongoing expenses are paid from fund assets and investors thus pay these expenses indirectly. Ongoing fund expenses cover portfolio management, fund
administration, shareholder services, distribution charges known as 12b-1 fees, and other operating costs.? He notes that these fees averaged 107 basis points in 2006, including 19 basis points from load fees and 88 basis points from the total expense ratio. While these figures are down from previous years (from a recent peak of 124, 25, and 99 basis points, respectively, in 2001), they still imply a lower cost structure to mutual fund investors than to hedge fund investors. If we consider the mutual fund expense ratio and hedge fund expense charge offs to balance each other (as both are approximately one hundred basis points on average), then the difference comes down to comparing mutual funds' load fees of approximately 19 basis points against hedge funds' one to two percent investment management fees. So, without even
considering the incentive allocation fee that is only applicable when the hedge fund provides gains for its investors, the analyses of Pearl (2006) and Collins (2007) indicate that hedge funds are, indeed, more expensive assets in which to invest. However, since mutual funds cannot offer investors the opportunity to benefit from investment strategies involving short selling, investors who desire to benefit from such strategies must be willing to pay these higher fees if they are not willing or able to follow the strategies on their own.
9
On their website, the ICI describes itself as ?the national association of U.S. investment companies, including mutual funds, closed-end funds, exchange-traded funds (ETFs), and unit investment trusts (UITs)? (About the Investment Company Institute (2007)). 30
III. C. 3.
Hedge Fund Styles
One of the issues with attempting to understand the source of hedge fund returns is that fund exposures to common risk factors varies greatly based on the investment style of the fund manager. The different hedge fund databases apply different labels and definitions to similar styles, so I will focus on the eight style definitions as put forth by the SEC in Staff Report (2003).10 The style relevant to this paper is the market trend style, which will be described first and in its own section. III. C. 3. a. Market Trend
Market trend strategies, also referred to as directional or tactical strategies, attempt to exploit broad market trends in some investable asset. Macro funds invest in various currencies based on their perceptions of the macroeconomic fundamentals of various countries. These funds usually do not hedge their investments. Long/short funds search for pricing anomalies to exploit, taking a long position in assets the manager believes to be undervalued and a short position in assets the manager believes to be overvalued. While not necessary to meet this definition, the assets on both the long and short side will almost always be the same general category of asset (e.g. all equities, all bonds, all currencies, etc.). Sector funds would be even more specific, focusing on a specific industry (e.g. long/short tech stocks) or a particular class of assets (e.g. long/short long-term government bonds). This categorization also does not assume anything about the relative sizes of the investments on the long side and short side, but those that place equal dollar weights on their long investment as their short investment would be referred to as market neutral or relative value funds.11 While not explicitly mentioned in the SEC report referenced above, some databases separate funds termed short selling funds as their own style
10 11
Unless otherwise specified, any specific information in this section comes from this document. This is the specific strategy that this paper will focus on. 31
instead of being a subclass of the long/short style. These funds focus on overvalued securities, taking only short positions in those securities they consider overvalued ?enough.? At most, the proceeds of these short sales would be invested in a risk-free asset. III. C. 3. b. Other Styles
Event-driven strategies look to profit from mispricings surrounding major market events. Distressed securities funds focus their attention on firms going through bankruptcy proceedings and/or reorganizations. Since outstanding securities of these firms tend to be rather illiquid (if not frozen), these funds often wait for new issuances out of these firms, taking long positions in the new securities of firms they believe will survive and, if allowed by regulations, short positions in the new securities of firms they believe will not survive. Risk/merger arbitrage funds look to profit from mispricings that result from firms going through a merger, acquisition, or leveraged buyout. If the fund believes the mispricing is large enough, it will take a long position in the firm being acquired and (if this is part of their desired strategy) a short position in the acquiring firm. Arbitrage strategies are similar to long/short strategies and in general can be considered as a possible sub-strategy for most other styles (with the previously noted general exception of the macro style). These strategies are similar to long/short in their search for pricing
discrepancies, but these discrepancies do not have to be the same category of asset. The key here is that the long asset and the short asset are very closely related to each other. Convertible arbitrage funds look for companies who have issued convertible securities (e.g. bonds, preferred stock, or warrants). They will invest in those convertible securities deemed to be undervalued relative to the company's common stock, in which they will then take a short position. Fixed income arbitrage funds search for price discrepancies in the bond market among securities with
32
similar or identical terms issued by the same borrower.
Statistical arbitrage funds use
mathematical models to locate pricing inefficiencies then invest accordingly under the belief that mean reversion will occur. If a hedge fund can be compared momentarily to a stock, then a fund of hedge funds (FOHF) would be analogous to a mutual fund. The FOHF manager looks to provide positive returns not by determining which investable assets are undervalued and overvalued, but by determining which other managers are the most adept at doing so. FOHFs thus provide a
diversification benefit for an entire class of investments that is not completely transparent to the investment community. In addition, the initial capital required to invest in an FOHF (ranging from $25,000 to $1 million) tends to be much less than that required to invest in the average hedge fund (ranging from $50,000 to $10 million), making this class of investments more accessible to the investment community. However, the cost of these benefits is the double layer of fees that investors in FOHFs face. For the hedge funds which the FOHF manager correctly determined would increase in value, the managers of those hedge funds will extract both their management fees and performance fees. If the FOHF manager picks enough correct funds and thus earns positive returns net of the hedge funds' fees, then he will also be able to extract management fees and performance fees before the investors see their returns. In a small bit of relief, the fees of FOHFs tend to be smaller than those observed in the overall hedge funds universe. Gregoriou and Rouah (2002) observe management fees on the high side at two percent with average performance fees at ten percent, usually with high-water mark and hurdle rate provisions. Bernstein (2002) reports management fees tending to range between 1% and 1.5% with performance fees between 5% and 10%.
33
III. C. 4.
A Focus on Market Neutral Hedge Funds
As mentioned earlier, a market neutral hedge fund places equal dollar weight on its portfolio of long investments as it does its portfolio of short investments. The intent here is not necessarily that the long portfolio would have a positive return while the short portfolio would have a negative return (although that would be the ideal). Instead, the long portfolio merely has to outperform the short portfolio by the amount of the costs of engaging in this strategy (including transactions costs and the interest on margin loans) and the management fees extracted from the fund for the market neutral manager to show a profit to his investors. Thus, a market neutral hedge fund manager merely has to discover a way to determine classes of stocks that should experience slightly different levels of performance from each other in the future in order to be successful. III. C. 5. Risk Exposures of Market Neutral Hedge Funds
When research on the performance of hedge funds started becoming more common approximately ten years ago, there seemed to be a belief that the traditional models of explaining returns, especially those applied to mutual funds, should suffice to provide adequate explanations, even if it was discovered that the sources of hedge fund returns were different than those observed for other classes of investments. As articles on the subject continued to be published, though, it was becoming more and more apparent that the traditional explanatory models were not explaining very much. This is especially true for the market neutral strategy that this study is focusing on, even though similar results would be found by exploring other strategies. Brown, Goetzmann, and Ibbotson (1999) point out that the market neutral style is the classic hedge fund style and was never intended to track broad indices. Liang (1999) says that the market neutral strategy is the only one to truly ?hedge? buy-and-hold market risk. In
34
Gregoriou and Rouah's (2002) study, they note that market neutral funds are designed to be neutral to first-order moments (actual market movements) but not second order moments (the volatility of market movements), even though their volatilities may still be low relative to other hedge fund styles.12 As such, there should not be much, if any, surprise when index-based and factor models fail to account for large portions of their returns. In spite of this, researchers have continued to look for ways to fit hedge fund returns into traditional models. Ackermann, McEnnally, and Ravenscraft (1999) note that market neutral funds have low average returns and standard deviations of returns relative to other hedge fund styles and to the S&P 500.13 They also note that Sharpe ratios for market neutral hedge funds tend to be high relative to other strategies, implying that despite having lower returns, market neutral hedge funds provide a superior risk-return tradeoff. Schneeweis, Kazemi, and Martin (2003) find that market neutral hedge funds have little to no exposure to equity, debt, volatility, credit spreads, or a term premium. Kouwenberg (2003) observes that relative to other hedge fund strategies, market neutral hedge funds have almost universally the smallest absolute correlation with various market (stock and bond) indices, option selling strategies, Fama-French factors (market excess return, size-based returns, book-to-market-based returns), and the analogous Carhart momentum factor (return differences between prior winners and prior losers). Agarwal and Naik (2004) conclude that, based on their negative factor loading on the momentum factor in their analysis, relative value funds are contrarian in nature. They explain the intuitiveness of this result by describing these funds as waiting for the prices of fundamentally similar stocks to
12 13
This is a measure of the importance of managerial skill in this hedge fund category. Earlier in the same paper, they find that market neutral hedge funds tend to have higher performance fees than other hedge fund styles. This could be a way to compensate the fund manager for the lower expected returns of this style. 35
diverge then purchasing the newly undervalued stocks (losers) and shorting the suddenly overvalued stocks (winners). Spurgin, Martin, and Schneeweis (2001) point out that the long/short equity style in general exhibits market neutrality when regressed against the market return and a quadratic term designed to estimate changes in correlation with the market return in periods of extreme market shifts (neither term is significant and R2 = 0.014). Ranaldo and Favre (2005) analyzed which form of the market model provides the most explanatory power for each hedge fund style: the traditional model with only a linear term, a model with a quadratic term to account for a coskewness premium (for securities whose return distributions are negatively skewed during positively skewed markets), or a model with a cubic term as well to account for a cokurtosis premium (for securities that are more likely to experience extreme returns when the market experiences extreme returns). For the equity market neutral strategy, they found the traditional model to be best. However, for the relative value strategy (which it can be argued some equity market neutral strategies fall under), the quadratic model provides the best fit, and this model indicates that such strategies require an estimated 2.60 - 2.80% premium for the coskewness they exhibit. III. C. 5. a. Return Persistence
It has been argued that factor-based models like the ones used later in this study have difficulty separating return premia from managerial skill, so some researchers have attempted to look for persistence in hedge fund returns as a way of determining managerial skill. Brown, Goetzmann, and Ibbotson (1999) search for risk-adjusted return persistence in offshore hedge funds and are unable to locate any when accounting for style category and managerial skill. Agarwal and Naik (2000b) find little evidence of return persistence across hedge fund strategies
36
beyond two periods and for longer than quarterly periods (i.e. on a month-to-month or quarter-toquarter basis, but no further). Additionally, where persistence can be found, there is greater evidence of it in hedge fund losers (relative to the median return) than in winners. In contrast to these results, Amenc, El Bied, and Martellini (2003) apply the Hurst exponent (an econometric measure of persistence in time series data comparing its range to the number of periods being analyzed) to their analysis and are able to locate monthly return persistence (note that most other studies tend to focus on quarterly or yearly return persistence, only, though). III. C. 5. b. Non-Normality of Returns
While there has not been a direct study that focuses on the distribution of returns for long/short hedge funds, several authors have shown that hedge fund returns in general are not normally distributed. Since metrics such as Jensen's alpha and Sharpe ratios are based on the assumption that returns are normally distributed, the need to account for the third and possibly the fourth moments of hedge fund returns (skewness and kurtosis) is considered by several authors, including Amenc, Martellini, and Vaissié (2003) and Mackey (2006). In reporting the non-normality of hedge fund returns, Mackey (2006) specifically points out that after sorting several individual hedge funds by their alphas as he calculated them, he finds that most of the variation in alpha (85%), excess return (73%), and risk premium (61%) is concentrated in the tails of the alpha-ranked distribution.14 Anecdotally, only 37.95% of the total variation is found in the tails of a normally distributed random variable, and only 48.8% of the total variation is found in the tails of a uniformly distributed random variable. This indicates that hedge fund returns may be either highly skewed or possibly bimodal towards the tails.
14
These tails are defined as the top ten percent and bottom ten percent combined of individual hedge funds after sorting by alpha. 37
When de Beus, Bressers, and de Graaf (2003) simulate hedge fund performance by using a normal inverse Gaussian distribution and then form a portfolio of traditional and alternative investments, they first optimize their portfolio mix by incorrectly assuming hedge fund returns are normal. This ?optimal? portfolio exhibits value-at-risk (VaR) that is fifty percent greater than expected and expected shortfall that is sixty percent greater than expected if hedge fund returns were normally distributed. When subsequently optimizing the portfolio mix using the ?true? distribution, the portfolio mix changes substantially, reducing the optimal weight in alternative investments from sixty-five percent under the incorrect normality assumption to only fifteen percent under the correct assumption. Amin and Kat (2003) attempt to create a metric to compare hedge fund returns with the S&P 500 without relying on this assumption and subsequently find that hedge funds do not compensate investors for their risk as well as the S&P 500. Unfortunately, their metric assumes that the hedge fund benchmark should have a payoff function that is a monotonic nondecreasing function of the market index, which is a questionable assumption; since hedge funds exhibit near-zero correlation with various market indices, it seems odd to create a benchmark that likely has a strong positive correlation with the market index. While they attempt to find an alternative way to explain hedge fund betas, Kouwenberg (2003) points out that the non-normality of hedge fund returns does not impact alpha significantly. III. C. 5. c. Absolute Versus Relative Return Targets
Most common investment tools are analyzed based on a relative return framework. Individual stocks are considered to do well if they outperform their industry average. Mutual funds are considered to do well if they outperform the market or some specific large segment of the market. Thus, even if a stock or mutual fund lost some of its value over a certain period, this
38
would not be considered poor performance if the benchmark against which it is being compared lost even more value (in terms of returns). This is not true for hedge funds. In fact, one of the diversification benefits that hedge funds claim to offer is their ability to provide positive returns across all market conditions. This is why a hedge fund is said to have an absolute return target, as opposed to a relative return target. In spite of near-zero correlation with the S&P 500, for example, Amenc, Martellini, and Vaissié (2003) found market neutral returns to be consistent across the different types of markets (bull, bear, and steady). Capocci, Corhay, and Hübner (2005) go further by pointing out that the market neutral strategy is the only one to show consistent abnormal positive performance during both bullish and bearish periods. Fung and Hsieh (1997) attempt to expand Sharpe's (1992) model for hedge fund managers who have more absolute return targets by adding trading strategy and leverage determinants to the asset return determinant. In this article, their systems/trend following
strategy15 has a very low R2 and is not related to any of nine standard asset classes. Graphing this strategy's returns against the market shows that it acts more like a straddle (long a put and a call) than anything else. In contrast, their 2004 paper shows that seven asset-based style risk factors (including market risk and small-cap/large-cap return differences) provide good predictors for the overall hedge fund industry in an arbitrage pricing theory framework with R2 values generally above 0.5. The additional factors would need to be included when focusing on specific hedge fund styles. III. C. 5. d. The Role of Leverage
As pointed out in the section on regulations, hedge funds have a much greater access to leverage than do traditional investment vehicles due to their ability to take short positions in
15
Fung and Hsieh (1997) do not explicitly look at an equity market neutral strategy, but the systems/trend following strategy described in their paper is the closest match to the market neutral style. 39
securities as part of their strategies, even though Regulations T and U still apply to hedge funds attempting to gain leverage through margin (Nadel (1998)). In the much publicized 1998
collapse of Long Term Capital Management, it was noted that the fund had reached leverage ratios of as much as 100-to-1. Clearly, it is crucial to understand, then, the potential impact leverage may have on hedge fund performance. Kao (2002) summarizes this issue by pointing out that it has been difficult to determine empirically the link between leverage and hedge fund performance. As expected, increased leverage would have a negative impact on survival metrics (Gregoriou (2002)); the leverage magnifies the extent to which any downward movement in the unlevered investment affects the levered investment. Fung, Xu, and Yau (2002), in their analysis of global hedge funds, note that leverage magnifies Sharpe ratios and Jensen's alpha, but not excess returns nor beta. While a levered hedge fund can face effectively unlimited possibility of bankruptcy (especially if the leverage is being utilized to take short positions in some asset), there is only limited benefit to using leverage. There seems to be a firm belief among hedge funds themselves that they will become inefficient if they reach a certain size, because the sizes of their potential trades may eclipse the market's capacity for supply or demand, thus limiting their liquidity. Leveraging the investment in a hedge fund can bring the fund closer to that inefficient point (depending on the size of the fund and the instruments being traded). This is possibly one of the reasons that hedge funds remove themselves from databases once they reach a certain size (which varies by the fund). In the same vein, Goetzmann et al (2003) argue that there is only a finite amount of arbitrage profits available in the economy at any point in time, so the benefits of leverage are limited to those profits that have not yet been captured.
40
III. C. 5. e.
Dynamic Versus Passive Strategies
Another factor plaguing researchers' attempts to model hedge fund returns is that traditional models assume that investments are purely passive buy-and-hold strategies or at most systematically rebalanced (equal-weighted benchmarks mimic this). Hedge fund managers, however, follow what would be considered dynamic trading strategies, potentially jumping in and out of investments whenever the need arises to protect their position. This is why Fung and Hsieh (1997) attempt to add three dynamic trading strategy factors to a more traditional assetbased factor model. If beta is considered to be an asset's exposure to traditional risk factors and alpha the return component derived from managerial skill, there is an unexplained middle ground that Fung and Hsieh (1997) begin to touch upon. Jaeger and Wagner (2005) refer to this middle ground as ?alternative beta,? whereas Leibowitz (2005) calls it ?allocation alpha.? In either case, there is a concept that some component of a hedge fund's return is purely a function of properly following a specific hedge fund strategy. Over time, this may become a more important
component of hedge fund returns to determine. If there is, in fact, only a finite amount of arbitrage profits, then hedge fund alphas will decline as more money chases them (Jaeger and Wagner (2005)). They also point out that the average alpha will decline as more hedge fund managers enter the market, eroding the overall average skill level of all hedge fund managers (assuming the earliest entrants to this industry contained a high concentration of the most capable managers, which is not necessarily true, especially in the long run where brand new entrants to the job market could be very highly skilled relative to existing fund managers).
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III. C. 5. f.
Biases in Databases
One of the major problems with studying hedge funds historically lies with the data itself. Since the main role of the most commonly used hedge fund databases has been to signal an openness for new investment (in other words, advertise), no single database has really been considered the best database of funds. Since funds choose the databases in which they want to be included, and there is no requirement that prohibits funds from going into one and only one database, the samples that make up each database tend to be vastly different. As such, using database-generated indices of fund returns as benchmarks (as is popular in equity research that benchmarks against the CRSP equal-weighted and value-weighted indices) can create results highly dependent on the database being used. For the market neutral strategy, indices from various databases vary by as much as five percent (Amenc, Martellini, and Vaissié (2003)). Fung and Hsieh (2002b) break down the biases generated by this situation into two categories. Natural biases are those ?that are consequences of sampling from an unobservable universe of hedge funds,? and spurious biases are ?those that arise from the way data vendors collect hedge fund information.? Natural biases, such as survivorship bias, are difficult if not impossible to rectify, but they are also common across different types of investment assets. Spurious biases, such as self-selection and instant history biases, are specific to the hedge fund industry, but are generally correctable through careful data manipulation. III. C. 5. f. 1) Survivorship Bias Survivorship bias in hedge fund databases is similar to the survivorship bias that plagues some more commonly used databases of financial information. In addition, since inclusion in these databases is voluntary, hedge funds no longer in operation for any reason may be thrown out of databases in which they were previously included. Liang (2001) estimates this bias to be
42
approximately 2.43% per annum. Others have put this bias at approximately three percent per annum (Brown, Goetzmann, and Ibbotson (1999); Fung and Hsieh (2000)). Unfortunately, these estimates are not analogous to the measurements of survivorship bias in other segments of the investment industry, which compare the average return of all of a particular type of investment asset over a time period to the average return of the members of that asset type still in operation at the end of the same period. Since the entire universe of hedge funds is unobservable, this calculation is impossible. In addition, the reliability of estimators of this bias for the hedge funs industry degrade as one tries to look further back in time, since hedge fund databases did not become very heavily populated until the mid-1990s (Fung and Hsieh (2002b)). III. C. 5. f. 2) Self-Selection Bias As mentioned earlier, hedge funds are not required to report their results to any database, and those that do are using the database as a means of advertising that they are accepting additional investment funds. The most logical reason a fund would not report its results is that its performance has not been good enough to expect that it would draw in any additional investors. The less obvious reason that has been touted as a reason to not report a fund's results to any database (or to choose to pull out of reporting to any database) is that some hedge funds stop reporting their results once they reach a certain size (Goetzmann et al (2003)). This implies that hedge fund managers believe there is some finite optimal level of assets to manage, as mentioned in the above section on leverage. These two factors make the net effect of this bias indeterminate. III. C. 5. f. 3) Instant History Bias The nature of the self-selection bias leads to yet another bias, the instant history bias. While hedge funds can decide when they want to consider reporting their results to a database,
43
commercial hedge fund databases do not generally allow new hedge funds to just begin reporting their information. Usually, they must have approximately twelve months of prior results to report. As such, hedge funds with poor performance over their first few months may choose not to report in any database. Those that do decide to report in one or more databases will have thus likely had strong prior performance, and this past performance is automatically included in the database, thus creating an ?instant history? that will almost always report positive results. III. C. 6. Alternative Risk Measures
Since traditional return models tend to experience difficulty in explaining the sources of hedge fund returns, researchers have had to look to different factors and different performance metrics to help explain what would otherwise appear to be strong, significant alphas. Amenc, El Bied, and Martellini (2003) find that market neutral hedge funds have statistically significant exposures to oil prices (a proxy for the short term business cycle) and changes in three-month T-bill rates (a proxy for changes in expectations of future economic activity). In other words, their results indicate that market neutral hedge funds are exposed to risks related to actual and expected future economic activity. Even though this model (like so many others) had a very low R2 value, it provided a very strong predictability for the direction of the returns on a market neutral hedge fund. While equal- and value-weighted indices of individual hedge funds might be a sensible benchmark to evaluate a fund's performance (similar to how CRSP indices are used), Fung and Hsieh (2002b) suggest using funds of funds as appropriate benchmarks. While funds of funds do have an additional layer of fees than other hedge funds, using the performance of funds of funds eliminates or reduces the impact of the survivorship, self-selection, and instant history biases described above.
44
Agarwal and Naik (2004) suggest conditional value-at-risk (CVaR), the expected value of the returns in the lowest tail of the distribution of returns, as a better estimate of hedge fund risk than variance. They support their contention by also noting that CVaR improves as an estimator over variance as volatility declines (which would be relevant for hedge funds that target and are able to claim lower volatilities than the market). According to Chan, Getmansky, Haas, and Lo (2006), market neutral hedge funds obtain higher expected returns during distressed periods, implying that returns generated by this strategy may come from volatility. This conclusion is further supported as they point out the recent struggles of this strategy as a result of recent (relative to their study) large fund inflows (thus increasing the sizes of these funds and bringing them closer to the aforementioned inefficient point) and changes in equity markets designed to reduce volatility and/or increase investor confidence, such as the decimalization of exchange-listed prices, the use of electronic communication networks that enhance communication between brokers and investors, the increased use of automated trading systems, and the fair disclosure provisions of Regulation FD. While associating declining performance with large inflows is not a surprise (as discussed above in the section on self-selection bias in databases), the other four items listed should all result in lower volatilities. This supports the use of an index such as VIX in a model attempting to explain market neutral strategy returns (in a factor-based regression, the difference between the average return on VIX call options, which profit from increased volatility, and VIX put options, which profit from decreased volatility, may be appropriate). Recalling Fung and Hsieh's (1997) contention that this style acts as a straddle on the market return further supports this inclusion. With many different possibilities for the ?right? model, none of which truly seem to do a great job of capturing hedge fund return variation, it would appear that any discussion of how
45
well a hedge fund performs would be heavily influenced by which model is being applied to explain that performance. Fortunately for investors who desire to place their money in a hedge fund, while different models will clearly result in different calculated values of alphas, Alexander and Dimitriu (2005b) show that the ranks of individual fund alphas relative to each other are mostly consistent across different models. In other words, while the various models may agree on which fund managers are providing the most value added to investments in their funds, there is great discrepancy across models as to precisely how much value is being added (or destroyed) by the managers.
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IV. Hypotheses and Model Development In order to come up with a proper basis for comparing the profitability of personal management of assets relative to hedge fund management of assets, this study will simulate the portfolios that would be formed by following the advice implied by DT85 and holding them for three-year periods under the two possible investment options discussed in Part III of this paper: using the services of a broker-dealer (and facing the institutional constraints subsequently imposed on margin investors and short sellers) and using a hedge fund manager who will provide convenience for the investor who desires to profit from this strategy but who will charge additional fees for this convenience. IV. A. Hypotheses to Test The first test that will need to be performed is to check that the strategy implied by DT85 still is viable in the years after it was announced. In its purest form, with no frictions, there is little to suggest that the phenomenon that was studied in DT85 could not still exist. H1a: Stocks that were the most extreme poor performers (losers) over a three-year period should outperform stocks that were the most extreme good performers (winners) over the subsequent three-year period.
To test this hypothesis, I will replicate the DT85 model as closely as possible and test the difference between the returns of the loser and winner portfolios. This hypothesis will be supported if the three-year returns on the loser portfolio exceed the three-year returns on the winner portfolio by a statistically significant amount. I will also test this hypothesis against relaxed assumptions relative to DT85, such as the inclusion of non-NYSE stocks and requiring fewer years of prior data to exist on included stocks. Additionally, the nature of the stocks studied suggests that the return difference between these two categories of stocks may simply be based on compensation for different risk factors. Fama and French (1996), sorting NYSE stocks on deciles of prior returns, note that when they
47
regressed future returns of each decile in their three-factor model (Fama and French (1993)), the factor loadings on size and book-to-market were both significant at the extremes and declined while moving from the lowest prior return decile to the highest prior return decile. The factor loading on the market premium exhibited a slight smile pattern across deciles with little difference (likely not significant based on an observation of the magnitude of the difference, though this was not tested in the original paper) between the market risk factor loadings of the lowest and highest deciles. Thus, it can be expected that the returns on a portfolio consisting of long positions of previous losers and short positions of previous winners should be affected by the size and book-to-market risk adjustments exhibited by the included stocks. H1b: The factor loadings on size and book-to-market of a portfolio long in prior loser stocks and short in prior winner stocks should both be positive, while the factor loading on market returns should not be significantly different than zero.
Similarly, Carhart (1997) developed a risk factor to account for persistence in stock returns (momentum). Since DT85 is based on reversals in stock returns, the opposite effect should be observed. H1c: The momentum factor loading of the same portfolio should be negative.
Using the same methodologies that will form the returns tested in the first hypothesis, these two hypotheses will be supported based on the coefficients that result from regressing the differences in returns described earlier in a market model, capital asset pricing model, three-factor model, and three-factor model with momentum. In all four models, the market risk factor should be near zero. In both three-factor models, the size and book-to-market coefficients should be positive. In the momentum model, the momentum coefficient should be negative. Also, while not a formally-tested hypothesis, it would be beneficial to this study if all the alphas of these models are positive and significant, indicating that there is potentially some risk-adjusted excess return to following this strategy.
48
Once this is shown to be a viable strategy, the focus will shift to using this strategy as a means of obtaining abnormal returns on an investment. This will allow a direct comparison of the two methods of investing detailed in this paper, personal/direct management of one's own investment and investment in a hedge fund. In either case, since both methods entail some form of cost or constraint, the returns on either strategy should be less than the difference between the returns of loser and winner stocks. This comparison, of course, needs to take into consideration the use of leverage in both strategies. H2a: After adjusting for leverage, the returns on the DT85 contrarian strategy through personal asset management should be less than the difference between the returns of DT85's loser stocks and DT85's winner stocks. After adjusting for leverage, the returns on the DT85 contrarian strategy through hedge fund investment should be less than the difference between the returns of DT85's loser stocks and DT85's winner stocks.
H3a:
Here, I will simply look for the raw returns from personal asset management to be significantly less than the returns calculated in testing H1a and for the raw returns from hedge fund investment to be significantly less than the returns calculated in testing H1a. Also, the restrictions imposed on investors attempting to employ leverage and engage in short selling are designed to lessen the risks associated with utilizing such investment tools. H2b: In absolute value terms, each risk factor loading from following the DT85 contrarian strategy through personal asset management should be less than the same loadings of the return differences analyzed in H1b and H1c. In absolute value terms, each risk factor loading from following the DT85 contrarian strategy through hedge fund investment should be less than the same loadings of the return differences analyzed in H1b and H1c.
H3b:
Two conclusions are wrapped up in this hypothesis. The crucial conclusion is that the absolute values of the slope coefficients of the various regressions should be significantly less in both the personal asset management and hedge fund investment cases than in the initial return difference case. The less crucial conclusion is that the signs of each risk factor should be the same across
49
all three cases, though this point becomes even less important if a particular risk factor is not statistically significant.
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V. Data and Results V. A. Data Collection Most data for this study were obtained from databases provided by the Wharton Research Data Services (WRDS). Monthly and daily stock returns (and other stock information) from January 1979 through December 2006 came from the Center for Research in Security Prices (CRSP) Stock Monthly and Daily files, respectively. The January 1986 through December 2006 values for the independent variables used in the factor regressions came from Kenneth French's Data Library web site at Dartmouth. Separate from WRDS, interest rate information was
obtained from the Federal Reserve Economic Data (FRED) database maintained by the Federal Reserve Bank of St. Louis, and hedge fund index information was obtained from Hedge Fund Research, Inc. (HFR). V. B. DT85 Cumulative Abnormal Returns The initial step in testing the above hypotheses is to verify that the results described in DT85 still apply to investors who may have attempted to take advantage of the anomaly since it was published. As the initial study was published in the July 1985 issue of The Journal of Finance, the first portfolio (chronologically) to be studied will be formed at the beginning of January 1986; this is to hopefully allow the mechanics of market efficiency more than enough time to exert their influences as a result of newly published information. Consistent with DT85, for a stock to be potentially included in a portfolio, it must have seven years of continuous information available prior to the formation date (January 1979 through December 1985 for the first portfolio). Any security that does not have this information available is removed from the pool of potential stocks to include. Also, only stocks priced at no less than five dollars on the formation date and traded on the NYSE are included initially in this study. Once these filters
51
have been applied, the returns of the stocks still in the pool are compounded over the previous three years (January 1983 through December 1985 for the first portfolio) and ranked according to these compounded returns.16 The thirty-five stocks with the highest such returns will be placed in the winner portfolio, and the thirty-five stocks with the lowest such returns will be placed in the loser portfolio. Then, for each month of the three-year testing period (January 1986 through December 1988 for the first portfolio), each stock's abnormal return is calculated relative to the market ( ) and summed up over the entire 36-month testing period to come up ). To avoid survivorship bias
with each stock's cumulative abnormal return (
at this point, any stock that is delisted before the end of the testing period is assumed to have zero return from that time forward. This is the equivalent of closing out one's position in a security at the end of the last month for which information about it is available and then doing nothing with the proceeds. While this may not be realistic (the proceeds from the sale of stock would at least be invested at a riskless rate), this should bias the results against finding a positive return differential, as extreme poor performers (loser stocks) are more likely candidates for delisting than extreme good performers (winner stocks). The average cumulative abnormal return is then computed for the portfolios of loser and winner stocks ( where X represents the loser (L) or winner (W) stocks and n = the number of stocks in each group). The difference between this figure for the loser portfolio and for the winner portfolio is the main test statistic used in DT85 ( ). If this study were to use ,
non-overlapping three-year periods, there would only be seven observations of DACAR to analyze (for the portfolios beginning in January of the following years: 1986, 1989, 1992, 1995,
16
This is a deviation from DT85, which ranked stocks by cumulative abnormal returns, but which is being done for consistency with later hypothesis tests that will use buy-and-hold (compounded) returns to both choose securities for the portfolios and to measure their results. 52
1998, 2001, and 2004). So, to have more data to analyze, DACAR is calculated for each of 217 portfolios beginning each month from January 1986 through January 2004. While this also deviates from DT85, it is not unprecedented in the literature focusing on DT85 to move away from non-overlapping testing periods (including DeBondt and Thaler (1987), their own followup to their original study). Initial results of this analysis indicate that the DT85-based approach to obtaining arbitrage profits has been arbitraged away. In the 217 testing periods, loser portfolios
underperformed the market by 3.57% over a 36-month period while winner portfolios underperformed the market by 3.59% over the same period, for a DACAR of 0.02% (p = 0.9932), ranging from a minimum of -83.51% to a maximum of 121.83%. While this might seem sufficient to refute the possibility of using DT85's overreaction hypothesis as a stock selection filter, the point of this paper is not simply to replicate DT85, but to assess its feasibility in a somewhat realistic investment environment. As such, it would make sense to expand the
population of stocks available for the loser and winner portfolios to include stocks traded on AMEX and NASDAQ as well. Doing so provides results along the same lines of DT85. Losers outperform the market by an average of 17.22%, and winners underperform the market by and average of 11.38%. DACAR then averages 28.60% (p < 0.0001), ranging from -56.77% to 259.92%. Given the difference between these results, it is tempting to consider that when AMEX and NASDAQ stocks became candidates for inclusion in the portfolios, they did so to the near complete exclusion of NYSE stocks from these portfolios. As such, this analysis also looked at the results of only incorporating AMEX and NASDAQ stocks through the initial filter. The assumption is, of course, that if there is little difference between these figures and the figures that
53
include all three exchanges, then NYSE stocks were effectively excluded from the loser and winner portfolios. The results do not bear this out. Losers outperformed the market by 28.21%, and winners underperformed the market by 10.29% for a mean DACAR of 38.49% (p < 0.0001) that ranges from -46.13% to 254.86%. Also, it may not make sense to require seven years of returns to exist prior to formation for a stock to be a candidate for either portfolio. Thus, a five-year cutoff was arbitrarily chosen to determine the pool of available stocks. While tests were not specifically performed to verify this, the performance of the various portfolios relative to the market tended to be magnified as a result of this adjustment: underperformers did even worse relative to the market, outperformers did better. For example, when all three exchanges are included, the loser portfolio outperformed the market by 23.75%, winners underperformed the market by 11.10%, and DACAR increased to 34.85% (p < 0.0001) while ranging from -64.01% to 223.92%. Table 1 summarizes these results. Overall, it would appear that the first hypothesis earlier is supported enough to continue with this study. While the original DT85 approach to comparing returns no longer results in a significant difference between the performance of prior losers and prior winners, the inclusion of stocks from AMEX and NASDAQ allows one to discover such a difference. V. C. DT85 Buy-and-Hold Returns While the previous analysis shows how the loser and winner portfolios perform relative to the market on average each month, it is more important for this study to observe how an investment made in the loser portfolio and held for thirty-six months compares to an investment made in the winner portfolio and held for thirty-six months. Table 2 shows that the amount by which the 36-month return on the loser portfolio exceeds the 36-month return on the winner portfolio is qualitatively similar to the DACARs of the previous section. There is no evidence of
54
a difference when only NYSE stocks are considered but strong evidence for a difference when stocks from AMEX and NASDAQ are incorporated into the analysis. With only NYSE stocks, the loser portfolio underperformed the winner portfolio by 1.75% (p = 0.5931) when seven years of prior data were required and by 4.87% (p = 0.1439) when only five years of prior data were required. When all three exchanges were included, the losers outperformed the winners by 37.93% (p < 0.0001) and 48.11% (p < 0.0001), respectively. Loser portfolios formed from only AMEX and NASDAQ stocks outperformed winners by 56.99% (p < 0.0001) and 66.54% (p < 0.0001), respectively. These figures again support the first hypothesis. These results were then tested to determine if the return differentials were generated by some uncertain anomaly or as premia for some risk factors. Three traditional models; the market model, CAPM, and the Fama-French three factor model; and a fourth model that adds a momentum factor to the Fama-French three factor model (Carhart (1997)) were used as explained below. Market model: CAPM: Three-factor model: Momentum model: where = the return generated by portfolio X in month t = the market return in month t = the risk-free rate of return in month t = the Fama-French size factor (small minus big) in month t = the Fama-French book-to-market factor (high minus low) in month t = the Carhart momentum factor (up minus down) in month t
55
For each of the 217 testing periods within a given parameter set (exchanges and years of prior information), the return differentials were divided up into their 36 months, resulting in 7,812 monthly return observations for each regression. The coefficients in each regression represent the sensitivity of the returns to the specific risk factors, and the intercept in each regression represents the unexplained (possibly anomalous) return per month. All the regression results are contained in Table 3. As expected, the return differentials were positively related to the size and book-to-market premia (all with p < 0.0001). The size factor was greatest when only NYSE stocks were included17 (ranging from 0.6499 to 0.7599), declining when AMEX and NASDAQ stocks were included (0.3230 to 0.3494), and declining again when NYSE stocks were removed (0.2655 to 0.2838). Also, decreasing the prior return requirement from seven years to five years increased the size factor loading in five out of six regressions, the exception being the momentum model without NYSE stocks, where the factor decreased from 0.2698 to 0.2655. For the book-to-market factor, the all-exchange regressions (0.5670 to 0.6418) have a greater value in three out of four cases than the NYSE-only regressions (0.5434 to 0.6241), and the non-NYSE book-to-market coefficients are universally lower than the rest (0.4384 to 0.4847). Reducing the data requirement increases this factor in the NYSE-only regressions but decreases it in the regressions that include AMEX and NASDAQ stocks (alone or all-inclusive). However, the rest of the results do not appear to line up with the expectations on the market and momentum factors as described in the second and third hypotheses above. Relative to the market risk factor, the expectation was that market factor loadings would not be significantly different than zero. Even if all twenty-four market factor loadings were statistically significant, this part of the second hypothesis could still be supported if the coefficients were
17
Even though there is no statistical evidence for any difference between the loser and winner returns when only NYSE stocks were included in the selection process, those returns are still analyzed due to their relationship with DT85. 56
economically insignificant or evenly distributed above and below zero. Instead, all twenty-four market factor loadings are negative with p < 0.0001. In absolute terms, the NYSE-only
coefficients were the smallest (-0.2171 to -0.3845), followed by the non-NYSE coefficients (0.3650 to -0.5940), followed by the largest such figures in the all-inclusive regressions (-0.4221 to -0.7261). Reducing prior data requirements increased the magnitude of this factor in all cases, with changes ranging from 0.0470 to 0.1290. Also, the momentum factor does not align with the predictions mentioned earlier. While the NYSE-only return differences experienced a negative momentum factor loading in both the five-year (-0.1495, p < 0.0001) and seven-year (-0.0719, p < 0.0001) data requirements, the inclusion of AMEX and NASDAQ stocks changes this coefficient to a positive or insignificant value, 0.1473 (p < 0.0001) and 0.0620 (p = 0.0059) for the all-inclusive cases and 0.1517 (p < 0.0001) and 0.0110 (p = 0.6061) when only AMEX and NASDAQ stocks are included. Note that this effect is also magnified when the data requirement is reduced from seven to five years. Before analyzing these coefficients more succinctly, note the promising results of the intercepts as they relate to moving forward to the next section, where these results form the justification for the investing strategy to be followed later. In all sixteen regressions that
included AMEX and NASDAQ stocks, the intercepts were positive and significant. The smallest and least significant of these intercepts was for the momentum regression when all exchanges are included and seven years of prior data are required: = 0.00372 and p = 0.0006, implying an
annual excess return of approximately 4.464%, or 13.392% over the entire three-year period. When looking at NYSE-only return differences, six of the eight regressions had negative intercepts; only the market model intercepts were positive (0.00323, p = 0.0001 for the sevenyear requirement; 0.00343, p = 0.0003 for the five-year requirement).
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It should also not be too surprising to note, based on the discussion earlier in section III. C. 5. of this paper, that the adjusted R2 values of these models are relatively low, ranging from 3.61% to 13.82%. Whether these returns are better explained by some of the alternative models described in that section is beyond the scope of this study. V. C. 1. Unexpected Positive Momentum Coefficients The especially surprising point about the positive coefficients to momentum is the nature of the momentum independent variable (UMD). Carhart (1997) defines this factor as ?the equalweight average of firms with the highest 30 percent eleven-month returns lagged one month minus the equal-weight average of firms with the lowest 30 percent eleven-month returns lagged one month. The portfolios include all NYSE, AMEX, and NASDAQ stocks and are re-formed monthly.? The similarity between this factor and the selection criteria for the portfolios tested in this paper is relatively clear. Since the UMD factor subtracts the returns of prior losers from the returns of prior winners, it should be inversely related to the return differences calculated above. To investigate this odd result, I performed the same regressions on the loser and winner portfolios separately. The results of these regressions are found in Tables 4a - c. Here, a possible explanation for the positive momentum factor loadings can be found. First, in all six cases, the momentum factor loadings on both the loser and winner portfolios are negative, ranging from -0.3569 to -0.2328 for the loser portfolios and from -0.4025 to -0.2039 for the winner portfolios, all with p < 0.0001. In the two NYSE-only cases, the factor loadings on the losers are greater than the factor loadings on the winners. In the other four cases, which all include AMEX and NASDAQ stocks, the factor loadings on the losers are all less than the factor loadings on the winners. So, while the positive coefficients on the momentum factor in the return difference regressions may result in rejection of the third hypothesis as stated above,
58
the results of the separate winner and loser regressions support the idea that there is a significant reversal component to the returns generated by both the loser and winner portfolios. For NYSE stocks, the reversal component is stronger in the losers than in the winners. For AMEX and NASDAQ stocks, the reversal component is stronger in the winners than in the losers, and that effect also dominates when combined with NYSE stocks, resulting in the positive momentum coefficient in the return difference regressions. It is also interesting to observe the breakdown of the excess returns as represented by the intercepts. In twenty of the twenty-four winner regressions, the intercept is negative and
significant. In the other four regressions, which are the momentum regressions with AMEX and NASDAQ stocks, the intercept is positive yet insignificant. On the other hand, in all sixteen loser regressions that include AMEX and NASDAQ stocks, the intercept is positive and significant; in the eight NYSE-only regressions, the intercept is either negative, insignificant, or both. Also, as a follow-up to the brief mention of the low adjusted R2 values, this breakdown also gives a strong impression that much of the inability to use these factor models to explain the variability in the return differences results from the low explanatory power of the various factor models to explain the returns to the loser portfolios (adjusted R2 ranging from 8.59% to 37.55%), as the winner portfolios tend to fit these models well (51.28% to 76.50%). V. D. Personal Asset Management As required by Regulation T, for every dollar an investor wishes to sell a security short, he will be required to post at least half that amount in cash as collateral with his broker. The sum of these two amounts (initial securities sold short + cash deposit) is called the investor's credit
59
balance (CR)18 and can earn interest. The current value of the securities sold short at any point in time is called the short market value (SMV). The difference between the two amounts is the investor's equity (EQ = CR - SMV). The investor could also take a long position in securities and use margin to leverage his position. According again to Regulation T, for every dollar of securities the investor wants to purchase, he would have to post at least half that amount in cash. The broker will loan the remaining amount that the investor does not provide to him; the amount of this loan is the investor's debit balance (DR). The current value of the securities purchased in this manner is called the long market value (LMV). The difference between the two amounts is the investor's equity (EQ = LMV - DR).19 The investor in this paper is taking both a long and short position in securities. In such a case, the two scenarios just presented are analyzed in tandem with each other. In other words, the two equity values are added together (EQ = LMV DR + CR - SMV).20 This equity value is adjusted whenever the broker marks-to-market. As an example, assume the investor has $100,000 that he would like to invest, he would like to both maximize his investment through using as much margin as Regulation T allows, and he would like to have his initial investment split equally among long and short positions. On the long side, he posts $50,000, borrows $50,000 (DR), and purchases $100,000 in securities (LMV). On the short side, he posts the other $50,000 (cash deposit) and is allowed to take short positions in $100,000 (SMV) worth of securities (thus, CR = $50,000 + $100,000 = $150,000). His initial equity would then be $100,000 - $50,000 + $150,000 - $100,000 = $100,000. At the first marking-to-market, two things occur immediately. First, the LMV and SMV are adjusted to reflect changes that occurred in the market values of the securities. If the securities held long
18
The terms introduced in this section are described in greater detail in the Securities Training Corp.'s study guide for the Series 7 exam. 19 Note that in both cases, the initial equity equals the investor's cash deposit. 20 LMV represents the value of the equal-weighted portfolio comprising the 3035 loser securities, and SMV represents the value of the equal-weighted portfolio comprising the 3035 winner securities. 60
declined in value by an average of 10% and the securities held short rose in value by an average of 20%, then the investor would have LMV = $90,000 and SMV = $120,000. Second, since the debit balance represents a loan, interest owed will accrue on that loan, thus increasing the debit balance. For simplicity's sake, temporarily assume the broker-dealer applies a monthly markingto-market and that the interest applied to the loan is 12% per annum (or 1% per month). The new debit balance would then be $50,500. Also, the credit balance could be invested in a money market fund if the broker-dealer provides such an option for the investor. Again for the sake of simplicity, I will temporarily assume this option is not available in working through this example (though it will certainly be considered as an option during the simulation). The new value of the investor's equity can now be determined: EQ = $90,000 - $50,500 + $150,000 - $120,000 = $69,500. In reality, the interest rate applied to debit balances each month varies, and is based off of what is known as the broker loan rate, which is the interest rate banks charge brokers to borrow funds. Brokers then generally charge investors a premium on the broker loan rate as interest on the debit balances in their margin accounts (a 3% premium is used in this analysis). Since the broker loan rate can vary depending on the broker (just as interest rates vary from one investor to another), it is estimated for the purposes of this analysis as that month's prime interest rate. Once all marking-to-market has been completed, the FINRA margin requirements must be satisfied. The requirement is that equity must be maintained at a minimum level of 25% of the LMV and 30% of the SMV. 21 The margin requirement could then be defined as REQ = 0.25 * LMV + 0.30 * SMV. In the example above, the investor's margin requirement after the first
21
Different brokers; such as E*Trade, Bank of America, UBS Paine Webber, and several others; were contacted to determine what margin requirements are actually imposed on investors. Although the federal minimum requirements of 25% and 30% are used in this example, brokers usually use requirements of 30% on long positions and 35% on short positions to protect themselves from the risk associated with providing margin. 61
marking-to-market would have been REQ = 0.25 ($90,000) + 0.30 ($120,000) = $22,500 + $36,000 = $58,500. Since EQ > REQ ($69,500 > $58,500), there would be no margin call imposed on the investor this period. Several months later, the new positions the investor faces may be as follows: LMV= $140,000, SMV = $160,000, DR = $56,000, CR = $150,000. In this case, EQ = $140,000 - $56,000 + $150,000 - $160,000 = $74,000 and REQ = 0.25 ($140,000) + 0.30 ($160,000) = $35,000 + $48,000 = $83,000. Since EQ < REQ, the investor would now receive a margin call. He would be forced to adjust his positions so that his equity would be at least equal to his margin requirement. One possibility would be to give the investor unlimited cash to deposit, but this option becomes uninteresting rather quickly, as it reduces to DeBondt and Thaler (1985) with the inclusion only of interest payments on the credit and debit balances. However, with unlimited cash, a profit maximizer would very likely pay off his loan immediately as well, which further reduces the problem to simply DeBondt and Thaler (1985), so we do not give the investor the ability to simply deposit cash. He decided at the outset that his initial deposit was all he was willing to deposit for this account. Whether this is because he needs the rest of his cash to pay his day-to-day living expenses or because he is simply stubborn does not matter. This gives the investor two options. He can sell off some of his long position, the proceeds of which would either be used to pay off some of his loan (thus reducing DR by the same amount) or go into his cash account (thus increasing CR by the same amount). Otherwise, he can close out some of his short position. Since this is equivalent to purchasing the securities in his short portfolio, the funds would either be obtained from the credits he has on hand with the broker (thus reducing CR by the same amount) or by borrowing additional funds from the broker (thus increasing DR by the same amount). Note how all these options result in no change to the
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investor's equity, but reduce the margin requirement he faces (since in either scenario, either LMV or SMV would decrease). This leads to two more decisions for the investor: which positions should he change and by how much. A real investor could analyze all the securities in his portfolios and then decide which specific positions he would like to liquidate/close out. The investor in this paper will follow a much simpler decision-making process.22 First, he will always make the minimum change necessary to meet the margin requirements. Then, when changing his portfolios, he will first analyze how his long and short positions are performing against each other. If his short position is outperforming his long position (SMV > LMV), he will close out his short position by the amount of the adjustment necessary to lower the margin requirement to his equity value as long as this will not lower his short position to below his long position in hopes of cutting future losses due to future gains in the short positions. If his long position is outperforming his short position (LMV > SMV) by a sufficient amount, he will liquidate his long position by the amount of the adjustment necessary to lower the margin requirement to his equity value as long as this will not lower his long position to below his short position (this has the effect of ?locking in? some of his gains). If this adjustment would make the position that was greater cross below the lesser position, he would adjust both positions by whichever amount would be necessary to both lower the margin requirement to his equity value and to set his long and short positions equal to each other (thus ?locking in? all gains or losses so far from the difference in portfolio returns). Whether DR or CR is adjusted is also based on the investor's preferences. If he decides to sell some of his long position, he would prefer to pay off his debt (thus reducing his future interest payments) above increasing his interest-earning balances (since the interest rate on the debit
22
The effect of this process will be to bias results of analyses in favor of efficiency ar35 loser securities, and SMV represents the value of the equal-weighted portfolio comprising the 35 maximization. 63
balance will tend to be greater than the interest rate on the credit balance). If he decides to close out some of his short position, he would prefer to obtain the funds to do so by using his interestearning balances above acquiring more debt with the broker (thus increasing his future interest payments). So, a reduction in LMV due to a margin call is accompanied by an equal reduction in DR and a reduction in SMV due to a margin call is accompanied by an equal reduction in CR. However, if the investor is actually earning greater returns on his credit balance than he is paying on his debit balance, then these conclusions would be reversed (increase CR when reducing LMV and increase DR when reducing SMV). The amount to change the portfolio mix by is simple in the first two scenarios. If the investor desires to reduce his short position, he would close out REQ EQ of his short position 0.30 (reducing both SMV and CR by this amount) as long as this does not reduce his short position below his long position. If he desires to reduce his long position, he would liquidate REQ EQ 0.25 of his long position (reducing both LMV and DR by this amount) as long as this does not reduce his long position below his short position. In the third scenario, recall that the equity value will remain unchanged after the adjustments have been made. Since he is readjusting his long and short positions to the same values, the new margin requirement after adjustments would be 0.25 * LMVpost-adj + 0.30 * SMVpost-adj. This amount also equals the equity though, since he is setting his portfolio up so that the requirement falls to exactly the equity value. Thus, LMVpost-adj = SMVpost-adj = EQ . It then becomes clear that the investor would liquidate his long position 0.55 (reducing LMV and DR) by LMV
EQ and close out his short position (reducing SMV and 0.55
64
CR) by SMV
EQ . Applying these rules to the example above, equity is $9,000 less than the 0.55
margin requirement ($74,000 vs. $83,000), and the short positions are outperforming the long positions ($160,000 vs. $140,000). Thus, the investor would initially want to close out $9,000 0.30 = $30,000 of his short positions. But this adjustment would lower his short position below his long position. This will cause the investor to instead adjust both his long and short positions to the same value, $74,000 = $134,545.45. The sale of some of his long positions will allow him 0.55 to pay off $140,000 - $134,545.45 = $5,454.55 of his debt. Closing out some of his short positions will use $160,000 - $134,545.45 = $25,454.55 of his credits with the broker. After this adjustment, his portfolio would have the following positions: LMV = $134,545.45, SMV = $134,545.45, DR = $50,545.45, CR = $124,545.45. Now, EQ = $134,545.45 - $50,545.45 + $134,545.45 - $124,545.45 = $74,000 and REQ = 0.25 ($134,545.45) + 0.30 ($134,545.45) = $33,636.36 + $40,363.64 = $74,000. Two other constraints must be imposed as well. First, none of the four portions of equity (LMV, SMV, DR, CR) can be negative. This may cause the investor to increase CR if he completely pays off his loan or to increase DR if he has no more credits with which to close out his short position. Second, if equity ever falls below zero, the investor cannot lower his margin requirement to equal his equity (since LMV and SMV cannot fall below zero), so if this circumstance ever occurred, he would completely liquidate this account. He will do the same if equity reaches zero exactly, since it defeats his purpose to lower his margin requirement to zero (possible only by setting LMV = SMV = 0) and then continue to allow his equity to erode as interest accumulates on his debit balance. On a complete liquidation, the investor most likely had to post additional funds that he did not intend to use at the outset. To represent the
65
(opportunity) cost of these additional funds, this amount is adjusted each month through the end of the testing period to accrue interest at the risk-free rate (i.e.: 3-month T-bill rate) in which he could have otherwise invested. V. D. 1. Results of Personal Asset Management To test H2 and H3, I am first going to focus solely on the scenario where only five years of prior data are required and where stocks can be chosen from NYSE, AMEX, and NASDAQ (thus providing the greatest population of stocks of the six scenarios analyzed earlier). Using the same selection criteria as was used to test the first set of hypotheses, I use the method described in the previous section with the following additional assumptions: Portfolios are formed on the first trading day of each month to allow for comparability with results from other sections. To lessen the problem of thinly traded stocks mentioned briefly during the literature review, stocks whose bid-ask spread is at least five percent of the open price on the portfolio formation date are removed from the population of selectable stocks. Balances are marked to market at the end of each trading day for the purpose of determining margin calls. Maintenance margin rates are set at 30% for long holdings (the loser portfolio) and 35% for short holdings (the winner portfolio). When a margin call is made, long (short) positions are sold (closed) to maintain the same weights in each security as there was after the marking-to-market but prior to the margin call. While not realistic (it would require the sale/purchase of fractional shares of stocks), it provides a middle ground between what actually are the best and worst possible margin call strategies.
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Dividends received from long holdings are added to the credit balance, and dividends paid to short holdings are subtracted from the credit balance. The credit balance is assumed to be invested in a money market account that earns a riskless rate of return (assumed to be the three-month T-bill return). The debit balance is a loan that accrues interest at a rate three percentage points above the prime rate of interest. No matter how well or how poorly the investment is performing, the investor will not withdraw his funds until the end of the three-year test period. Figure 1a presents a flowchart describing the algorithm used in this simulation. Table 5 details the results of following this strategy. The personal asset management strategy averaged a 51.44% return (p < 0.0001) over the 217 three-year testing periods studied, ranging from -40.83% to 187.36%. While this exceeds the 48.11% return differences observed in the DT85-based analysis, it is not by a significant amount (p-value of difference = 0.4934), and the unlevered value of the return from this strategy (25.72%)23 is less than the DT85 return differences (p-value of difference < 0.0001). This lines up with the expectations of H2a. Table 6 provides the results of running the factor regressions on the personal asset management results, including the breakdowns by loser and winner portfolios. Focusing on the overall results first, most of the expectations for the coefficients discussed for DT85 (insignificant market factor, positive size and book-to-market factors, and negative momentum factor) are met in the personal asset management strategy.24 In the market model and CAPM regressions, the loading on the market return (or excess market return) is positive and insignificant in both cases, 0.0181 (p = 0.2599) and 0.0224 (p = 0.1629). The adjusted R2 of
Since the maximum leverage allowed by Regulation T, 50%, was used, allowing the investor to ?double ? their investment, the unlevered returns in all cases are determined simply by halving the levered returns. 24 Unless stated otherwise, all coefficients from this table had p < 0.0001.
23
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both models is only 0.02%. In the three-factor and momentum regressions, the excess market return factor became positive and statistically significant (0.1801 and 0.1421, respectively), and both the size (0.4877 and 0.5075) and book-to-market (0.6289 and 0.5948) factors are positive and significant; the momentum factor is negative and significant (-0.1646). Also, while greater than the other two models, the adjusted R2 values of these two models are still relatively small at 9.80% and 11.25%, respectively. Finally, all four intercepts are positive and significant:
0.01201, 0.00832, 0.00469, and 0.00645, respectively. This last intercept (from the momentum model) implies an annual excess return of approximately 7.74% for the astute investor, or 23.22% over the entire three-year period. Breaking down this regression into its component loser and winner portfolios finds substantively similar results to what were shown in the DT85 loser/winner regressions. The intercepts are positive and significant for the loser portfolios and negative or insignificant for the winner portfolio. The (excess) market return factor loadings are positive and significant for all the loser and winner portfolios, and the magnitude is greater for the winners than the losers (though this difference is only 0.0237 in the three-factor model and 0.0202 in the momentum model). The loadings on the size factor are positive and significant for the losers and winners in both models in which it is included, and the loading has a greater magnitude on the losers than on the winners. The book-to-market loadings are positive and significant for the loser portfolios and negative and significant for the winner portfolios. One difference from the DT85 case is looking at the momentum factor. It is negative and significant for both the loser and winner portfolios, with the value being greater for the winners (though only by 0.0151), as opposed to the value for the loser being greater in the DT85 case. The regressions on the separate loser and winner portfolios have greater explanatory power as measured by adjusted R2 than the combined
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portfolio.
The main difference between this case and the DT85 case, though, is that the
explanatory power of these models on the loser portfolios is approximately 30% higher in all four models under personal asset management than their DT85 counterparts. V. E. Additional Hedge Fund Expenses As mentioned earlier, an investor who would like to take advantage of the profit potential of this strategy but has neither the time, inclination, nor ability to do so directly through personally managing his own account can invest in a hedge fund that follows a strategy similar to their desired strategy. This investor would then face not only the margin regulations described earlier but also the fees that hedge funds assess. Figure 1b presents a flowchart describing the algorithm used in this simulation and includes the following additional assumptions: Management and performance fees are assessed at the end of each calendar quarter and at the end of the three-year test period (if it does not already fall on the end of a quarter). These fees result in a reduction of the credit balance in the investor's account with the hedge fund. The management fee is one percent of the average daily balance of the assets under management of the investor's account since the previous fee assessment. Assets under management are calculated as the sum of the long holdings and the credit balance of the account after each day's marking-to-market and after any margin call has been resolved. The performance fee is twenty percent of the equity balance above the high watermark. If equity on the fee assessment date is above the high watermark, it becomes the new high watermark.
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No hurdle rate is applied to the high watermark. This will create more fees for the hedge fund to extract and bias the results of the simulation against being profitable for the investor. Table 5 also details the results of following this approach, which averaged 32.54% net of fees over the 217 three-year testing periods (p < 0.0001), ranging from -45.44% to 140.56%. The management fee averaged 8.17% per three-year period, ranging from 4.87% to 10.82%; and the performance fee averaged 9.76% per three-year period, ranging from 0% to 33.75%. Even including the benefits of leverage in these results, the investor in the hedge fund earns significantly less than the pure DT85 return difference (p-value of difference < 0.0001), which is in line with the expectations of H3a. Table 7 provides the results of running the factor regressions on the hedge fund results, including the breakdowns by loser and winner portfolios, and the results are similar to the personal asset management results (the next section will compare these two approaches in further detail).25 In the market model and CAPM model, the (excess) market return factors are 0.0342 (p = 0.0398) and 0.0387 (p = 0.0203), respectively. The market factor is positive and significant in the three-factor and momentum models as well, at 0.1985 and 0.1521. The size (0.4984 and 0.5226) and book-to-market (0.6391 and 0.5976) are positive and significant, and the momentum factor is negative and significant (-0.2006). These results all line up with the expectations of performing these regressions on the DT85 return differences as described in H1b and H1c. The adjusted R2 values for the market and CAPM models are extremely small at 0.04% and 0.06%, while the explanatory power of the three-factor model is 9.48% and that of the momentum model is 11.52%. All four intercepts are positive, at 0.00837, 0.00475, 0.00106, and 0.00320, For the
respectively, with only the three-factor intercept being insignificant (p = 0.1391).
25
Unless stated otherwise, results in this section are also assumed to have p-values < 0.0001. 70
momentum model, the intercept indicates a risk-adjusted return of 3.84% per year, or 11.52% over a three-year period. V. F. Changes in Risk Comparing the momentum regression results of this strategy with that of the DT85 return differences indicates that, in line with the expectations of H2b and H3b, the imposition of institutional constraints does indeed lessen the investor's exposure to the various risk factors analyzed. However, maximizing leverage like the investor in this study brings some of that risk back. Table 8 compares the momentum regression coefficients between the DT85 return
differences and both the levered and unlevered personal asset management and hedge fund approaches. The momentum model was reanalyzed by combining the two results datasets being compared and creating a dummy variable equal to 1 if the observation was from the DT85 return difference and 0 if it was from the personal asset management approach or hedge fund approach (each comparison performed separately). The comparison results are the coefficients for the dummy variable and the four interaction terms between the dummy and the four factors. Focusing on the unlevered results first, notice that applying institutional constraints alone had a significant impact on not only the investor's risk exposures, but also his ability to earn abnormal returns. For the personal asset management approach, exposure to market- and momentumbased risk has been reversed but reduced in absolute value terms (by 86.64% and 55.87%), exposure to size- and book-to-market-based risk has been reduced (23.49% and 50.23%), and risk-adjusted returns have been reduced by 41.67% (from 0.552% per month to 0.322% per month). For the hedge fund approach, the changes in risk are similar: reversals and reductions of market- and momentum-based risk (85.68% and 31.91%) and reductions in size- and book-tomarket-based risk (21.20% and 50.00%) accompanied by the loss of 71.01% of risk-adjusted
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returns (from 0.552% per month to 0.160% per month).
Incorporating leverage, however,
appears to eliminate most of the risk reductions and may have even made the strategy riskier than the pure return differences suggested. Compared to the DT85 return differences, there is no statistical change in either book-to-market-based risk (p-value of changes = 0.9530 for personal asset management and 0.9998 for hedge fund investment) or the ability to extract abnormal returns (p-value of changes = 0.4760 and 0.0561). The exposure to size-based risk increases (53.05% and 57.60%), as does the absolute exposure to momentum-based risk (11.74% and 36.18%). Only the market-based exposure is still reduced, though its reduction (73.26% and 71.38%) is less than in the unlevered situation. Table 8 also compares the results of the momentum model regressions from the personal asset management and hedge fund approaches using the same dummy variable method described above (dummy = 1 for personal asset management and 0 for hedge fund). While none of the changes to the risk factor loadings are statistically significant (p-values of 0.6953, 0.6083, 0.9390, and 0.0861), it is interesting to note that all four factor loadings have greater absolute values when using the hedge fund approach. However, the risk-adjusted return falls significantly when shifting from the personal asset management approach to the hedge fund approach. The unlevered 0.00325 decrease in the intercept indicates the loss of 3.90% risk-adjusted return per year, or 11.70% over three years. V. G. Other Results Two other points that were discussed earlier in this paper were the concept of arbitrage and the January effect. While the results gathered above indicate that the return differences discovered in DT85 have not on average been arbitraged away over the 1986 - 2006 period studied in this paper, the effects may have slowly been arbitraged away. If so, then the positive
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returns found would have been the result of high returns early in the period analyzed that would have declined to some equilibrium level at some point along the way. Figure 2 shows the average monthly return of each of the 217 portfolios. For both the personal asset management and hedge fund approaches, it appears that the average returns rise for approximately the first 67 portfolios (formed January 1986 - July 1991), follow a ?smile? pattern through the next 112 portfolios (August 1991 - November 2000), then decline for the remaining 38 portfolios (December 2000 - January 2004). Figure 3 shows the model regressions on the 217 portfolios. values of performing momentum
For both approaches, while there seems to be
fluctuations up and down for the first 96 portfolios (January 1986 - December 1993) that make it difficult to discern a pattern visually, the values decline on average for the remainder of the
portfolios (January 1994 - January 2004), indicating that the ability of this strategy to provide returns beyond the risk premia for the investor has diminished or possibly even disappeared. Figure 4 shows the average returns in each calendar month for both approaches. This figure clearly indicates there was a January effect during the period analyzed in this study. Returns in January following the personal asset management approach averaged 6.09%, over 2.5 times as much as the next highest month (February, 2.23%); the hedge fund approach was comparable, with a January average of 6.36% compared to February's 2.29%. This does not seem to be the result of tax-loss selling, though, as both the loser and winner portfolios experience positive and significant returns in both November (2.57% and 2.47% for personal asset management, 2.49% and 2.39% for hedge funds, all p < 0.0001) and December (2.08% and 1.39%, 1.91% and 1.27%, all p < 0.0001). Figure 5 presents the values of performing
momentum model regressions on each month (651 observations in each regression). There seems to be a January effect in the intercepts as well, as the value for January (0.03593 for
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personal asset management and 0.03745 for hedge funds) is more than three times the next highest value (February, 0.01148 and 0.01196). This, however, seems to be driven by the loser portfolio (0.03564 and 0.03462 in January), as the portfolios all have absolute values less than 0.01. Finally, since the hedge fund approach did result in positive values, it would be values for each month in the winner
interesting to see if some hedge funds are actually applying this strategy in practice. To look at this, I first took the average monthly return results from the hedge fund simulation for all months in which there were 36 months of simulation results. I then used these averages as independent variables in various factor regressions on HFRI and HFRX indices designed to track the performance of funds that follow equity-based strategies (e.g.: equity market neutral, equity hedge, and equity non-hedge). In none of these regressions was the factor based on the
simulation in this paper significant, whether it was the only factor in the model or whether it was included with the four factors from the momentum model used in earlier analyses. Thus, this study cannot provide evidence that the strategy described herein is actually followed by existing hedge funds. However, this non-result could simply be caused by the use of indices as
dependent variables that incorporate many approaches to equity investment even within the same category, so this also does not provide evidence that there are no hedge funds that follow this strategy.
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VI. Conclusion and Directions for Future Research This study revisited the overreaction hypothesis studied by DeBondt and Thaler (1985). In their original paper, they found that stocks that performed the poorest over the previous three years could outperform stocks that performed the best over the previous three years by an average of 24.6%, as measured by subsequent three-year cumulative abnormal returns. While subsequent studies debated the source of this return differential, Fama and French (1996) seemed to be able to account for this (and other anomalies) using risk factor analysis, resulting in little subsequent research that directly focused on the findings of DT85. However, by using a
different sampling technique (sorting stocks by deciles) than DT85 used (top/bottom 35 stocks), Fama and French (1996) did not fully explain if those same risk factors are the source of the return differential among the most extreme prior performers. As such, this paper replicated the DT85 study by forming portfolios following their method with starting months from January 1986 through January 2004. Using the same filters as DT85, the prior losers only outperformed the prior winners by 0.02% over the subsequent three years, indicating that whatever results DT85 found, they did not exist any longer. However, DT85 only observed NYSE stocks. The inclusion of AMEX and NASDAQ stocks resulted in a cumulative abnormal return differential of 28.60%; this difference increased to 34.85% when the requirement of preexisting data was reduced from seven years to five years. Qualitatively similar results were found when the analysis shifted from looking at cumulative abnormal returns to looking at buy-and-hold returns. The buy-and-hold returns were then analyzed to determine if, in the spirit of Fama and French (1996), the return differences can be accounted for by differences in risk. While it was found that all six buy-and-hold return results faced significant exposure to market, size, book-to-
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market, and momentum-based risk, the explanatory power of models incorporating these factors was relatively low (maximum 13.82%), and there still existed significant risk-adjusted returns as determined by the intercept of the regressions (maximum when all four factors are included was 0.824% per month). Additionally, while the factor regressions on the positive return differences (those that included AMEX and NASDAQ stocks) yielded the expected results for the size and book-to-market factor loadings, the momentum factor loading was positive, indicating a tendency towards return continuation instead of reversal. Breaking down the factor analysis to be run on the two sets of stocks (losers and winners) separately showed that both losers and winners experienced reversals in their returns, as indicated by significant negative momentum factor loadings, and that these reversals are stronger in the winners than the losers. These results provide the justification for determining whether a private investor could earn positive risk-adjusted returns by following a contrarian strategy based on the DT85 loser/winner portfolio selection criteria. The simulations performed in this study indicate that there are profits available to those investors willing to pursue this strategy. The investor willing to manage his own account and maximize his leverage within the legal limits established by Regulation T could earn an average 51.44% return over a three-year period, with only 28.22% being compensation for risk and the other 23.22% considered abnormal return. The investor who, on the other hand, invests in a hypothetical hedge fund following this strategy because he could not or desires not to follow this strategy on his own would earn an average 32.54% return over a three-year period, with only 21.02% being compensation for risk and the other 11.52% considered abnormal return while compensating the hedge fund manager with 17.92% of the initial investment in the form of management and performance fees. While the institutional constraints in place designed to protect investors who engage in the type of short selling required
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to implement this strategy succeed in reducing the investor's general exposure to various risk factors, the legal use of maximum leverage actually eliminates most of the risk-reducing benefits of these constraints without providing compensation in the form of additional returns (either on a raw or risk-adjusted basis). Additional analyses indicate that the effects discovered by DT85 have not been arbitraged away over time and that there appears to be a January effect that is not the result of tax-loss selling that may be impacting the results. The average monthly returns to following this strategy only began to steadily decline during the last few years analyzed, approximately fifteen years after DT85 was published. Average returns in January are over 2.5 times as much as the returns in any other month, and November and December returns do not show declines that would indicate investors are selling poor performers to realize losses. Finally, there is no indication from any results in this study of the extent to which this strategy is followed in practice. One acknowledged area for improvement in this simulation is the manner in which the investor manages his account. This investor (or hedge fund manager) makes his investment decision once at the formation of the portfolio and then does not take any other action to change the relative positions within his long and short portfolios. A more active investor may be able to make decisions regarding his margin calls in order to offset some losses that the less active investor would face. For example, an active investor may decide to close out some of his short position when he expects a margin call instead of selling off some of his long position, as the broker does for the investor in this analysis, if he believes that some stocks he is holding short will make large gains in the future. More simply, instead of selling off owned stocks on a proportional basis, the active investor would be able to pick and choose which stocks to sell off (or cover) to avoid a margin call. Also, the costs of engaging in various purchases and sales
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were not incorporated in this study. By making all transactions at the relevant open or close prices, transactions costs were ignored. Once the simulation is updated to allow the
selling/closure of specific positions when a margin call is received, a simple way to incorporate transaction costs would be to make all purchases at the ask price and all sales at the bid price as reported in the database on the date of each transaction. This would also expand the population of securities available for investment, as it would then account for much of the costs of buying and selling thinly-traded stocks, which was the motivation for filtering out low-priced and highspread securities on the portfolio formation date. On a different path, running this simulation on an expanded parameter set should create a more robust set of results to analyze (e.g.: different hurdle rates to set the high watermark and different interest rates on margin debt).
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85
Table 1: Cumulative Abnormal Return Differentials The following table provides information on the 36-month average cumulative abnormal returns (ACAR) of the loser and winner portfolios and the amount by which ACARL exceeded ACARW under two sets of parameters: exchanges allowed and years of data prior to the formation date required. In all cases, n = 217 36-month testing period returns; p-values of mean returns are in parentheses.
Exchanges NYSE 5 Formation Years Return DACAR ACARL ACARW DACAR ACARL ACARW DACAR ACARL ACARW DACAR ACARL ACARW DACAR ACARL ACARW DACAR ACARL ACARW Mean -1.23% (0.6552) -5.68% (0.0734) -4.45% (0.0027) 0.02% (0.9932) -3.57% (0.2266) -3.59% (0.0165) 34.85% (<0.0001) 23.75% (<0.0001) -11.10% (<0.0001) 28.60% (<0.0001) 17.22% (<0.0001) -11.38% (<0.0001) 45.06% (<0.0001) 32.82% (<0.0001) -12.24% (<0.0001) 38.49% (<0.0001) 28.21% (<0.0001) -10.29% (<0.0001) Minimum -82.06% -92.40% -69.97% -83.51% -88.09% -57.96% -64.01% -69.06% -77.95% -56.77% -84.38% -98.18% -48.89% -58.67% -88.91% -46.13% -82.86% -97.29% Maximum 159.75% 163.48% 53.75% 121.83% 127.10% 57.14% 223.92% 205.27% 63.89% 259.92% 221.94% 60.17% 292.44% 255.41% 69.06% 254.86% 207.74% 66.66%
7
NYSE/AMEX/ NASDAQ
5
7
AMEX/NASDAQ
5
7
86
Table 2: Buy-and-Hold Return Differentials The following table provides information on the amount by which the 36-month return on a portfolio of prior losers exceeded the 36-month return on a portfolio of prior winners under two sets of parameters: exchanges allowed and years of data prior to the formation date required. In all cases, n = 217 36-month testing period returns; p-values of mean returns are in parentheses.
Exchanges NYSE NYSE/AMEX/NASDAQ AMEX/NASDAQ Formation Years 5 7 5 7 5 7 Mean -4.87% (0.1439) -1.75% (0.5931) 48.11% (<0.0001) 37.93% (<0.0001) 66.54% (<0.0001) 56.99% (<0.0001) Minimum -90.43% -84.21% -40.17% -83.68% -41.27% -69.41% Maximum 321.80% 260.47% 654.33% 371.48% 662.33% 532.02%
87
Table 3: Regression Results on Buy-and-Hold Return Differentials The following table provides the regression coefficients from analyzing the returns described in Table 2: market risk factor loading, = the size factor loading, = the book-to-market factor loading, and loading. In all cases, n = 7,812 monthly returns; p-values of regression coefficients are in parentheses.
Exchanges NYSE Formation Years 5 (mkt model) 0.00343 (0.0003) -0.00175 (0.0592) 0.00538 (<0.0001 )0.00378 (<0.0001 ) 0.00323 (0.0001) 0.00175 (0.0345) 0.00499 (<0.0001 )0.00423 (<0.0001 ) 0.01681 (<0.0001) 0.01036 (<0.0001) 0.00709 (<0.0001) 0.00552 (<0.0001) 0.01407 (<0.0001) 0.00800 (<0.0001) 0.00438 (<0.0001) 0.00372 (0.0006) -0.3845 (<0.0001) -0.3789 (<0.0001) -0.2641 (<0.0001) -0.2986 (<0.0001) -0.3289 (<0.0001) -0.3221 (<0.0001) -0.2171 (<0.0001) -0.2337 (<0.0001) -0.7261 (<0.0001) -0.7222 (<0.0001) -0.5654 (<0.0001) -0.5314 (<0.0001) -0.6244 (<0.0001) -0.6195 (<0.0001) -0.4364 (<0.0001) -0.4221 (<0.0001) 0.3305 (<0.0001) 0.3230 (<0.0001) 0.6289 (<0.0001) 0.6418 (<0.0001) 0.3494 (<0.0001) 0.3316 (<0.0001) 0.5670 (<0.0001) 0.5976 (<0.0001) 0.6499 (<0.0001) 0.6586 (<0.0001) 0.5584 (<0.0001) 0.5434 (<0.0001) 0.7419 (<0.0001) 0.7599 (<0.0001) 0.6241 (<0.0001) 0.5931 (<0.0001) (other models)
= the intercept, = the = the momentum factor
Adj. R2 4.07% 3.95% 13.16% -0.1495 (<0.0001) 13.82% 3.78% 3.61% 12.61% -0.0719 (<0.0001) 12.81% 10.36% 10.24% 12.89% 0.1473 (<0.0001) 13.35% 8.12% 7.98% 11.20% 0.0620 (0.0059) 11.29%
7
NYSE/AMEX/ NASDAQ
5
7
88
Exchanges AMEX/NASDAQ
Formation Years 5
(mkt model) 0.01835 (<0.0001) 0.01239 (<0.0001) 0.00986 (<0.0001) 0.00824 (<0.0001) 0.01570 (<0.0001) 0.01005 (<0.0001) 0.00727 (<0.0001) 0.00720 (<0.0001) -0.5940 (<0.0001)
(other models)
Adj. R2 7.73%
-0.5895 (<0.0001) -0.4705 (<0.0001) -0.4355 (<0.0001) -0.5105 (<0.0001) -0.5052 (<0.0001) -0.3676 (<0.0001) -0.3650 (<0.0001)
7.60% 0.2838 (<0.0001) 0.2655 (<0.0001) 0.4384 (<0.0001) 0.4698 (<0.0001) 9.42% 0.1517 (<0.0001) 9.96% 6.19% 6.05% 0.2712 (<0.0001) 0.2698 (<0.0001) 0.4824 (<0.0001) 0.4847 (<0.0001) 8.27% 0.0110 (0.6061) 8.27%
7
89
Table 4: Regression Results on Buy-and-Hold Return Differentials and Loser and Winner Portfolios The following tables expand the results explained in Table 3 by running the loser and winner portfolios that formed the differences through the same regressions: = the intercept, = the market risk factor loading, = the size factor loading, = the book-to-market factor loading, and = the momentum factor loading. In all cases, n = 7,812 monthly returns; p-values of regression coefficients are in parentheses.
90
Table 4a: NYSE Stocks
Formation Years 5 Portfolio Difference Loser Winner Difference Loser Winner Difference Loser Winner Difference Loser Winner 7 Difference Loser Winner Difference Loser Winner Difference Loser Winner Difference Loser Winner 0.00343 (0.0003) 0.00113 (0.2230) -0.00230 (<0.0001 )0.00175 (0.0592) 0.00007 (0.9471) -0.00191 (<0.0001) -0.00538 (<0.0001) -0.00501 (<0.0001) -0.00343 (<0.0001) -0.00378 (<0.0001) -0.00121 (0.1520) 0.00120 (0.0004) 0.00323 (0.0001) 0.00136 (0.0942) 0.00187 (<0.0001) -0.00175 (0.0345) 0.00042 (0.6008) 0.00155 (<0.0001) -0.00499 (<0.0001) -0.00427 (<0.0001) -0.00307 (<0.0001) -0.00423 (<0.0001) -0.00135 (0.0680) 0.00089 (0.0067) (mkt model) -0.3845 (<0.0001) 0.7240 (<0.0001) 1.1085 (<0.0001) (other models) Adj. R2 4.07% 13.45% 70.58% -0.3789 (<0.0001) 0.7311 (<0.0001) 1.1108 (<0.0001) -0.2641 (<0.0001) 0.8946 (<0.0001) 1.1619 (<0.0001) -0.2986 (<0.0001) 0.8121 (<0.0001) 1.1134 (<0.0001) -0.3289 (<0.0001) 0.7600 (<0.0001) 1.0889 (<0.0001) -0.3221 (<0.0001) 0.7682 (<0.0001) 1.0911 (<0.0001) -0.2171 (<0.0001) 0.9229 (<0.0001) 1.1432 (<0.0001) -0.2337 (<0.0001) 0.8595 (<0.0001) 1.0960 (<0.0001) 3.95% 13.67% 70.69% 0.7419 (<0.0001) 1.0236 (<0.0001) 0.2931 (<0.0001) 0.7599 (<0.0001) 1.0667 (<0.0001) 0.3184 (<0.0001) 0.6241 (<0.0001) 0.8745 (<0.0001) 0.2617 (<0.0001) 0.5931 (<0.0001) 0.8005 (<0.0001) 0.2193 (<0.0001) 13.16% 30.06% 73.76% -0.1495 (<0.0001) -0.3569 (<0.0001) -0.2094 (<0.0001) 13.82% 33.58% 76.47% 3.78% 18.18% 70.67% 3.61% 18.49% 70.77% 0.6499 (<0.0001) 0.9239 (<0.0001) 0.2854 (<0.0001) 0.6586 (<0.0001) 0.9570 (<0.0001) 0.3100 (<0.0001) 0.5584 (<0.0001) 0.8081 (<0.0001) 0.2611 (<0.0001) 0.5434 (<0.0001) 0.7514 (<0.0001) 0.2189 (<0.0001) 12.61% 35.02% 73.83% -0.0719 (<0.0001) -0.2738 (<0.0001) -0.2039 (<0.0001) 12.81% 37.55% 76.50%
91
Table 4b: NYSE/AMEX/NASDAQ Stocks
Formation Years 5 Portfolio Difference Loser Winner Difference Loser Winner Difference Loser Winner Difference Loser Winner 7 Difference Loser Winner Difference Loser Winner Difference Loser Winner Difference Loser Winner 0.01681 (<0.0001) 0.01010 (<0.0001) -0.00671 (<0.0001) 0.01036 (<0.0001) 0.00874 (<0.0001) -0.00535 (<0.0001) 0.00709 (<0.0001) 0.00719 (<0.0001) -0.00369 (<0.0001) 0.00552 (<0.0001) 0.00989 (<0.0001) 0.00060 (0.2393) 0.01407 (<0.0001) 0.00814 (<0.0001) -0.00593 (<0.0001) 0.00800 (<0.0001) 0.00683 (<0.0001) -0.00489 (<0.0001) 0.00438 (<0.0001) 0.00427 (<0.0001) -0.00390 (<0.0001) 0.00372 (0.0006) 0.00753 (<0.0001) 0.00005 (0.9230) (mkt model) -0.7261 (<0.0001) 0.6431 (<0.0001) 1.3692 (<0.0001) (other models) Adj. R2 10.36% 8.59% 54.10% -0.7222 (<0.0001) 0.6490 (<0.0001) 1.3720 (<0.0001) -0.5654 (<0.0001) 0.5769 (<0.0001) 1.1456 (<0.0001) -0.5314 (<0.0001) 0.5184 (<0.0001) 1.0525 (<0.0001) -0.6244 (<0.0001) 0.6575 (<0.0001) 1.2819 (<0.0001) -0.6195 (<0.0001) 0.6640 (<0.0001) 1.2843 (<0.0001) -0.4364 (<0.0001) 0.6655 (<0.0001) 1.1052 (<0.0001) -0.4221 (<0.0001) 0.5949 (<0.0001) 1.0197 (<0.0001) 10.24% 8.73% 54.23% 0.3494 (<0.0001) 1.0441 (<0.0001) 0.7060 (<0.0001) 0.3316 (<0.0001) 1.0746 (<0.0001) 0.7546 (<0.0001) 0.5670 (<0.0001) 0.2565 (<0.0001) -0.2992 (<0.0001) 0.5976 (<0.0001) 0.2040 (<0.0001) -0.3826 (<0.0001) 12.89% 21.84% 67.39% 0.1473 (<0.0001) -0.2531 (<0.0001) -0.4025 (<0.0001) 13.35% 23.28% 72.43% 8.12% 9.05% 54.68% 7.98% 9.21% 54.80% 0.3305 (<0.0001) 1.0024 (<0.0001) 0.6833 (<0.0001) 0.3230 (<0.0001) 1.0393 (<0.0001) 0.7279 (<0.0001) 0.6289 (<0.0001) 0.4344 (<0.0001) -0.1831 (<0.0001) 0.6418 (<0.0001) 0.3711 (<0.0001) -0.2598 (<0.0001) 11.20% 20.88% 67.27% 0.0620 (0.0059) 0.3057 (<0.0001) -0.3697 (<0.0001) 11.29% 22.98% 72.17%
92
Table 4c: AMEX/NASDAQ Stocks
Formation Years 5 Portfolio Difference Loser Winner Difference Loser Winner Difference Loser Winner Difference Loser Winner 7 Difference Loser Winner Difference Loser Winner Difference Loser Winner Difference Loser Winner 0.01835 (<0.0001) 0.01206 (<0.0001) -0.00629 (<0.0001) 0.01239 (<0.0001) 0.01090 (<0.0001) -0.00521 (<0.0001) 0.00986 (<0.0001) 0.01025 (<0.0001) -0.00340 (<0.0001) 0.00824 (<0.0001) 0.01273 (<0.0001) 0.00072 (0.1583) 0.01570 (<0.0001) 0.01071 (<0.0001) -0.00499 (<0.0001) 0.01005 (<0.0001) 0.00958 (<0.0001) -0.00420 (<0.0001) 0.00727 (<0.0001) 0.00813 (<0.0001) -0.00293 (<0.0001) 0.00720 (<0.0001) 0.01148 (<0.0001) 0.00056 (0.2476) (mkt model) -0.5940 (<0.0001) 0.7006 (<0.0001) 1.2946 (<0.0001) (other models) Adj. R2 7.73% 10.51% 51.28% -0.5895 (<0.0001) 0.7073 (<0.0001) 1.2976 (<0.0001) -0.4705 (<0.0001) 0.5873 (<0.0001) 1.0611 (<0.0001) -0.4355 (<0.0001) 0.5335 (<0.0001) 0.9717 (<0.0001) -0.5105 (<0.0001) 0.7068 (<0.0001) 1.2172 (<0.0001) -0.5052 (<0.0001) 0.7134 (<0.0001) 1.2200 (<0.0001) -0.3676 (<0.0001) 0.6508 (<0.0001) 1.0216 (<0.0001) -0.3650 (<0.0001) 0.5783 (<0.0001) 0.9461 (<0.0001) 7.60% 10.68% 51.43% 0.2838 (<0.0001) 0.9799 (<0.0001) 0.7075 (<0.0001) 0.2655 (<0.0001) 1.0080 (<0.0001) 0.7542 (<0.0001) 0.4384 (<0.0001) 0.1015 (0.0043) 0.3255 (<0.0001) 0.4698 (<0.0001) 0.0532 (0.1341) 0.4057 (<0.0001) 9.42% 23.38% 65.88% 0.1517 (<0.0001) -0.2328 (<0.0001) -0.3866 (<0.0001) 9.96% 24.63% 70.81% 6.19% 11.07% 51.89% 6.05% 11.26% 52.02% 0.2712 (<0.0001) 0.9506 (<0.0001) 0.6909 (<0.0001) 0.2698 (<0.0001) 0.9885 (<0.0001) 0.7303 (<0.0001) 0.4824 (<0.0001) 0.2401 (<0.0001) -0.2310 (<0.0001) 0.4847 (<0.0001) 0.1750 (<0.0001) -0.2987 (<0.0001) 8.27% 22.84% 66.19% 0.0110 (0.6061) 0.3137 (<0.0001) -0.3268 (<0.0001) 8.27% 25.18% 70.22%
93
Table 5: Comparison of 36-Month Testing Period Returns This table presents the returns that would be expected by an investor following the personal asset management and hedge fund approaches to following the DT85-based strategy allowing all exchanges and requiring five years of prior data and compares them with each other and with the DT85 return differences detailed in Table 2. In all cases, n = 217 36-month testing period returns; p-values of mean returns and of comparisons are in parentheses.
Approach (<0.0001) Personal Asset Management (Unlevered) Hedge Fund, net of fees (Unlevered) Management Fees Performance Fees Comparison DT85 - Pers. Asset Mgmt. DT85 - Pers. Asset Mgmt. (Unlevered) DT85 - Hedge Fund DT85 - Hedge Fund (Unlevered) Pers. Asset Mgmt. - Hedge Fund Pers. Asset Mgmt. - Hedge Fund (Both Unlevered) Mean Minimum -40.17% 51.44% (<0.0001) 25.72% (<0.0001) 32.54% (<0.0001) 16.27% (<0.0001) 8.17% (<0.0001) 9.76% (<0.0001) Mean -3.33% (0.4934) 22.39% (<0.0001) 15.57% (0.0011) 31.84% (<0.0001) 18.90% (<0.0001) 9.45% (<0.0001) Maximum DT85 654.33% -40.83% -20.42% -45.44% -22.72% 4.87% 0.00% 48.11% 187.36% 93.68% 140.56% 70 .28 % 10.82% 33.75% Maximum 563.21% 608.77% 588.63% 621.48% 4 7 .10 %23 .55%
Minimum -198.54% -116.58% 161.91% -99.96% 4.60% 2.30%
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Table 6: Regression Results on Personal Asset Management Returns and Loser and Winner Portfolios The following table provides the regression coefficients from analyzing the returns from following the personal asset management approach: = the intercept, = the market risk factor loading, = the size factor loading, = the book-to-market factor loading, and = the momentum factor loading. Loser and winner portfolios were run through the same regressions. In all cases, n = 7,812 monthly returns; p-values of regression coefficients are in parentheses.
(mkt Portfolio Total Loser Winner Total Loser Winner Total Loser Winner Total Loser Winner 0.01201 (<0.0001) 0.00727 (<0.0001) -0.00524 (<0.0001) 0.00832 (<0.0001) 0.00760 (<0.0001) -0.00418 (<0.0001) 0.00469 (<0.0001) 0.00460 (<0.0001) -0.00381 (<0.0001) 0.00645 (<0.0001) 0.00787 (<0.0001) -0.00038 (0.4404) 0.0181 (0.2599) 1.0987 (<0.0001) 1.2911 (<0.0001) 0.0224 (0.1629) 1.1042 (<0.0001) 1.2937 (<0.0001) 0.1801 (<0.0001) 1.1441 (<0.0001) 1.1678 (<0.0001) 0.1421 (<0.0001) 1.0733 (<0.0001) 1.0935 (<0.0001) (other Adj. R2 model) models) 0.02% 42.58% 57.09% 0 .02 % 42.84% 57.22% 0.4877 (<0.0001) 0.9468 (<0.0001) 0.6104 (<0.0001) 0.5075 (<0.0001) 0.9838 (<0.0001) 0.6492 (<0.0001) 0.6289 (<0.0001) 0.5126 (<0.0001) -0.0728 (0.0001) 0.5948 (<0.0001) 0.4491 (<0.0001) -0.1394 (<0.0001) 9.80% 60.35% 66.34% -0.1646 (<0.0001) -0.3063 (<0.0001) -0.3214 (<0.0001) 11.25% 63.91% 70.15%
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Table 7: Regression Results on Hedge Fund Investment Returns and Loser and Winner Portfolios The following table provides the regression coefficients from analyzing the returns from following the hedge fund investment approach: = the intercept, = the market risk factor loading, = the size factor loading, = the book-to-market factor loading, and = the momentum factor loading. Loser and winner portfolios were run through the same regressions. In all cases, n = 7,812 monthly returns; p-values of regression coefficients are in parentheses.
(mkt Portfolio Total Loser Winner Total Loser Winner Total Loser Winner Total Loser Winner 0.00837 (<0.0001) 0.00637 (<0.0001) -0.00615 (<0.0001) 0.00475 (<0.0001) 0.00667 (<0.0001) -0.00511 (<0.0001) 0.00106 (0.1391) 0.00362 (<0.0001) -0.00476 (<0.0001) 0.00320 (<0.0001) 0.00695 (<0.0001) -0.00128 (0.0099) 0.0342 (0.0398) 1.0877 (<0.0001) 1.2824 (<0.0001) 0.0387 (0.0203) 1.0931 (<0.0001) 1.2851 (<0.0001) 0.1985 (<0.0001) 1.1371 (<0.0001) 1.1606 (<0.0001) 0.1521 (<0.0001) 1.0649 (<0.0001) 1.0853 (<0.0001) (other Adj. R2 model) models) 0.04% 41.13% 56.11% 0.06% 41.39% 56.25% 0.4984 (<0.0001) 0.9417 (<0.0001) 0.6078 (<0.0001) 0.5226 (<0.0001) 0.9794 (<0.0001) 0.6471 (<0.0001) 0.6391 (<0.0001) 0.5212 (<0.0001) -0.0701 (0.0002) 0.5976 (<0.0001) 0.4564 (<0.0001) -0.1376 (<0.0001) 9.48% 58.48% 65.22% -0.2006 (<0.0001) -0.3123 (<0.0001) -0.3255 (<0.0001) 11.52% 62.12% 69.11%
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Table 8: Momentum Regression Results for All Approaches The following table compares the regression coefficients from analyzing the returns from following the three approaches studies in this paper: = the intercept, = the market risk factor loading, = the size factor loading, = the book-to-market factor loading, and = the momentum factor loading. In all cases, n = 7,812 monthly returns for strategy regressions and 15,632 for comparative regressions; p-values of regression coefficients are in parentheses.
Portfolio DT85 Personal Asset Management (Unlevered) Personal Asset Management Hedge Fund (Unlevered) Hedge Fund Comparison DT85 - P.A.M. (Unlevered) DT85 - P.A.M. DT85 - H.F. (Unlevered) DT85 - H.F. P.A.M. - H.F. (Both Unlevered) P.A.M. - H.F. 0.00552 (<0.0001) 0.00322 (<0.0001) 0.00645 (<0.0001) 0.00160 (<0.0001) 0.00320 (<0.0001) 0.00230 (<0.0001) -0.00093 (0.4760) 0.00392 (<0.0001) 0.00232 (0.0561) 0.00163 (0.0012) 0.00325 (<0.0001) -0.5314 (<0.0001) 0.0710 (<0.0001) 0.1421 (<0.0001) 0.0761 (<0.0001) 0.1521 (<0.0001) -0.6024 (<0.0001) -0.6735 (<0.0001) -0.6074 (<0.0001) -0.6835 (<0.0001) -0.0050 (0.6953) -0.0100 (0.6953) 0.3316 (<0.0001) 0.2538 (<0.0001) 0.5075 (<0.0001) 0.2613 (<0.0001) 0.5226 (<0.0001) 0.0779 (0.0206) -0.1759 (<0.0001) 0.0703 (0.0145) -0.1910 (<0.0001) -0.0075 (0.6083) -0.0151 (0.6083) 0.5976 (<0.0001) 0.2974 (<0.0001) 0.5948 (<0.0001) 0.2988 (<0.0001) 0.5976 (<0.0001) 0.3002 (<0.0001) 0.0028 (0.9530) 0.2988 (<0.0001) 0.0000 (0.9998) -0.0014 (0.9390) -0.0028 (0.9390) 0.1473 (<0.0001) -0.0823 (<0.0001) -0.1646 (<0.0001) -0.1003 (<0.0001) -0.2006 (<0.0001) 0.2296 (<0.0001) 0.3119 (<0.0001) 0.2476 (<0.0001) 0.3479 (<0.0001) 0.0180 (0.0861) 0.0360 (0.0861)
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Figure 1a: Personal Asset Management Simulation Flowchart
Determine stocks to include in wi n n e r a n d l o se r portfolios
Ma r k l o n g a n d short positions to ma r k e t a t e n d o f day
Adjust credit balance for d i vi d e n d s r e ce i ve d and/or paid
Accrue interest to cr e d i t a n d d e b i t balances
Will LMV fall below SMV if it is only account changed?
No
Re d u c e L MV by shortfall/ 0.30
Yes
Yes
Calculate maintenance margin requirement
Is equity> requirement?
No
Is LMV > SMV?
Reduce both LMV and SMV to EQ/ 0.65
Adjust debit and cr e d i t b a l a n ce s a ccord ing ly
Yes
No
Yes
No Go to next day Is this the last day of the three-year test period?
Will SMV fall below L MV i f i t i s o n l y a c c o u n t changed? No
Reduce SMV by shortfall/ 0.35
Yes
End simulation
98
Figure 1b: Hedge Fund Simulation Flowchart
Determine stocks to include in wi n n e r a n d l o se r portfolios
Ma r k l o n g a n d short positions to ma r k e t a t e n d o f day
Adjust credit balance for d i vi d e n d s r e ce i ve d and/or paid
Accrue interest to cr e d i t a n d d e b i t b a lances
Will LMV fall below SMV if it is only account cha nge d?
No
Re d u c e L MV by shortfall/ 0.30
Yes
Yes
Calculate maintenance mar gin r eq ui reme nt
Is equity> requirement?
No
Is LMV > SMV?
Reduce both LMV and SMV to EQ/ 0.65
Adjust debit and cr e d i t b a l a n ce s a ccord ing ly
Go to next day
Yes
No
Yes
No No Is this the last day of the three-year test p eri od? Yes End simulation Yes No Assess hedge fund fees Is this the last day of the three-year test p eri od? Assess hedge fund fees Yes Is this the last day of a quarter? Will SMV fall below L MV i f i t i s o n l y a c c o u n t cha nge d? Reduce SMV by shortfall/ 0.35
No
99
Figure 2: Average Monthly Returns for Each 36-Month Testing Period
3.5%
3.0%
2.5%
2.0%
1.5%
1.0%
0.5%
0.0%
Jan 1986
Jan 1987
Jan 1988
Jan 1989
Jan 1990
Jan 1991
Jan 1992
Jan 1993
Jan 1994
Jan 1995
Jan 1996
Jan 1997
Jan 1998
Jan 1999
Jan 2000
Jan 2001
Jan 2002
Jan 2003
-0.5%
-1.0%
-1.5%
-2.0%
Formation Month Personal Asset Management Hedge Fund
100
Jan 2004
Figure 3: Momentum Model Intercepts for Each 36-Month Testing Period
3.5%
3.0%
2.5%
2.0%
1.5%
1.0%
0.5%
0.0%
Jan 1986
Jan 1987
Jan 1988
Jan 1989
Jan 1990
Jan 1991
Jan 1992
Jan 1993
Jan 1994
Jan 1995
Jan 1996
Jan 1997
Jan 1998
Jan 1999
Jan 2000
Jan 2001
Jan 2002
Jan 2003
-0.5%
-1.0%
-1.5%
-2.0%
-2.5% Formation Month Personal Asset Management Hedge Fund
101
Jan 2004
Figure 4: Average Monthly Returns for Each Calendar Month
6.5% 6.0% 5.5% 5.0% 4.5% 4.0% 3.5% 3.0% 2.5% 2.0% 1.5% 1.0% 0.5% 0.0% January -0.5% -1.0% -1.5% -2.0% Personal Asset Management Hedge Fund February March April May June July August September October November December
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Figure 5: Momentum Model Intercepts for Each Calendar Month
4.0%
3.5%
3.0%
2.5%
2.0%
1.5%
1.0%
0.5%
0.0% January -0.5% February March April May June July August September October November December
-1.0% Personal Asset Management Hedge Fund
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