Description
The purpose of this paper is to examine the efficacy of recent policy initiatives taken by
the US Securities and Exchange Commission banning naked “short-selling” of specific financial stocks.
The paper also considers the merits of reinstating “uptick rule” 10a-1, which prohibits short-selling
securities on a downtick.
Journal of Financial Economic Policy
Regulating noisy short-selling of troubled firms?
Carlos A. Ulibarri Ionut Florescu J oel M. Eidsath
Article information:
To cite this document:
Carlos A. Ulibarri Ionut Florescu J oel M. Eidsath, (2009),"Regulating noisy short-selling of troubled firms?",
J ournal of Financial Economic Policy, Vol. 1 Iss 3 pp. 227 - 245
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Regulating noisy short-selling
of troubled ?rms?
Carlos A. Ulibarri
Department of Management, New Mexico Institute of Mining and Technology,
Socorro, New Mexico, USA
Ionut Florescu
Department of Mathematical Sciences, Stevens Institute of Technology,
Hoboken, New Jersey, USA, and
Joel M. Eidsath
Department of Management, New Mexico Institute of Mining and Technology,
Socorro, New Mexico, USA
Abstract
Purpose – The purpose of this paper is to examine the ef?cacy of recent policy initiatives taken by
the US Securities and Exchange Commission banning naked “short-selling” of speci?c ?nancial stocks.
The paper also considers the merits of reinstating “uptick rule” 10a-1, which prohibits short-selling
securities on a downtick.
Design/methodology/approach – The paper studies theoretical implications of short-selling in a
simple state-claim model, re?ecting varying amounts of short interest in a representative ?rm and
noise trading in the market. Price discovery depends on the proportion of noise trading compared to
rational short-selling. The empirical analysis focuses on price volatility under short-selling constraints
employing simple regressions, EGARCH analysis and simulated price behavior under a hypothetical
uptick rule.
Findings – The EGARCH results suggest short-selling constraints had non-uniform impacts on the
persistence and leverage effects associated with price volatility. The corresponding price simulations
indicate a hypothetical uptick rule might have helped stabilize price behavior in some cases, depending
on the nature of the stochastic process and whether or not quantity constraints on short-selling are
binding.
Originality/value – The theoretical arguments and empirical ?ndings suggest a “focused approach”
to market regulation would be a more ef?cient means of discouraging trend chasing without
compromising “informed trading” – that is to say, safeguarding price discovery and market liquidity
without impeding arbitrage or confounding probability beliefs regarding ?rm survival. These
conclusions are largely in accord with recent policy analysis and proposals outlined in Avgouleas.
Keywords Selling, Financial markets, Securities markets, United States of America
Paper type Research paper
1. Introduction
Short-sellers participate in ?nancial markets by ?rst borrowing and then selling
securities. The aim is to repurchase the security at a lower price in the near future,
thereby making a pro?t if the asset’s price decreases between the time of sale and
purchase. Thus, regulatory constraints on short-selling transactions can take various
forms. Of present concern are strict prohibitions that ban short-sales’ altogether
The current issue and full text archive of this journal is available at
www.emeraldinsight.com/1757-6385.htm
JEL classi?cation – G-13, G-14, G15
Regulating noisy
short-selling of
troubled ?rms?
227
Journal of Financial Economic Policy
Vol. 1 No. 3, 2009
pp. 227-245
qEmerald Group Publishing Limited
1757-6385
DOI 10.1108/17576380911041719
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(sales constraints), and conditional prohibitions that rule-out short-selling in situations
where price declines are persistent (price constraints). We treat these two types of
regulation as heuristic representations of the recent ban on short-sales and the potential
tick-test governing short-selling, i.e. rule 10a-1 which prohibits short-selling of a
security in a “down” market[1].
Clearly, short-selling stocks can have adverse impacts on the valuation of troubled
?rms, and perhaps even the likelihood of their survival. However, the implications of
regulating short-selling remain open to question in situations where rational and
non-rational agents take “short interest” positions in troubled ?rms (as measured by the
total amount of shares sold short and yet to be repurchased to close out the positions).
Presumably, high levels of short interest re?ect beliefs that share values will fall
further. The extent to which these beliefs re?ect fundamental information is a matter of
present concern.
Theoretical analysis of short-sales constraints begins with Miller’s (1977)
stock-pricing hypothesis and extensions by Harrison and Kreps (1978), Jarrow (1980),
Diamond and Verrecchia (1987), Allen et al. (1993), Morris (1996) and Hong and Stein
(2002). This literature considers how constraints on short-selling affect the propensity
to trade and the ability for prices to adjust to good or bad news (O’Hara, 1994). If agents
are free to short-sell a stock, then the stock’s price will tend to re?ect relatively
pessimistic beliefs of the ?rms’ prospects (Diamond and Verrecchia, 1987)[2]. This begs
the following questions:
.
Are short-sellers acting as rational agents?
.
Are the policy implications of imposing a moratorium on short-selling
substantively different from imposing conditional price restrictions?
Short-sellers may include passive investors, arbitragers, and noise-traders. Collectively,
these agents share common (pessimistic) beliefs regarding the ?rms’ future prospects.
These beliefs are rational to the extent they re?ect available information concerning
fundamental valuations; that is, the net present value of future cash ?ows,
appropriately discounted for risk considerations. On the contrary, non-rational
valuations are based on some less exacting basis. For example, non-rational agents may
apply trading strategies that are independent or correlated, such as “reading tea leafs”
or “trading with the crowd.” In either case, the asset price may still approximate
fundamental value as reviewed in Shleifer (2000).
First, non-rational trading strategies that are independent could cancel-out,
permitting rational investors to determine a price consistent with fundamental value.
Second, non-rational trading strategies that are correlated tend to create pro?table
investment opportunities. In this case, it has been famously argued that market-clearing
prices remain ef?cient signals of fundamental value so long as rational agents take
positions against-the-crowd and hold these positions for suf?ciently long periods of
time (Freidman, 1953; Fama, 1965). Non-rational traders who persist in selling the
underpriced security eventually lose money to better-informed traders, along with their
in?uence over price.
The present paper considers regulatory policy governing short-selling when noise
trading is persistent. Policy implications are drawn from a simple state-claim model
re?ecting varying amounts of short interest in the ?rm and noise trading in the stock
market. The study maintains noise traders are key in applying market regulations
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since these agents increasingly sell a troubled asset the lower its price becomes,
motivating “smart money to chase dumb money.” In particular, if rational agents
(arbitrageurs) hold short interest then selective use of price limits would bene?t the
market relative to more intrusive market regulations, e.g. imposing a blanket ban on
short-selling or market-wide uptick rules, which are more likely to impede arbitrage or
confound probability beliefs. The argument for “focused regulation” is largely in
accord with recent policy recommendations offered by Avgouleas (2010) in terms of
discouraging non-rational trading while improving price discovery and market
liquidity. Some empirical evidence in support of the limited regulation approach is
offered from the recent market experience.
2. State-contingent asset pricing
An ef?cient securities market allows free-exchange of state-claims over the residual
cash ?ows of a ?rm. In this environment, risk is priced into securities as information
emerges concerning the ?rm’s prospects. However, if noise-traders dominate the market
then prices become noisy signals of intrinsic value. Under these conditions, the
relatively strong hypothesis of market ef?ciency is subject to doubt, as noise-traders
take short positions in the ?rm. This behavior potentially distorts fundamental
valuation and the ability to attract capital resources. To put this argument in concrete
terms, we consider a simple state-claim model of asset pricing.
Following Arrow (1971), let corporate shares (the risky asset) represent
state-contingent claims on the ?rm’s cash ?ows. Thus, a share of stock is desired by
an individual because of the chance it will provide a payoff contingent on some future
state-of-the-world (SOW). A standard treatment of the problem is given in Hirshleifer
and Riley (2002). Let Z
as
denote the income from asset a ¼ 1, 2 in SOW, s ¼ 1, 2. Asset
prices are denoted by P
A
1
and P
A
2
and their quantities by q
1
and q
2
. The (representative)
investor’s budget constraint in asset units is given by:
W ¼ P
A
1
q
1
þ P
A
2
q
2
: ð1Þ
If the individual is endowed with asset quantities q
1
and q
2
and wealth
W then the
individual’s state-claims (c
1
, c
2
) re?ect payoffs from the two-asset portfolio:
c
1
c
2
_ _
¼ k
1
W
P
A
1
Z
11
Z
12
_ _
þ k
2
W
P
A
2
Z
21
Z
22
_ _
ð2Þ
where k
i
, i ¼ 1, 2 denote wealth-shares in assets 1 and 2 with k
1
þ k
2
¼ 1. Complete
markets in tradable assets exist if the market system allows trading in all elementary
state-claims. Let p
1
; p
2
denote subjective probability beliefs of an investor over two
SOW. The investor’s portfolio choice problem is then given by:
k
1
;k
2
max EU ¼ p
1
yðc
1
Þ þp
2
yðc
2
Þ subject to : ð3Þ
c
1
¼ k
1
W
P
A
1
Z
11
þ k
2
W
P
A
2
Z
21
ð¼ q
1
Z
11
þ q
2
Z
21
Þ ð4Þ
Regulating noisy
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c
2
¼ k
1
W
P
A
1
Z
12
þ k
2
W
P
A
2
Z
22
ð¼ q
1
Z
12
þ q
2
Z
22
Þ ð5Þ
k
1
þ k
2
¼ 1: ð6Þ
In this set-up optimal risk, bearing requires the investor equalize the expected marginal
utility per dollar held (invested) in each asset (fundamental theorem of risk bearing):
P
A
2
P
A
1
¼
p
1
y
0
ðc
1
ÞZ
21
þp
2
y
0
ðc
2
ÞZ
22
p
1
y
0
ðc
1
ÞZ
11
þp
2
y
0
ðc
2
ÞZ
12
: ð7Þ
For expositional purposes, assume asset 2 (risky asset) has payoffs ðZ
21
; Z
22
Þ ¼ ð4; 0Þ
and price P
A
2
, while asset 1 (risk-free numeraire) has payoffs ðZ
11
; Z
12
Þ ¼ ð1; 1Þ and
price P
A
1
. Under these assumptions, the fundamental theorem of risk bearing is
represented by:
P
A
2
P
A
1
¼
4
1 þf
_ _
; f ¼
p
2
y
0
ðc
2
Þ
p
1
y
0
ðc
1
Þ
; c
1
¼ q
1
þ 4q
2
c
2
¼ q
1
: ð8Þ
Increasing the odds of failure, i.e. " ðp
2
=p
1
Þ or # ðp
1
=p
2
Þ, implies a higher f-value
consistent with a lower share price P
A
2
relative to the risk-free asset price P
A
1
.
Essentially, increased risk of a zero-payoff is priced into the asset, depending on the
shareholder’s marginal rate of substitution between state-contingent income claims. We
use a numerical example to consider the in?uence of information on investors taking
long or short positions in the stock.
Numerical example
The investor’s choice problem is examined numerically assuming exponential
preferences over state-claims yðc
i
Þ ¼ 1 2e
2Ac
i
where A denotes constant absolute risk
aversion (CARA). In this case, the optimal risk-bearing condition becomes:
P
A
2
P
A
1
¼
4
1 þ ðp
2
=p
1
Þe
Aðc
1
2c
2
Þ
¼
4
1 þ ðp
2
=p
1
Þe
A4q
2
: ð9Þ
Taking the natural log and rearranging terms yields the following investment decision
rule:
q
2
¼
1
4A
ln
p
1
p
2
_ _
4P
A
1
P
A
2
21
_ _ _ _
: ð10Þ
Whether the agent takes a long or short position in the risky asset (q
2
. 0 or q
2
, 0)
depends on the agent’s probability beliefs and risk aversion. Arisk-free trading portfolio
implies asset demand q
2
¼ 0, corresponding to the “certainty state-claims.” Long
positions are taken based on probability beliefs p
2
, p
1
, otherwise short positions are
taken. By shorting the agent assumes a liability in SOW1, i.e. jq
2
Z
21
j ¼ 4jq
2
j. Increased
CARA reduces the size of the positions taken (either long or short), as the individual
becomes less responsive to given changes in the odds of failure. Further consideration
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of this argument is given in a market-clearing model allowing for rational and
non-rational investment behavior. The market equilibrium takes the form of a “noisy
rational expectations equilibrium” to the extent noise trading is active[3].
Noise traders, information, and market-clearing
As Black (1986) put it, noise traders are agents who “trade on noise rather than
information.” Accordingly, noise traders (denoted by N) follow a “non-Bayesian”
approach in forming expectations; that is, they systematically violate Bayes’ Rule in
predicting the ?rm’s prospects for survival. For example, noise traders would place
market orders to sell shares at lower prices, ignoring information regarding ?rm
fundamentals. For reasons of tractability, suppose noise traders are risk neutral and
apply the following ad hoc decision rule in taking short positions:
q
N
3
¼ bln
4
P
A
2
_ _
; where b . 0: ð11Þ
Clearly, no rational investor (Bayesian agent) would follow this “dumb-money” trading
strategy. Instead, we assume rational investors (denoted by superscript R) follow a
Bayesian process in forming their beliefs. The decision rules governing investment are
de?ned by equation (10), depending on risk preferences ðA
R
1
; A
R
2
Þ and probability beliefs
ðp
1
=p
2
Þ
R1
; ðp
1
=p
2
Þ
R2
:
q
R
1
¼
1
4 A
R
1
ln
p
1
p
2
_ _
R1
4
P
A
2
21
_ _ _ _
; q
R
2
¼
1
4 A
R
2
ln
p
1
p
2
_ _
R2
4
P
A
2
21
_ _ _ _
: ð12Þ
Referring to Table I, assume rational investors have common prior beliefs
p
1
¼ p
2
¼ 0:5. To allow for divergent beliefs, each SOW is interpreted as having a
given likelihood of occurring, depending on a noisy signal of the ?rm’s prospects
(positive or negative). Assume the signal is conditioned by the degree of noise trading in
the market as characterized in the likelihood matrix. If the true SOW is non-failure then
a positive signal corresponds to a 60 percent chance of non-failure; a negative signal
corresponds to a 40 percent chance of failure. Alternatively, if the true SOW is failure,
then a positive signal implies a 20 percent chance of non-failure while a negative signal
implies an 80 percent chance of failure. Applying Bayes theorem, the positive signal
results in a posterior distribution (0.75, 0.25), while a negative signal results in the
posterior distribution (0.33, 0.67). The implications for market clearing are considered
below in the presence of noise traders.
Likelihood
matrix Joint (pr.) Posterior (pr.)
Noisy signal Noisy signal Noisy signal
States-of-the-world Good Bad Good Bad Prior (Pr.) Good Bad
SOW1: non-failure 0.6 0.4 1.0 0.3 0.2 0.5 0.75 0.33
SOW2: failure 0.2 0.8 1.0 0.1 0.4 0.5 0.25 0.67
0.4 0.6 1.0 1.0 1.0
Table I.
Bayesian probability
analysis
Regulating noisy
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Market clearing with noise traders
In the absence of monopoly power over the stock price, we can assume agents treat
price as parametric and submit excess demand schedules for the stock to a “Walrasian
auctioneer”[4]. The market-clearing price balances the volume of long and short
positions, thereby re?ecting informed and uninformed probability beliefs, risk
aversion, and the degree of noise trading in the market, a:
n
1
q
R
1
þa n
2
q
R
2
_ _
þ ð1 2aÞn
3
q
N
3
¼ 0: ð13Þ
Table II summarizes relationships among the various model parameters. If Bayesian
investors have common priors p
1
¼ p
2
¼ 0:5, then they only take long positions in the
market. Consequently, the short side of the market consists entirely of noise traders,
with the market-clearing price decreasing in the degree of noise and the degree of risk
aversion. The bottom portion of the table summarizes the same relationships assuming
some agents incorporate bad news in revising their prior beliefs. In this informative
case, short-sellers consist of rational and non-rational agents, and the market-clearing
price decreases further as rational short-sellers become better-informed of ?rm
fundamentals.
What emerges from the above analysis is a noisy rational expectations hypothesis
about the nature of short-selling behavior and stock price adjustments. From a policy
perspective, this relationship can be regulated by imposing constraints on either
short-sellers themselves (a ban), or on short-sale transaction prices (a price test). An
empirical look at these policy measures follows based on the SEC’s recent ban on
short-selling ?nancial stocks.
3. Empirical analysis
The SEC (2008c) ban on “naked” short-selling was motivated by the potential to “cause
sudden and excessive ?uctuations of security prices, thereby impairing the operation
of fair and orderly markets”[5]. Thus, on July 15, 2008, the SEC announced regulations
Degree of
noise Risk aversion
Rational long
traders (q
R
1
)
Rational short
traders (q
R
2
)
Short noise
traders (q
N
3
)
Market-clearing
price (P
*
)
Priors R1 : p
1
¼ p
2
¼ 1=2
R2 : p
1
¼ p
2
¼ 1=2
a ¼ 0:1 A ¼ 0.25 0.0374 0.0337 0.0712 1.96
A ¼ 0.30 0.0377 0.0339 0.0716 1.95
a ¼ 0:5 A ¼ 0.25 0.2812 0.1406 0.4218 1.72
A ¼ 0.30 0.2953 0.1476 0.4429 1.65
a ¼ 0:9 A ¼ 0.25 1.1925 0.1190 1.3110 0.93
A ¼ 0.30 2.4150 0.2415 2.6500 0.21
Posteriors R1 : p
1
¼ 1=2; p
2
¼ 1=2
R2 : p
1
¼ 1=3; p
2
¼ 2=3
a ¼ 0:1 A ¼ 0.25 0.3828 20.2927 0.0903 1.62
A ¼ 0.30 0.3273 20.2365 0.0908 1.61
a ¼ 0:5 A ¼ 0.25 0.5769 20.0656 0.5113 1.44
A ¼ 0.30 0.5576 20.0163 0.5413 1.35
a ¼ 0:9 A ¼ 0.25 1.3716 0.0663 1.4379 0.81
A ¼ 0.30 3.5682 0.2978 3.8661 0.05
Table II.
Market-clearing
relationships
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banning naked short-selling in Fannie Mae (FNM), Freddie Mac (FRE) and 17 other
?nancial stocks (effective July 21 to August 12). The regulations were expanded on
September 18, prohibiting all short-selling in an additional 780 ?nancial stocks
(effective September 19 to October 8). Finally on July 27, 2009, the emergency rule
banning the practice of naked short-selling was made permanent[6]. To study the
price-effects of the ban, we use simple regressions, EGARCH analysis (Nelson, 1991),
and simulated price behavior under a hypothetical uptick rule. We focus on the 25 most
shorted stocks on the NYSE and NYSE ACRA for which short-selling was prohibited
on July 15, 2008. Presumably, increased short interest re?ected beliefs that stock values
would fall further (SEC 2008a, b).
We take an initial look at the empirical relationship between short interest and stock
price behavior using ordinary least squares (OLS) regressions around the time of the
July 15 announcement. Table III identi?es the initial sample of ?rms and their symbols,
the amounts of short interest and stock prices for the months of July and August, and
the percentage of the stock shorted. We are interested in the coef?cient of correlation
between short interest and stock prices ðr ¼
??????
R
2
p
Þ, and the OLS parameter estimates
for short interest. Thus, to avoid measurement bias with autocorrelations or spuriously
in?ated correlations, we regress percentage changes in short interest (%DS) on
percentage changes in stock prices (%DP). The bottom of Table III reports regression
results for three sample periods: a six-week period overlapping the announcement ( July
1 2008 to August 16, 2008), and a two- and four-week period before and after the
announcement ( July 1 2008 to 16, 2008 and July 16 2008 to August 16, 2008)[7].
The OLS estimates of the short interest parameter (%DS ¼ 21.19, 20.68) indicate
the inverse relationship between short interest and stock returns weakened following
the regulatory announcement. Correspondingly, the correlation value between the two
variables ðr ¼
??????
R
2
p
Þ dropped from 0.66 to 0.32. The results also indicate that daily
stock returns tended to increase after the ban was imposed, as shown by the upward
shift in the constant term (from 20.04 to 0.15) and increase in statistical signi?cance
(t-statistics from 21.36 to 3.22)[8]. Nonetheless, the average return to an equally
weighted portfolio of the most shorted stocks was approximately 26 percent over the
two-month period ( July-August), with a standard deviation of 27 percent[9].
The continuation of “falling security prices” and “excessive price ?uctuations”
motivated the SEC to ban all short-selling of nearly 800 ?nancial stocks, effective
September 19, 2008. We examine how the expanded ban affected daily stock returns
ðR
t
Þ and their volatility for our working sample using EGARCH models. EGARCH
models measure the log of the conditional variance of stock returns ðlog s
2
t
Þ as a
weighted average of the long-run variance ð4Þ, the log of the variance for the previous
period (the GARCH term, log s
2
t21
), and any new information revealed through the
previous error in predicting mean returns (the ARCH term containing 1
t21
). We
estimate the following EGARCH (1, 1) model for each ?rm in our working sample:
R
t
¼ c þ1
t
ð14Þ
log s
2
t
¼ 4þblog s
2
t21
þg
1
t21
s
t21
þa
j1
t21
j
s
t21
ð15Þ
where 4; b; g and a are constant parameters. The EGARCH process ensures the
conditional variance of stock returns is positive without ad hoc restrictions on the
model parameters.
Regulating noisy
short-selling of
troubled ?rms?
233
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(
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We assume market participants identify “good news” as a signal of increased stock
returns (positive shocks, 1
t21
. 0) and “bad news” as a signal of lower returns
(negative shocks, 1
t21
, 0). Thus, a previous shock of good news contributes
to current volatility with ða þgÞj1
t21
j=js
t21
j, and a previous shock of bad news with
ða 2gÞj1
t21
j=s
t21
. When g ¼ 0, it follows positive and negative shocks have
symmetric effects on volatility; and when g , 0 negative shocks generate more
Short interest in
million
Stock price in
million
Firm (symbol) July 2008
August
2008
Percentage of
stock shorted
July 1,
2008
August
29, 2008
Washington Mutual,
Inc. (WM) 338.6 382.4 22.4 5.25 4.05
Ford Motor Co. (F) 311.3 320.8 14.7 4.71 4.46
Wachovia Corp. (WB) 271.9 269.1 12.5 16.13 15.89
Fannie Mae (FNM) 141.4 182.7 17.0 19.59 6.84
Wells Fargo & Co. (WFC) 165.8 176.1 5.3 24.12 30.27
National City Corp. (NCC) 161.7 166.1 21.8 4.60 5.04
Freddie Mac (FRE) 118.6 158.5 24.5 16.21 4.51
Citigroup, Inc. (C) 149.6 150.3 2.8 17.13 18.99
General Motors Corp. (GM) 143.1 146.2 25.8 11.75 10.00
Bank of America Corp. (BAC) 112.8 117.5 2.6 23.81 31.14
Advanced Micro Devices
Inc. (AMD) 93.4 96.4 15.9 5.65 6.29
Regions Financial Corp. (RF) 90.2 91.4 13.2 11.59 9.27
Ambac Financial Group
Inc. (ABK) 83.5 91.0 31.7 1.18 7.16
BB&T Corp. (BBT) 84.8 90.3 16.4 23.97 30.00
American Intl. Group Inc. AIG) 78.7 85.8 3.2 26.73 21.49
Micron Technology Inc. (MU) 85.8 85.2 11.2 5.79 4.24
MBIA Inc. (MBI) 86.1 83.6 30.6 4.28 16.22
Sprint Nextel Corp. (S) 88.5 82.7 3.0 8.83 8.72
U.S. Bancorp. (USB) 76.5 79.2 4.6 28.40 31.86
Coeur d’Alene Mines Corp.
(CDE) 72.8 77.1 14.0 2.81 1.79
Lehman Bros. Holdings
Inc. (LEH) 70.6 76.9 11.1 20.96 16.09
Capital One Financial Corp.
(COF) 73.7 73.5 19.6 40.14 44.14
The Colonial BancGroup
Inc. (CNB) 70.1 72.0 35.6 4.96 6.32
The Walt Disney Co. (DIS) 72.6 71.2 3.8 31.05 32.35
Synovus Financial
Corp. (SNV) 65.0 69.7 21.1 9.10 9.20
OLS regression results
Constant
term t-statistic %DS t-statistic R
2
r
July 1 2008 to August 16, 2008 0.0855 1.7815 21.6815 23.7234 0.3976 0.6306
Pre-SEC ban: July 1 2008 to 16,
2008 20.0431 21.3556 21.1928 23.9891 0.43111 0.6565
Post-SEC ban: July 16 2008 to
August 16, 2008 0.1500 3.2223 20.6782 21.5484 0.1025 0.3201
Table III.
Short interest and stock
prices on the NYSE
July-August, 2008
JFEP
1,3
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(
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)
volatility than positive shocks, so bad news is said to have a “leverage effect.” The
“persistence” of volatility following a news shock is captured by b !1: as beta tends to
unity volatility becomes more persistent, indicating slower mean reversion.
We study how the expanded ban affected volatility persistence and leverage by
comparing EGARCH parameter estimates for two periods: a 125-day period before
September 19 and a 125-day period after October 18. Table IV reports summary
statistics for the cross-sectional time series of closing prices ( p) and daily stock returns
(R)[10]. The coef?cient of variation gives a simple indication of the degree of
randomness, combining a measure of central tendency (sample mean, m) with a
measure dispersion (sample standard deviation, s), i.e. CV ¼ s/m. The CV statistics for
closing prices and the percent-change in closing prices suggests there was an increase
in price dispersion after the expanded ban on short-selling was imposed.
Table V reports the maximum-likelihood estimates for the EGARCH models.
The statistically signi?cant parameter estimates are denoted by asterisks (
*
95 and
**
99 percent levels).
Tables VI and VII identify ?rms by changes in their volatility persistence and
leverage effect parameters (b and g). We consider cases where persistence or leverage
remained about the same after introduction of the wide-spread ban, and cases where
persistence or leverage changed. We differentiate among the latter category according
to whether persistence or leverage became stronger or weaker.
Columns 1 and 2 in Table VI list ?rms for which volatility persistence was roughly
unchanged after the wide-spread ban was imposed. Non-persistence is relatively rare,
limited to AMD, FNM, and FRE. Strong persistence is more common, as seen in AIG,
Bank of America (BAC), CP, CDE, F, GM, US Bancorp (USB), and WFC[11]. Columns 3
and 4 list ?rms, which experienced change in volatility persistence. Persistence became
stronger for DIS, MU, RF, and S, and became weaker for BBT, COF, ABK, CNB, and
SNV. Accordingly, the expanded ban may have dampened volatility persistence in ?ve
out of 21 cases studied.
Columns 1 and 2 in Table VII list ?rms whose leverage effects seem unchanged by
the wide-spread ban: ?ve ?rms had no leverage effects (AMD, CNB, COF, F, and GM);
and four ?rms had strong leverage effects (CP, RF, USB, and WFC). Column 3 lists
?rms where the leverage effects became stronger (ABK, CDE, and MU), implying bad
news began having a greater impact on volatility than good news. Column 4 lists ?rms
where leverage effects became weaker (AIG, BAC, BBT, and SNV), with bad news
having less impact on price volatility[12]. Finally, Column 5 reports several cases
Variable
Sample
period
Average
mean
Average
min
Average
max
Average
SD CV
Closing prices (P ) Before 17.35 9.85 23.88 3.66 0.21
After 7.96 3.56 13.86 2.74 0.34
Percent-change closing
prices
Before
After
20.0043
2 0.0057
20.3899
2 0.3155
0.2318
0.3099
0.0714
0.0991
216.50
2 17.43
Notes: The summary statistics are averages, calculated over the sample means from the cross-
sectional time series; the CV statistics are calculated as the ratio of the average standard deviation and
the average of the sample means
Table IV.
Summary statistics for
second event sample
Regulating noisy
short-selling of
troubled ?rms?
235
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.
7
7
6
(
c
o
n
t
i
n
u
e
d
)
Table V.
EGARCH (1, 1) parameter
estimates
JFEP
1,3
236
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n
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o
a
d
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d
b
y
P
O
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D
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A
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3
6
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
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Table V.
Regulating noisy
short-selling of
troubled ?rms?
237
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A
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2
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:
3
6
2
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a
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6
(
P
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)
where good news generated more volatility than bad news: FNM in both periods, FRE
in the second period, and Disney and MBIA Inc. in the ?rst period.
We complete our empirical analysis of short-selling policy with a simulation of price
adjustments under a hypothetical “uptick rule.” An uptick rule, such as 10-a1, is akin to
a regulated price in executing short sales. The argument for its use rests on promoting
more ef?cient pricing of securities under speculative attack. On the NYSE, short sales
would only be transacted on a plus tick (uptick) or a “zero-plus tick”, i.e. a price higher
than the last price, or a price equal to the last price but higher than the last different
price. For example, a short sale could be executed at $4 if the previous price sequence
(beginning with the oldest price) is 3.875, 3.875 and 4. However, if the previous price
sequence is 4.125, 4.125 and 4, then a trade at $4 would be on a “zero-minus tick” and
not allowed.
Non-existent Remained strong Became strong Became weak Other
Advanced Micro
Devices Inc. (AMD)
American Intl.
Group Inc. (AIG)
The Walt Disney
Co. (DIS)
BB&T Corp. (BBT) MBIA Inc.
(MBI)
Fannie Mae (FNM)
Bank of America
Corp. (BAC)
Micron Tech. Inc.
(MU)
Capital One Fin. Corp.
(COF)
Freddie Mac (FRE)
Canadian Paci?c
Rail. Ltd (CP)
Regions Financial
Corp. (RF)
Ambac Financial
Group Inc. (ABK)
Coer d’Alene Mines
Corp. (CDE)
Sprint Nextel
Corp. (S)
The Colonial Banc
Group Inc. (CNB)
Ford Motor Co. (F) Synovus Financial
Corp. (SNV)
General Motors
Corp. (GM)
US Bancorp (USB)
Wells Fargo & Co.
(WFC)
Table VI.
Persistence of volatility
before and after
expanded ban
Non-existent
Remained
strong Became strong Became weak Other
Advanced Micro
Devices Inc. (AMD)
(CP) Ambac Financial
Group Inc. (ABK)
American Intl.
Group Inc. (AIG)
MBIA Inc.
(MBI)
The Colonial Banc
Group Inc. (CNB)
Regions
Financial Corp.
(RF)
Coer d’Alene Mines
Corp. (CDE)
Bank of America
Corp. (BAC)
The Walt
Disney Co.
(DIS)
Capital One Fin.
Corp. (COF)
US Bancorp
(USB)
Micron Tech. Inc.
(MU)
BB&T Corp.
(BBT)
Fannie Mae
(FNM)
Ford Motor Co. (F) Wells Fargo &
Co. (WFC)
Synovus Financial
Corp. (SNV)
Freddie Mac
(FRE)
General Motors
Corp. (GM)
Sprint Nextel Corp. (S)
Table VII.
Leverage effect before
and after expanded ban
JFEP
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238
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:
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(
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We simulate the affect of imposing price tests on four ?rms drawn from our
working sample: BAC, FNM, FRE, and USB[13]. We assume the security prices follow
?rm-speci?c stochastic processes subject to the suspension of dividend payments to
shareholders:
DP
P
¼ mDt þs1
?????
Dt
p
: ð16Þ
where DP=P is the proportional return provided by the stock in time interval Dt; mDt is
the expected value of the return; and s1
?????
Dt
p
is the stochastic component of the return.
We assume short-selling in the underlying stock constitutes one-?fth of trading
activity, implying the uptick rule applies in 20 percent of the simulations. Random
“news shocks” are introduced using normally- and Cauchy-distributed 1-values[14], in
conjunction with ?rm-speci?c estimates for drift and volatility (m and s) derived from
the EGARCH analysis (i.e. the parameter sets c; 4; a; b; g)[15]. The simulation period
covers 44 days of stock trading.
Figure 1(a)-(d) shows differences in simulated prices with and without an uptick rule
under the normal distribution. Figure 2(a)-(d) shows simulation results under the
Cauchy distribution. We consider price performance for two sample-periods
corresponding to the EGARCH parameter sets. The simulated prices are drawn
using quotes to the nearest $1/8 if the price is above $3 and $1/16 if the price is at or
below $3 (standard tick sizes on US stock exchanges). Since we are interested in price
differentials with and without the uptick rule (price spreads), we illustrate all
Figure 1.
Uptick rule simulations
under normally
distributed “news shocks”
–0.8
–0.6
–0.4
–0.2
0.0
0.2
0.4
0.6
50 100 150
(a) (b)
(c) (d)
200 250 300 350
50 100 150 200 250 300 350
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
50 100 150 200 250 300 350
50 100 150 200 250 300 350
–0.06
–0.04
–0.02
0.00
0.02
0.04
0.06
FREN 1 FREN 2
BACN 1 BACN 2
USBN 1 USBN 2
FNMN 1 FNMN 2
–1.6
–1.2
–0.8
–0.4
0.0
0.4
Regulating noisy
short-selling of
troubled ?rms?
239
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2
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:
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2
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a
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2
0
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6
(
P
T
)
simulations beginning with a common spread value of zero. Thus, as the trials
progress positive values imply the regulated price exceeded the free market price,
creating a positive spread. Negative values imply the uptick rule was ineffective at
supporting the simulated price.
Figure 1(a) shows results for BAC prices under the normal distribution. The solid
line (BACN1) re?ects EGARCH parameters from the ?rst observation period (before
the wide-spread ban), and the dotted line (BACN2) from the second observation period
(after the ban was introduced). The simulations suggest the uptick rule provides more
stable price-support under the second set of BAC parameters. Figure 1(b) and (d)
shows the same policy impact for FNM and USB: the uptick rule gives more stable
price support under the second set of EGARCH parameters. Conversely, the price
simulations for FRE show the uptick rule giving more stable price-support under
the ?rst set of parameters.
Figure 2(a)-(d) shows the performance of the uptick rule under the Cauchy process.
Here, the price support function behaves more randomly, most likely due to the
heavy-tail properties of the Cauchy distribution. Figure 2(a) shows the case of BAC.
Here, again the uptick rule provides more certain price support over the second
observation period, and Figure 2(b) and (d) again show similar (albeit noisier) policy
performance for FNM and USB. Figure 2(c) shows a somewhat different policy impact
for FRE, with prices generally supported in both observation periods, though more
randomly.
Figure 2.
Uptick rule simulations
under Cauchy-distributed
“news shocks”
–0.4
0.0
0.4
0.8
1.2
1.6
2.0
50 100 150 200 250 300 350
50 100 150 200 250 300 350
–0.5
–0.4
–0.3
–0.2
–0.1
0.0
0.1
0.2
50 100 150 200 250 300 350
50 100 150 200 250 300 350
–0.2
–0.1
0.0
0.1
0.2
0.3
0.4
0.5
–1.6
–1.2
–0.8
–0.4
0.0
0.4
FREC 1 FREC 2
BACC 1 BACC 2
USBC 1 USBC 2
FNMC 1
FNMC 2
(a) (b)
(c) (d)
JFEP
1,3
240
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A
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2
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:
3
6
2
4
J
a
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2
0
1
6
(
P
T
)
The various simulations provide some support for the argument that uptick rules
can be effective constraints on noise-driven short-selling, potentially contributing to a
more rational price discovery process. However, at least two key quali?cations stand in
the way of offering general conclusions. First, the EGARCH results show ?rm-speci?c
volatility varies across ?rms according to persistence and leverage, and the presence or
absence of quantity constraints on short-selling. Second, our simulation analysis is
somewhat simpli?ed in ignoring the potential for dynamic “feedback effects” between
price volatility and the degree of short interest in troubled ?rms. Nonetheless, the
results obtained suggest a blanket uptick rule has disparate impacts on price stability,
depending on the ?rm-speci?c parameters that govern the stochastic process.
4. Concluding remarks
On July 27, 2009, the SEC made permanent the order prohibiting the practice of naked
short-selling of certain ?nancial stocks. Previously, the SEC banned all short-selling of
nearly 800 stocks. To help maintain liquidity, certain exceptions were made for
registered market makers. The SEC has also considered reinstating “uptick rule” 10a-1,
which prohibits short-selling securities on a downtick. These policy measures were
taken to moderate “sudden and excessive ?uctuations in security prices.” In taking
these steps, regulators noted that:
[. . .] sudden price declines give rise to questions about the underlying ?nancial conditions of
an issuer, which in turn can create a crises of con?dence without a fundamental underlying
basis. This crisis of con?dence can impair the liquidity and ultimate viability of an issuer,
with potentially broad market consequences (SEC, 2008c).
Important cost-bene?t questions arise in regulating short-selling, since high levels of
short interest re?ect beliefs that share values will fall further. Whether these beliefs
re?ect fundamental information is a focal point of the present study. Certainly, “bad
news” concerning a troubled ?rm motivates rational short and long sellers to post the
same shares at the same time, thus exacerbating negative price pressure. Clearly, if
agents are free to short-sell then share prices will tend to re?ect relatively more
pessimistic beliefs of the ?rms’ prospects. Interestingly, a study by the Of?ce of
Economic Analysis (2008) found “long-sellers” (who sell their own stock) were the
primary cause of price drops during the recent high-volatility periods in US markets.
The observation of falling prices during high-volatility periods coincides with the
predictions given by our noisy rational expectations model, wherein some agents are
rational sellers. Under free-market conditions, our model predicts the equilibrium
price decreases in the degree of noise trading and investor risk aversion, with rational
and non-rational agents taking short positions in troubled ?rms. Imposing a sales
constraint under these conditions results in less-informed beliefs regarding ?rm
fundamentals to the extent “informed traders” withdraw from the market[16]. Hence,
the SEC’s exception of registered market-makers was important in terms of ensuring
the provision of liquidity to rational arbitrageurs, who otherwise might have
withdrawn from shrinking securities markets.
Our empirical analysis of short-selling constraints focuses on price volatility,
employing simple regressions, EGARCH analysis and simulated price behavior
under a hypothetical uptick rule. The EGARCH results suggest short-selling
constraints had non-uniform impacts on the persistence and leverage effects associated
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with price volatility. Moreover, the corresponding price simulations indicate a
hypothetical uptick rule might have helped stabilize price behavior in some cases,
depending on the nature of the stochastic process and whether or not quantity
constraints on short-selling were binding. Consequently, our ?ndings indicate blanket
uptick rules are prone to some degree of failure in supporting stock valuations, given
the wide-ranging response to news observed in our sample of troubled ?rms.
Based on our ?ndings, we are inclined to join the chorus of ?nancial economists
arguing for a “focused approach” to market regulation. As described here, the “focused
approach” corresponds more closely with the SEC’s interpretation of a “security-speci?c,
temporary approach” as opposed to a “market-wide, permanent approach” (SEC, 2009).
In these regards, our ?ndings support recent policy prescriptions outlined in Avgouleas
(2010), which call for selective use of price limits and disclosure of short-selling positions.
These policy measures are capable of discouraging trend chasing (herding) without
compromising “informed trading” – that is to say, not impeding arbitrage or confounding
probability beliefs regarding ?rm survival.
En ?n, we remind the reader of Milton Friedman’s persuasive argument, that
non-rational traders who persist in selling a truly underpriced security will eventually
lose money to better-informed traders, along with their in?uence over price. But this
assumes better-informed traders are not constrained from participating in markets.
Notes
1. The US uptick rule (10a-1) was adopted in 1938 following an inquiry into the effects of
concentrated short-selling during the market break of 1937. The Securities and Exchange
Commission (SEC, 2007) eliminated the rule on July 6, noting that price test restrictions
“modestly reduce liquidity and do not appear necessary to prevent market manipulation”.
2. See Avgouleas (2010, pp. 21-6) for a comprehensive survey of empirical literature identifying
various forms of ef?ciency bene?ts from short-selling, see Bris et al. (2007).
3. See O’Hara (1994) for a discussion of the “noisy rational expectations framework,” esp.
Chapter 6.
4. Note that the total stock of the risky asset is treated as being zero. An alternative would be to
treat the aggregate supply of the risky asset as a random variable. However, as noted by
Hirshleifer and Riley (2002), this approach is not easily justi?able in many contexts
(Section 7.3).
5. “Naked” short-selling occurs when sellers do not even borrow the underlying shares before
selling them and then look to cover their positions sometime after the sale.
6. Importantly, the permanent ruling requires that brokers must promptly buy or borrow the
underlying security to deliver on a short sale.
7. The SEC “emergency action” temporarily banned investors from short-selling 799 ?nancial
?rms (and a few others closely related to the ?nancial sector). This expanded regulation
followed the bankruptcy of Lehman Bros. and ?nancial disclosures by American Intl. Group.
The policy actions also ushered in the debate over the “too big to fail” argument for ?nancial
regulation. See Helwege (2009) for an insightful discussion of these events.
8. This ?nding is in accord with observations reported by Boehmer et al. (2008a, b), which ?nd
an initial bounce in share prices on NYSE-listed stocks subject to the early ban. A similar
bounce was reported by FSA (2009) comparing returns on FTSE-traded stocks.
9. That heavily shorted stocks tend to exhibit negative returns is well-documented in previous
studies, e.g. Desai et al. (2002).
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10. Relative to the initial sample of ?rms our working sample excludes Washington Mutual,
Lehman Bros, Citigroup, Natl. City Corp., and the Wachovia Group. Statistics for all of the
remaining ?rms are reported in Table AI in the Appendix.
11. The observation of no signi?cant changes in volatility persistence coincides with
observations reported by the FSA (2009) in comparing returns for the FTSE 350 over
pre- and post-ban periods.
12. This observation is consistent with the argument that unencumbered short-selling allows
markets to adjust faster to “bad news,”, e.g. see Bai et al. (2006).
13. Referring to Table V, two of the ?rms show strong persistence and leverage effect in both
sample periods (BAC and USB); the other two show non-persistence and “good news” adding
volatility (FNM and FRE) in both periods.
14. Cauchy distributions look similar to normal distributions, but with much heavier tails. Thus,
when studying hypothesis tests that assume normality, the Cauchy distribution is a good
indicator of how sensitive the tests are to so-called “heavy-tail departures from normality.”
15. We compute epsilon values at each tick under normal and Cauchy distributions by “mixing”
the initial sigma from the EGARCH with pseudo-randomness generated through a
“Mersenne Twister” (MT19937). The resulting normally- or Cauchy-distributed epsilon is
then applied in obtaining an epsilon for the next tick.
16. Boehmer et al. (2008a, b) provide empirical evidence that short-sellers tend to be
well-informed and trade-on fundamentals.
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Corresponding author
Carlos A. Ulibarri can be contacted at: [email protected]
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l
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o
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p
.
(
R
F
)
1
3
.
7
2
6
.
7
2
4
.
7
7
2
.
8
4
3
4
.
7
4
2
.
3
2
0
.
0
0
3
0
2
0
.
0
0
8
1
0
.
0
6
4
1
0
.
1
0
2
8
2
1
.
4
1
2
.
7
S
p
r
i
n
t
N
e
x
t
e
l
C
o
r
p
.
(
S
)
8
.
1
9
2
.
8
8
0
.
9
4
0
.
7
7
1
1
.
6
2
6
.
7
0
.
0
0
0
3
0
.
0
0
0
4
0
.
0
4
0
6
0
.
0
9
5
9
1
3
5
.
3
2
3
9
.
8
S
y
n
o
v
u
s
F
i
n
a
n
c
i
a
l
C
o
r
p
.
(
S
N
V
)
1
0
.
0
5
5
.
8
7
1
.
1
8
2
.
5
0
1
1
.
7
4
2
.
4
2
0
.
0
0
0
0
2
0
.
0
0
6
7
0
.
0
4
5
1
0
.
0
8
3
9
4
5
1
.
0
1
2
.
5
U
S
B
a
n
c
o
r
p
.
(
U
S
B
)
3
0
.
2
6
2
0
.
7
2
2
.
2
9
6
.
6
4
7
.
5
3
2
.
0
0
.
0
0
0
7
2
0
.
0
0
6
4
0
.
0
3
3
3
0
.
0
6
9
8
4
7
.
6
1
0
.
9
W
e
l
l
s
F
a
r
g
o
&
C
o
.
(
W
F
C
)
2
7
.
4
8
2
2
.
2
0
2
.
7
1
7
.
2
7
9
.
8
3
2
.
7
0
.
0
0
1
3
2
0
.
0
0
6
1
0
.
0
4
3
7
0
.
0
8
8
6
3
3
.
6
1
4
.
5
Table AI.
Summary statistics
for prices and
percent-changes in prices
before/after trade ban
Regulating noisy
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245
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This article has been cited by:
1. Carlos A. Ulibarri. 2013. Multivariate GARCH analysis of Fannie Mae, Freddie Mac, and American
International Group: Did the short-selling ban reduce systemic return-risk?. The North American Journal
of Economics and Finance 25, 60-69. [CrossRef]
2. Michael Devaney, William L. Weber. 2013. Short?sell moratorium effects on regional bank performance.
Journal of Financial Economic Policy 5:2, 92-110. [Abstract] [Full Text] [PDF]
3. Michael Devaney. 2012. Financial crisis, REIT short-sell restrictions and event induced volatility. The
Quarterly Review of Economics and Finance 52, 219-226. [CrossRef]
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doc_976785154.pdf
The purpose of this paper is to examine the efficacy of recent policy initiatives taken by
the US Securities and Exchange Commission banning naked “short-selling” of specific financial stocks.
The paper also considers the merits of reinstating “uptick rule” 10a-1, which prohibits short-selling
securities on a downtick.
Journal of Financial Economic Policy
Regulating noisy short-selling of troubled firms?
Carlos A. Ulibarri Ionut Florescu J oel M. Eidsath
Article information:
To cite this document:
Carlos A. Ulibarri Ionut Florescu J oel M. Eidsath, (2009),"Regulating noisy short-selling of troubled firms?",
J ournal of Financial Economic Policy, Vol. 1 Iss 3 pp. 227 - 245
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Liuqing Mai, Robert van Ness, Bonnie van Ness, (2009),"Short sales around M&A
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Regulating noisy short-selling
of troubled ?rms?
Carlos A. Ulibarri
Department of Management, New Mexico Institute of Mining and Technology,
Socorro, New Mexico, USA
Ionut Florescu
Department of Mathematical Sciences, Stevens Institute of Technology,
Hoboken, New Jersey, USA, and
Joel M. Eidsath
Department of Management, New Mexico Institute of Mining and Technology,
Socorro, New Mexico, USA
Abstract
Purpose – The purpose of this paper is to examine the ef?cacy of recent policy initiatives taken by
the US Securities and Exchange Commission banning naked “short-selling” of speci?c ?nancial stocks.
The paper also considers the merits of reinstating “uptick rule” 10a-1, which prohibits short-selling
securities on a downtick.
Design/methodology/approach – The paper studies theoretical implications of short-selling in a
simple state-claim model, re?ecting varying amounts of short interest in a representative ?rm and
noise trading in the market. Price discovery depends on the proportion of noise trading compared to
rational short-selling. The empirical analysis focuses on price volatility under short-selling constraints
employing simple regressions, EGARCH analysis and simulated price behavior under a hypothetical
uptick rule.
Findings – The EGARCH results suggest short-selling constraints had non-uniform impacts on the
persistence and leverage effects associated with price volatility. The corresponding price simulations
indicate a hypothetical uptick rule might have helped stabilize price behavior in some cases, depending
on the nature of the stochastic process and whether or not quantity constraints on short-selling are
binding.
Originality/value – The theoretical arguments and empirical ?ndings suggest a “focused approach”
to market regulation would be a more ef?cient means of discouraging trend chasing without
compromising “informed trading” – that is to say, safeguarding price discovery and market liquidity
without impeding arbitrage or confounding probability beliefs regarding ?rm survival. These
conclusions are largely in accord with recent policy analysis and proposals outlined in Avgouleas.
Keywords Selling, Financial markets, Securities markets, United States of America
Paper type Research paper
1. Introduction
Short-sellers participate in ?nancial markets by ?rst borrowing and then selling
securities. The aim is to repurchase the security at a lower price in the near future,
thereby making a pro?t if the asset’s price decreases between the time of sale and
purchase. Thus, regulatory constraints on short-selling transactions can take various
forms. Of present concern are strict prohibitions that ban short-sales’ altogether
The current issue and full text archive of this journal is available at
www.emeraldinsight.com/1757-6385.htm
JEL classi?cation – G-13, G-14, G15
Regulating noisy
short-selling of
troubled ?rms?
227
Journal of Financial Economic Policy
Vol. 1 No. 3, 2009
pp. 227-245
qEmerald Group Publishing Limited
1757-6385
DOI 10.1108/17576380911041719
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(sales constraints), and conditional prohibitions that rule-out short-selling in situations
where price declines are persistent (price constraints). We treat these two types of
regulation as heuristic representations of the recent ban on short-sales and the potential
tick-test governing short-selling, i.e. rule 10a-1 which prohibits short-selling of a
security in a “down” market[1].
Clearly, short-selling stocks can have adverse impacts on the valuation of troubled
?rms, and perhaps even the likelihood of their survival. However, the implications of
regulating short-selling remain open to question in situations where rational and
non-rational agents take “short interest” positions in troubled ?rms (as measured by the
total amount of shares sold short and yet to be repurchased to close out the positions).
Presumably, high levels of short interest re?ect beliefs that share values will fall
further. The extent to which these beliefs re?ect fundamental information is a matter of
present concern.
Theoretical analysis of short-sales constraints begins with Miller’s (1977)
stock-pricing hypothesis and extensions by Harrison and Kreps (1978), Jarrow (1980),
Diamond and Verrecchia (1987), Allen et al. (1993), Morris (1996) and Hong and Stein
(2002). This literature considers how constraints on short-selling affect the propensity
to trade and the ability for prices to adjust to good or bad news (O’Hara, 1994). If agents
are free to short-sell a stock, then the stock’s price will tend to re?ect relatively
pessimistic beliefs of the ?rms’ prospects (Diamond and Verrecchia, 1987)[2]. This begs
the following questions:
.
Are short-sellers acting as rational agents?
.
Are the policy implications of imposing a moratorium on short-selling
substantively different from imposing conditional price restrictions?
Short-sellers may include passive investors, arbitragers, and noise-traders. Collectively,
these agents share common (pessimistic) beliefs regarding the ?rms’ future prospects.
These beliefs are rational to the extent they re?ect available information concerning
fundamental valuations; that is, the net present value of future cash ?ows,
appropriately discounted for risk considerations. On the contrary, non-rational
valuations are based on some less exacting basis. For example, non-rational agents may
apply trading strategies that are independent or correlated, such as “reading tea leafs”
or “trading with the crowd.” In either case, the asset price may still approximate
fundamental value as reviewed in Shleifer (2000).
First, non-rational trading strategies that are independent could cancel-out,
permitting rational investors to determine a price consistent with fundamental value.
Second, non-rational trading strategies that are correlated tend to create pro?table
investment opportunities. In this case, it has been famously argued that market-clearing
prices remain ef?cient signals of fundamental value so long as rational agents take
positions against-the-crowd and hold these positions for suf?ciently long periods of
time (Freidman, 1953; Fama, 1965). Non-rational traders who persist in selling the
underpriced security eventually lose money to better-informed traders, along with their
in?uence over price.
The present paper considers regulatory policy governing short-selling when noise
trading is persistent. Policy implications are drawn from a simple state-claim model
re?ecting varying amounts of short interest in the ?rm and noise trading in the stock
market. The study maintains noise traders are key in applying market regulations
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since these agents increasingly sell a troubled asset the lower its price becomes,
motivating “smart money to chase dumb money.” In particular, if rational agents
(arbitrageurs) hold short interest then selective use of price limits would bene?t the
market relative to more intrusive market regulations, e.g. imposing a blanket ban on
short-selling or market-wide uptick rules, which are more likely to impede arbitrage or
confound probability beliefs. The argument for “focused regulation” is largely in
accord with recent policy recommendations offered by Avgouleas (2010) in terms of
discouraging non-rational trading while improving price discovery and market
liquidity. Some empirical evidence in support of the limited regulation approach is
offered from the recent market experience.
2. State-contingent asset pricing
An ef?cient securities market allows free-exchange of state-claims over the residual
cash ?ows of a ?rm. In this environment, risk is priced into securities as information
emerges concerning the ?rm’s prospects. However, if noise-traders dominate the market
then prices become noisy signals of intrinsic value. Under these conditions, the
relatively strong hypothesis of market ef?ciency is subject to doubt, as noise-traders
take short positions in the ?rm. This behavior potentially distorts fundamental
valuation and the ability to attract capital resources. To put this argument in concrete
terms, we consider a simple state-claim model of asset pricing.
Following Arrow (1971), let corporate shares (the risky asset) represent
state-contingent claims on the ?rm’s cash ?ows. Thus, a share of stock is desired by
an individual because of the chance it will provide a payoff contingent on some future
state-of-the-world (SOW). A standard treatment of the problem is given in Hirshleifer
and Riley (2002). Let Z
as
denote the income from asset a ¼ 1, 2 in SOW, s ¼ 1, 2. Asset
prices are denoted by P
A
1
and P
A
2
and their quantities by q
1
and q
2
. The (representative)
investor’s budget constraint in asset units is given by:
W ¼ P
A
1
q
1
þ P
A
2
q
2
: ð1Þ
If the individual is endowed with asset quantities q
1
and q
2
and wealth
W then the
individual’s state-claims (c
1
, c
2
) re?ect payoffs from the two-asset portfolio:
c
1
c
2
_ _
¼ k
1
W
P
A
1
Z
11
Z
12
_ _
þ k
2
W
P
A
2
Z
21
Z
22
_ _
ð2Þ
where k
i
, i ¼ 1, 2 denote wealth-shares in assets 1 and 2 with k
1
þ k
2
¼ 1. Complete
markets in tradable assets exist if the market system allows trading in all elementary
state-claims. Let p
1
; p
2
denote subjective probability beliefs of an investor over two
SOW. The investor’s portfolio choice problem is then given by:
k
1
;k
2
max EU ¼ p
1
yðc
1
Þ þp
2
yðc
2
Þ subject to : ð3Þ
c
1
¼ k
1
W
P
A
1
Z
11
þ k
2
W
P
A
2
Z
21
ð¼ q
1
Z
11
þ q
2
Z
21
Þ ð4Þ
Regulating noisy
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c
2
¼ k
1
W
P
A
1
Z
12
þ k
2
W
P
A
2
Z
22
ð¼ q
1
Z
12
þ q
2
Z
22
Þ ð5Þ
k
1
þ k
2
¼ 1: ð6Þ
In this set-up optimal risk, bearing requires the investor equalize the expected marginal
utility per dollar held (invested) in each asset (fundamental theorem of risk bearing):
P
A
2
P
A
1
¼
p
1
y
0
ðc
1
ÞZ
21
þp
2
y
0
ðc
2
ÞZ
22
p
1
y
0
ðc
1
ÞZ
11
þp
2
y
0
ðc
2
ÞZ
12
: ð7Þ
For expositional purposes, assume asset 2 (risky asset) has payoffs ðZ
21
; Z
22
Þ ¼ ð4; 0Þ
and price P
A
2
, while asset 1 (risk-free numeraire) has payoffs ðZ
11
; Z
12
Þ ¼ ð1; 1Þ and
price P
A
1
. Under these assumptions, the fundamental theorem of risk bearing is
represented by:
P
A
2
P
A
1
¼
4
1 þf
_ _
; f ¼
p
2
y
0
ðc
2
Þ
p
1
y
0
ðc
1
Þ
; c
1
¼ q
1
þ 4q
2
c
2
¼ q
1
: ð8Þ
Increasing the odds of failure, i.e. " ðp
2
=p
1
Þ or # ðp
1
=p
2
Þ, implies a higher f-value
consistent with a lower share price P
A
2
relative to the risk-free asset price P
A
1
.
Essentially, increased risk of a zero-payoff is priced into the asset, depending on the
shareholder’s marginal rate of substitution between state-contingent income claims. We
use a numerical example to consider the in?uence of information on investors taking
long or short positions in the stock.
Numerical example
The investor’s choice problem is examined numerically assuming exponential
preferences over state-claims yðc
i
Þ ¼ 1 2e
2Ac
i
where A denotes constant absolute risk
aversion (CARA). In this case, the optimal risk-bearing condition becomes:
P
A
2
P
A
1
¼
4
1 þ ðp
2
=p
1
Þe
Aðc
1
2c
2
Þ
¼
4
1 þ ðp
2
=p
1
Þe
A4q
2
: ð9Þ
Taking the natural log and rearranging terms yields the following investment decision
rule:
q
2
¼
1
4A
ln
p
1
p
2
_ _
4P
A
1
P
A
2
21
_ _ _ _
: ð10Þ
Whether the agent takes a long or short position in the risky asset (q
2
. 0 or q
2
, 0)
depends on the agent’s probability beliefs and risk aversion. Arisk-free trading portfolio
implies asset demand q
2
¼ 0, corresponding to the “certainty state-claims.” Long
positions are taken based on probability beliefs p
2
, p
1
, otherwise short positions are
taken. By shorting the agent assumes a liability in SOW1, i.e. jq
2
Z
21
j ¼ 4jq
2
j. Increased
CARA reduces the size of the positions taken (either long or short), as the individual
becomes less responsive to given changes in the odds of failure. Further consideration
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of this argument is given in a market-clearing model allowing for rational and
non-rational investment behavior. The market equilibrium takes the form of a “noisy
rational expectations equilibrium” to the extent noise trading is active[3].
Noise traders, information, and market-clearing
As Black (1986) put it, noise traders are agents who “trade on noise rather than
information.” Accordingly, noise traders (denoted by N) follow a “non-Bayesian”
approach in forming expectations; that is, they systematically violate Bayes’ Rule in
predicting the ?rm’s prospects for survival. For example, noise traders would place
market orders to sell shares at lower prices, ignoring information regarding ?rm
fundamentals. For reasons of tractability, suppose noise traders are risk neutral and
apply the following ad hoc decision rule in taking short positions:
q
N
3
¼ bln
4
P
A
2
_ _
; where b . 0: ð11Þ
Clearly, no rational investor (Bayesian agent) would follow this “dumb-money” trading
strategy. Instead, we assume rational investors (denoted by superscript R) follow a
Bayesian process in forming their beliefs. The decision rules governing investment are
de?ned by equation (10), depending on risk preferences ðA
R
1
; A
R
2
Þ and probability beliefs
ðp
1
=p
2
Þ
R1
; ðp
1
=p
2
Þ
R2
:
q
R
1
¼
1
4 A
R
1
ln
p
1
p
2
_ _
R1
4
P
A
2
21
_ _ _ _
; q
R
2
¼
1
4 A
R
2
ln
p
1
p
2
_ _
R2
4
P
A
2
21
_ _ _ _
: ð12Þ
Referring to Table I, assume rational investors have common prior beliefs
p
1
¼ p
2
¼ 0:5. To allow for divergent beliefs, each SOW is interpreted as having a
given likelihood of occurring, depending on a noisy signal of the ?rm’s prospects
(positive or negative). Assume the signal is conditioned by the degree of noise trading in
the market as characterized in the likelihood matrix. If the true SOW is non-failure then
a positive signal corresponds to a 60 percent chance of non-failure; a negative signal
corresponds to a 40 percent chance of failure. Alternatively, if the true SOW is failure,
then a positive signal implies a 20 percent chance of non-failure while a negative signal
implies an 80 percent chance of failure. Applying Bayes theorem, the positive signal
results in a posterior distribution (0.75, 0.25), while a negative signal results in the
posterior distribution (0.33, 0.67). The implications for market clearing are considered
below in the presence of noise traders.
Likelihood
matrix Joint (pr.) Posterior (pr.)
Noisy signal Noisy signal Noisy signal
States-of-the-world Good Bad Good Bad Prior (Pr.) Good Bad
SOW1: non-failure 0.6 0.4 1.0 0.3 0.2 0.5 0.75 0.33
SOW2: failure 0.2 0.8 1.0 0.1 0.4 0.5 0.25 0.67
0.4 0.6 1.0 1.0 1.0
Table I.
Bayesian probability
analysis
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Market clearing with noise traders
In the absence of monopoly power over the stock price, we can assume agents treat
price as parametric and submit excess demand schedules for the stock to a “Walrasian
auctioneer”[4]. The market-clearing price balances the volume of long and short
positions, thereby re?ecting informed and uninformed probability beliefs, risk
aversion, and the degree of noise trading in the market, a:
n
1
q
R
1
þa n
2
q
R
2
_ _
þ ð1 2aÞn
3
q
N
3
¼ 0: ð13Þ
Table II summarizes relationships among the various model parameters. If Bayesian
investors have common priors p
1
¼ p
2
¼ 0:5, then they only take long positions in the
market. Consequently, the short side of the market consists entirely of noise traders,
with the market-clearing price decreasing in the degree of noise and the degree of risk
aversion. The bottom portion of the table summarizes the same relationships assuming
some agents incorporate bad news in revising their prior beliefs. In this informative
case, short-sellers consist of rational and non-rational agents, and the market-clearing
price decreases further as rational short-sellers become better-informed of ?rm
fundamentals.
What emerges from the above analysis is a noisy rational expectations hypothesis
about the nature of short-selling behavior and stock price adjustments. From a policy
perspective, this relationship can be regulated by imposing constraints on either
short-sellers themselves (a ban), or on short-sale transaction prices (a price test). An
empirical look at these policy measures follows based on the SEC’s recent ban on
short-selling ?nancial stocks.
3. Empirical analysis
The SEC (2008c) ban on “naked” short-selling was motivated by the potential to “cause
sudden and excessive ?uctuations of security prices, thereby impairing the operation
of fair and orderly markets”[5]. Thus, on July 15, 2008, the SEC announced regulations
Degree of
noise Risk aversion
Rational long
traders (q
R
1
)
Rational short
traders (q
R
2
)
Short noise
traders (q
N
3
)
Market-clearing
price (P
*
)
Priors R1 : p
1
¼ p
2
¼ 1=2
R2 : p
1
¼ p
2
¼ 1=2
a ¼ 0:1 A ¼ 0.25 0.0374 0.0337 0.0712 1.96
A ¼ 0.30 0.0377 0.0339 0.0716 1.95
a ¼ 0:5 A ¼ 0.25 0.2812 0.1406 0.4218 1.72
A ¼ 0.30 0.2953 0.1476 0.4429 1.65
a ¼ 0:9 A ¼ 0.25 1.1925 0.1190 1.3110 0.93
A ¼ 0.30 2.4150 0.2415 2.6500 0.21
Posteriors R1 : p
1
¼ 1=2; p
2
¼ 1=2
R2 : p
1
¼ 1=3; p
2
¼ 2=3
a ¼ 0:1 A ¼ 0.25 0.3828 20.2927 0.0903 1.62
A ¼ 0.30 0.3273 20.2365 0.0908 1.61
a ¼ 0:5 A ¼ 0.25 0.5769 20.0656 0.5113 1.44
A ¼ 0.30 0.5576 20.0163 0.5413 1.35
a ¼ 0:9 A ¼ 0.25 1.3716 0.0663 1.4379 0.81
A ¼ 0.30 3.5682 0.2978 3.8661 0.05
Table II.
Market-clearing
relationships
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banning naked short-selling in Fannie Mae (FNM), Freddie Mac (FRE) and 17 other
?nancial stocks (effective July 21 to August 12). The regulations were expanded on
September 18, prohibiting all short-selling in an additional 780 ?nancial stocks
(effective September 19 to October 8). Finally on July 27, 2009, the emergency rule
banning the practice of naked short-selling was made permanent[6]. To study the
price-effects of the ban, we use simple regressions, EGARCH analysis (Nelson, 1991),
and simulated price behavior under a hypothetical uptick rule. We focus on the 25 most
shorted stocks on the NYSE and NYSE ACRA for which short-selling was prohibited
on July 15, 2008. Presumably, increased short interest re?ected beliefs that stock values
would fall further (SEC 2008a, b).
We take an initial look at the empirical relationship between short interest and stock
price behavior using ordinary least squares (OLS) regressions around the time of the
July 15 announcement. Table III identi?es the initial sample of ?rms and their symbols,
the amounts of short interest and stock prices for the months of July and August, and
the percentage of the stock shorted. We are interested in the coef?cient of correlation
between short interest and stock prices ðr ¼
??????
R
2
p
Þ, and the OLS parameter estimates
for short interest. Thus, to avoid measurement bias with autocorrelations or spuriously
in?ated correlations, we regress percentage changes in short interest (%DS) on
percentage changes in stock prices (%DP). The bottom of Table III reports regression
results for three sample periods: a six-week period overlapping the announcement ( July
1 2008 to August 16, 2008), and a two- and four-week period before and after the
announcement ( July 1 2008 to 16, 2008 and July 16 2008 to August 16, 2008)[7].
The OLS estimates of the short interest parameter (%DS ¼ 21.19, 20.68) indicate
the inverse relationship between short interest and stock returns weakened following
the regulatory announcement. Correspondingly, the correlation value between the two
variables ðr ¼
??????
R
2
p
Þ dropped from 0.66 to 0.32. The results also indicate that daily
stock returns tended to increase after the ban was imposed, as shown by the upward
shift in the constant term (from 20.04 to 0.15) and increase in statistical signi?cance
(t-statistics from 21.36 to 3.22)[8]. Nonetheless, the average return to an equally
weighted portfolio of the most shorted stocks was approximately 26 percent over the
two-month period ( July-August), with a standard deviation of 27 percent[9].
The continuation of “falling security prices” and “excessive price ?uctuations”
motivated the SEC to ban all short-selling of nearly 800 ?nancial stocks, effective
September 19, 2008. We examine how the expanded ban affected daily stock returns
ðR
t
Þ and their volatility for our working sample using EGARCH models. EGARCH
models measure the log of the conditional variance of stock returns ðlog s
2
t
Þ as a
weighted average of the long-run variance ð4Þ, the log of the variance for the previous
period (the GARCH term, log s
2
t21
), and any new information revealed through the
previous error in predicting mean returns (the ARCH term containing 1
t21
). We
estimate the following EGARCH (1, 1) model for each ?rm in our working sample:
R
t
¼ c þ1
t
ð14Þ
log s
2
t
¼ 4þblog s
2
t21
þg
1
t21
s
t21
þa
j1
t21
j
s
t21
ð15Þ
where 4; b; g and a are constant parameters. The EGARCH process ensures the
conditional variance of stock returns is positive without ad hoc restrictions on the
model parameters.
Regulating noisy
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We assume market participants identify “good news” as a signal of increased stock
returns (positive shocks, 1
t21
. 0) and “bad news” as a signal of lower returns
(negative shocks, 1
t21
, 0). Thus, a previous shock of good news contributes
to current volatility with ða þgÞj1
t21
j=js
t21
j, and a previous shock of bad news with
ða 2gÞj1
t21
j=s
t21
. When g ¼ 0, it follows positive and negative shocks have
symmetric effects on volatility; and when g , 0 negative shocks generate more
Short interest in
million
Stock price in
million
Firm (symbol) July 2008
August
2008
Percentage of
stock shorted
July 1,
2008
August
29, 2008
Washington Mutual,
Inc. (WM) 338.6 382.4 22.4 5.25 4.05
Ford Motor Co. (F) 311.3 320.8 14.7 4.71 4.46
Wachovia Corp. (WB) 271.9 269.1 12.5 16.13 15.89
Fannie Mae (FNM) 141.4 182.7 17.0 19.59 6.84
Wells Fargo & Co. (WFC) 165.8 176.1 5.3 24.12 30.27
National City Corp. (NCC) 161.7 166.1 21.8 4.60 5.04
Freddie Mac (FRE) 118.6 158.5 24.5 16.21 4.51
Citigroup, Inc. (C) 149.6 150.3 2.8 17.13 18.99
General Motors Corp. (GM) 143.1 146.2 25.8 11.75 10.00
Bank of America Corp. (BAC) 112.8 117.5 2.6 23.81 31.14
Advanced Micro Devices
Inc. (AMD) 93.4 96.4 15.9 5.65 6.29
Regions Financial Corp. (RF) 90.2 91.4 13.2 11.59 9.27
Ambac Financial Group
Inc. (ABK) 83.5 91.0 31.7 1.18 7.16
BB&T Corp. (BBT) 84.8 90.3 16.4 23.97 30.00
American Intl. Group Inc. AIG) 78.7 85.8 3.2 26.73 21.49
Micron Technology Inc. (MU) 85.8 85.2 11.2 5.79 4.24
MBIA Inc. (MBI) 86.1 83.6 30.6 4.28 16.22
Sprint Nextel Corp. (S) 88.5 82.7 3.0 8.83 8.72
U.S. Bancorp. (USB) 76.5 79.2 4.6 28.40 31.86
Coeur d’Alene Mines Corp.
(CDE) 72.8 77.1 14.0 2.81 1.79
Lehman Bros. Holdings
Inc. (LEH) 70.6 76.9 11.1 20.96 16.09
Capital One Financial Corp.
(COF) 73.7 73.5 19.6 40.14 44.14
The Colonial BancGroup
Inc. (CNB) 70.1 72.0 35.6 4.96 6.32
The Walt Disney Co. (DIS) 72.6 71.2 3.8 31.05 32.35
Synovus Financial
Corp. (SNV) 65.0 69.7 21.1 9.10 9.20
OLS regression results
Constant
term t-statistic %DS t-statistic R
2
r
July 1 2008 to August 16, 2008 0.0855 1.7815 21.6815 23.7234 0.3976 0.6306
Pre-SEC ban: July 1 2008 to 16,
2008 20.0431 21.3556 21.1928 23.9891 0.43111 0.6565
Post-SEC ban: July 16 2008 to
August 16, 2008 0.1500 3.2223 20.6782 21.5484 0.1025 0.3201
Table III.
Short interest and stock
prices on the NYSE
July-August, 2008
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volatility than positive shocks, so bad news is said to have a “leverage effect.” The
“persistence” of volatility following a news shock is captured by b !1: as beta tends to
unity volatility becomes more persistent, indicating slower mean reversion.
We study how the expanded ban affected volatility persistence and leverage by
comparing EGARCH parameter estimates for two periods: a 125-day period before
September 19 and a 125-day period after October 18. Table IV reports summary
statistics for the cross-sectional time series of closing prices ( p) and daily stock returns
(R)[10]. The coef?cient of variation gives a simple indication of the degree of
randomness, combining a measure of central tendency (sample mean, m) with a
measure dispersion (sample standard deviation, s), i.e. CV ¼ s/m. The CV statistics for
closing prices and the percent-change in closing prices suggests there was an increase
in price dispersion after the expanded ban on short-selling was imposed.
Table V reports the maximum-likelihood estimates for the EGARCH models.
The statistically signi?cant parameter estimates are denoted by asterisks (
*
95 and
**
99 percent levels).
Tables VI and VII identify ?rms by changes in their volatility persistence and
leverage effect parameters (b and g). We consider cases where persistence or leverage
remained about the same after introduction of the wide-spread ban, and cases where
persistence or leverage changed. We differentiate among the latter category according
to whether persistence or leverage became stronger or weaker.
Columns 1 and 2 in Table VI list ?rms for which volatility persistence was roughly
unchanged after the wide-spread ban was imposed. Non-persistence is relatively rare,
limited to AMD, FNM, and FRE. Strong persistence is more common, as seen in AIG,
Bank of America (BAC), CP, CDE, F, GM, US Bancorp (USB), and WFC[11]. Columns 3
and 4 list ?rms, which experienced change in volatility persistence. Persistence became
stronger for DIS, MU, RF, and S, and became weaker for BBT, COF, ABK, CNB, and
SNV. Accordingly, the expanded ban may have dampened volatility persistence in ?ve
out of 21 cases studied.
Columns 1 and 2 in Table VII list ?rms whose leverage effects seem unchanged by
the wide-spread ban: ?ve ?rms had no leverage effects (AMD, CNB, COF, F, and GM);
and four ?rms had strong leverage effects (CP, RF, USB, and WFC). Column 3 lists
?rms where the leverage effects became stronger (ABK, CDE, and MU), implying bad
news began having a greater impact on volatility than good news. Column 4 lists ?rms
where leverage effects became weaker (AIG, BAC, BBT, and SNV), with bad news
having less impact on price volatility[12]. Finally, Column 5 reports several cases
Variable
Sample
period
Average
mean
Average
min
Average
max
Average
SD CV
Closing prices (P ) Before 17.35 9.85 23.88 3.66 0.21
After 7.96 3.56 13.86 2.74 0.34
Percent-change closing
prices
Before
After
20.0043
2 0.0057
20.3899
2 0.3155
0.2318
0.3099
0.0714
0.0991
216.50
2 17.43
Notes: The summary statistics are averages, calculated over the sample means from the cross-
sectional time series; the CV statistics are calculated as the ratio of the average standard deviation and
the average of the sample means
Table IV.
Summary statistics for
second event sample
Regulating noisy
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1
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v
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n
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2
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0
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7
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1
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6
1
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2
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9
0
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2
4
6
0
.
0
9
6
0
.
7
7
6
(
c
o
n
t
i
n
u
e
d
)
Table V.
EGARCH (1, 1) parameter
estimates
JFEP
1,3
236
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
3
6
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
F
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r
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&
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a
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e
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F
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&
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o
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F
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2
0
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1
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2
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4
.
6
1
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2
4
9
*
*
-
7
.
2
9
1
N
o
t
e
s
:
z
-
s
t
a
t
i
s
t
i
c
s
;
t
h
e
s
t
a
t
i
s
t
i
c
a
l
s
i
g
n
i
?
c
a
n
c
e
l
e
v
e
l
s
o
f
t
h
e
b
e
t
a
p
a
r
a
m
e
t
e
r
s
:
*
9
5
a
n
d
*
*
9
9
p
e
r
c
e
n
t
l
e
v
e
l
s
Table V.
Regulating noisy
short-selling of
troubled ?rms?
237
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
3
6
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
where good news generated more volatility than bad news: FNM in both periods, FRE
in the second period, and Disney and MBIA Inc. in the ?rst period.
We complete our empirical analysis of short-selling policy with a simulation of price
adjustments under a hypothetical “uptick rule.” An uptick rule, such as 10-a1, is akin to
a regulated price in executing short sales. The argument for its use rests on promoting
more ef?cient pricing of securities under speculative attack. On the NYSE, short sales
would only be transacted on a plus tick (uptick) or a “zero-plus tick”, i.e. a price higher
than the last price, or a price equal to the last price but higher than the last different
price. For example, a short sale could be executed at $4 if the previous price sequence
(beginning with the oldest price) is 3.875, 3.875 and 4. However, if the previous price
sequence is 4.125, 4.125 and 4, then a trade at $4 would be on a “zero-minus tick” and
not allowed.
Non-existent Remained strong Became strong Became weak Other
Advanced Micro
Devices Inc. (AMD)
American Intl.
Group Inc. (AIG)
The Walt Disney
Co. (DIS)
BB&T Corp. (BBT) MBIA Inc.
(MBI)
Fannie Mae (FNM)
Bank of America
Corp. (BAC)
Micron Tech. Inc.
(MU)
Capital One Fin. Corp.
(COF)
Freddie Mac (FRE)
Canadian Paci?c
Rail. Ltd (CP)
Regions Financial
Corp. (RF)
Ambac Financial
Group Inc. (ABK)
Coer d’Alene Mines
Corp. (CDE)
Sprint Nextel
Corp. (S)
The Colonial Banc
Group Inc. (CNB)
Ford Motor Co. (F) Synovus Financial
Corp. (SNV)
General Motors
Corp. (GM)
US Bancorp (USB)
Wells Fargo & Co.
(WFC)
Table VI.
Persistence of volatility
before and after
expanded ban
Non-existent
Remained
strong Became strong Became weak Other
Advanced Micro
Devices Inc. (AMD)
(CP) Ambac Financial
Group Inc. (ABK)
American Intl.
Group Inc. (AIG)
MBIA Inc.
(MBI)
The Colonial Banc
Group Inc. (CNB)
Regions
Financial Corp.
(RF)
Coer d’Alene Mines
Corp. (CDE)
Bank of America
Corp. (BAC)
The Walt
Disney Co.
(DIS)
Capital One Fin.
Corp. (COF)
US Bancorp
(USB)
Micron Tech. Inc.
(MU)
BB&T Corp.
(BBT)
Fannie Mae
(FNM)
Ford Motor Co. (F) Wells Fargo &
Co. (WFC)
Synovus Financial
Corp. (SNV)
Freddie Mac
(FRE)
General Motors
Corp. (GM)
Sprint Nextel Corp. (S)
Table VII.
Leverage effect before
and after expanded ban
JFEP
1,3
238
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
3
6
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
We simulate the affect of imposing price tests on four ?rms drawn from our
working sample: BAC, FNM, FRE, and USB[13]. We assume the security prices follow
?rm-speci?c stochastic processes subject to the suspension of dividend payments to
shareholders:
DP
P
¼ mDt þs1
?????
Dt
p
: ð16Þ
where DP=P is the proportional return provided by the stock in time interval Dt; mDt is
the expected value of the return; and s1
?????
Dt
p
is the stochastic component of the return.
We assume short-selling in the underlying stock constitutes one-?fth of trading
activity, implying the uptick rule applies in 20 percent of the simulations. Random
“news shocks” are introduced using normally- and Cauchy-distributed 1-values[14], in
conjunction with ?rm-speci?c estimates for drift and volatility (m and s) derived from
the EGARCH analysis (i.e. the parameter sets c; 4; a; b; g)[15]. The simulation period
covers 44 days of stock trading.
Figure 1(a)-(d) shows differences in simulated prices with and without an uptick rule
under the normal distribution. Figure 2(a)-(d) shows simulation results under the
Cauchy distribution. We consider price performance for two sample-periods
corresponding to the EGARCH parameter sets. The simulated prices are drawn
using quotes to the nearest $1/8 if the price is above $3 and $1/16 if the price is at or
below $3 (standard tick sizes on US stock exchanges). Since we are interested in price
differentials with and without the uptick rule (price spreads), we illustrate all
Figure 1.
Uptick rule simulations
under normally
distributed “news shocks”
–0.8
–0.6
–0.4
–0.2
0.0
0.2
0.4
0.6
50 100 150
(a) (b)
(c) (d)
200 250 300 350
50 100 150 200 250 300 350
0.00
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0.10
0.15
0.20
0.25
0.30
0.35
0.40
50 100 150 200 250 300 350
50 100 150 200 250 300 350
–0.06
–0.04
–0.02
0.00
0.02
0.04
0.06
FREN 1 FREN 2
BACN 1 BACN 2
USBN 1 USBN 2
FNMN 1 FNMN 2
–1.6
–1.2
–0.8
–0.4
0.0
0.4
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simulations beginning with a common spread value of zero. Thus, as the trials
progress positive values imply the regulated price exceeded the free market price,
creating a positive spread. Negative values imply the uptick rule was ineffective at
supporting the simulated price.
Figure 1(a) shows results for BAC prices under the normal distribution. The solid
line (BACN1) re?ects EGARCH parameters from the ?rst observation period (before
the wide-spread ban), and the dotted line (BACN2) from the second observation period
(after the ban was introduced). The simulations suggest the uptick rule provides more
stable price-support under the second set of BAC parameters. Figure 1(b) and (d)
shows the same policy impact for FNM and USB: the uptick rule gives more stable
price support under the second set of EGARCH parameters. Conversely, the price
simulations for FRE show the uptick rule giving more stable price-support under
the ?rst set of parameters.
Figure 2(a)-(d) shows the performance of the uptick rule under the Cauchy process.
Here, the price support function behaves more randomly, most likely due to the
heavy-tail properties of the Cauchy distribution. Figure 2(a) shows the case of BAC.
Here, again the uptick rule provides more certain price support over the second
observation period, and Figure 2(b) and (d) again show similar (albeit noisier) policy
performance for FNM and USB. Figure 2(c) shows a somewhat different policy impact
for FRE, with prices generally supported in both observation periods, though more
randomly.
Figure 2.
Uptick rule simulations
under Cauchy-distributed
“news shocks”
–0.4
0.0
0.4
0.8
1.2
1.6
2.0
50 100 150 200 250 300 350
50 100 150 200 250 300 350
–0.5
–0.4
–0.3
–0.2
–0.1
0.0
0.1
0.2
50 100 150 200 250 300 350
50 100 150 200 250 300 350
–0.2
–0.1
0.0
0.1
0.2
0.3
0.4
0.5
–1.6
–1.2
–0.8
–0.4
0.0
0.4
FREC 1 FREC 2
BACC 1 BACC 2
USBC 1 USBC 2
FNMC 1
FNMC 2
(a) (b)
(c) (d)
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The various simulations provide some support for the argument that uptick rules
can be effective constraints on noise-driven short-selling, potentially contributing to a
more rational price discovery process. However, at least two key quali?cations stand in
the way of offering general conclusions. First, the EGARCH results show ?rm-speci?c
volatility varies across ?rms according to persistence and leverage, and the presence or
absence of quantity constraints on short-selling. Second, our simulation analysis is
somewhat simpli?ed in ignoring the potential for dynamic “feedback effects” between
price volatility and the degree of short interest in troubled ?rms. Nonetheless, the
results obtained suggest a blanket uptick rule has disparate impacts on price stability,
depending on the ?rm-speci?c parameters that govern the stochastic process.
4. Concluding remarks
On July 27, 2009, the SEC made permanent the order prohibiting the practice of naked
short-selling of certain ?nancial stocks. Previously, the SEC banned all short-selling of
nearly 800 stocks. To help maintain liquidity, certain exceptions were made for
registered market makers. The SEC has also considered reinstating “uptick rule” 10a-1,
which prohibits short-selling securities on a downtick. These policy measures were
taken to moderate “sudden and excessive ?uctuations in security prices.” In taking
these steps, regulators noted that:
[. . .] sudden price declines give rise to questions about the underlying ?nancial conditions of
an issuer, which in turn can create a crises of con?dence without a fundamental underlying
basis. This crisis of con?dence can impair the liquidity and ultimate viability of an issuer,
with potentially broad market consequences (SEC, 2008c).
Important cost-bene?t questions arise in regulating short-selling, since high levels of
short interest re?ect beliefs that share values will fall further. Whether these beliefs
re?ect fundamental information is a focal point of the present study. Certainly, “bad
news” concerning a troubled ?rm motivates rational short and long sellers to post the
same shares at the same time, thus exacerbating negative price pressure. Clearly, if
agents are free to short-sell then share prices will tend to re?ect relatively more
pessimistic beliefs of the ?rms’ prospects. Interestingly, a study by the Of?ce of
Economic Analysis (2008) found “long-sellers” (who sell their own stock) were the
primary cause of price drops during the recent high-volatility periods in US markets.
The observation of falling prices during high-volatility periods coincides with the
predictions given by our noisy rational expectations model, wherein some agents are
rational sellers. Under free-market conditions, our model predicts the equilibrium
price decreases in the degree of noise trading and investor risk aversion, with rational
and non-rational agents taking short positions in troubled ?rms. Imposing a sales
constraint under these conditions results in less-informed beliefs regarding ?rm
fundamentals to the extent “informed traders” withdraw from the market[16]. Hence,
the SEC’s exception of registered market-makers was important in terms of ensuring
the provision of liquidity to rational arbitrageurs, who otherwise might have
withdrawn from shrinking securities markets.
Our empirical analysis of short-selling constraints focuses on price volatility,
employing simple regressions, EGARCH analysis and simulated price behavior
under a hypothetical uptick rule. The EGARCH results suggest short-selling
constraints had non-uniform impacts on the persistence and leverage effects associated
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with price volatility. Moreover, the corresponding price simulations indicate a
hypothetical uptick rule might have helped stabilize price behavior in some cases,
depending on the nature of the stochastic process and whether or not quantity
constraints on short-selling were binding. Consequently, our ?ndings indicate blanket
uptick rules are prone to some degree of failure in supporting stock valuations, given
the wide-ranging response to news observed in our sample of troubled ?rms.
Based on our ?ndings, we are inclined to join the chorus of ?nancial economists
arguing for a “focused approach” to market regulation. As described here, the “focused
approach” corresponds more closely with the SEC’s interpretation of a “security-speci?c,
temporary approach” as opposed to a “market-wide, permanent approach” (SEC, 2009).
In these regards, our ?ndings support recent policy prescriptions outlined in Avgouleas
(2010), which call for selective use of price limits and disclosure of short-selling positions.
These policy measures are capable of discouraging trend chasing (herding) without
compromising “informed trading” – that is to say, not impeding arbitrage or confounding
probability beliefs regarding ?rm survival.
En ?n, we remind the reader of Milton Friedman’s persuasive argument, that
non-rational traders who persist in selling a truly underpriced security will eventually
lose money to better-informed traders, along with their in?uence over price. But this
assumes better-informed traders are not constrained from participating in markets.
Notes
1. The US uptick rule (10a-1) was adopted in 1938 following an inquiry into the effects of
concentrated short-selling during the market break of 1937. The Securities and Exchange
Commission (SEC, 2007) eliminated the rule on July 6, noting that price test restrictions
“modestly reduce liquidity and do not appear necessary to prevent market manipulation”.
2. See Avgouleas (2010, pp. 21-6) for a comprehensive survey of empirical literature identifying
various forms of ef?ciency bene?ts from short-selling, see Bris et al. (2007).
3. See O’Hara (1994) for a discussion of the “noisy rational expectations framework,” esp.
Chapter 6.
4. Note that the total stock of the risky asset is treated as being zero. An alternative would be to
treat the aggregate supply of the risky asset as a random variable. However, as noted by
Hirshleifer and Riley (2002), this approach is not easily justi?able in many contexts
(Section 7.3).
5. “Naked” short-selling occurs when sellers do not even borrow the underlying shares before
selling them and then look to cover their positions sometime after the sale.
6. Importantly, the permanent ruling requires that brokers must promptly buy or borrow the
underlying security to deliver on a short sale.
7. The SEC “emergency action” temporarily banned investors from short-selling 799 ?nancial
?rms (and a few others closely related to the ?nancial sector). This expanded regulation
followed the bankruptcy of Lehman Bros. and ?nancial disclosures by American Intl. Group.
The policy actions also ushered in the debate over the “too big to fail” argument for ?nancial
regulation. See Helwege (2009) for an insightful discussion of these events.
8. This ?nding is in accord with observations reported by Boehmer et al. (2008a, b), which ?nd
an initial bounce in share prices on NYSE-listed stocks subject to the early ban. A similar
bounce was reported by FSA (2009) comparing returns on FTSE-traded stocks.
9. That heavily shorted stocks tend to exhibit negative returns is well-documented in previous
studies, e.g. Desai et al. (2002).
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10. Relative to the initial sample of ?rms our working sample excludes Washington Mutual,
Lehman Bros, Citigroup, Natl. City Corp., and the Wachovia Group. Statistics for all of the
remaining ?rms are reported in Table AI in the Appendix.
11. The observation of no signi?cant changes in volatility persistence coincides with
observations reported by the FSA (2009) in comparing returns for the FTSE 350 over
pre- and post-ban periods.
12. This observation is consistent with the argument that unencumbered short-selling allows
markets to adjust faster to “bad news,”, e.g. see Bai et al. (2006).
13. Referring to Table V, two of the ?rms show strong persistence and leverage effect in both
sample periods (BAC and USB); the other two show non-persistence and “good news” adding
volatility (FNM and FRE) in both periods.
14. Cauchy distributions look similar to normal distributions, but with much heavier tails. Thus,
when studying hypothesis tests that assume normality, the Cauchy distribution is a good
indicator of how sensitive the tests are to so-called “heavy-tail departures from normality.”
15. We compute epsilon values at each tick under normal and Cauchy distributions by “mixing”
the initial sigma from the EGARCH with pseudo-randomness generated through a
“Mersenne Twister” (MT19937). The resulting normally- or Cauchy-distributed epsilon is
then applied in obtaining an epsilon for the next tick.
16. Boehmer et al. (2008a, b) provide empirical evidence that short-sellers tend to be
well-informed and trade-on fundamentals.
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Corresponding author
Carlos A. Ulibarri can be contacted at: [email protected]
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Table AI.
Summary statistics
for prices and
percent-changes in prices
before/after trade ban
Regulating noisy
short-selling of
troubled ?rms?
245
D
o
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d
b
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P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
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Y
A
t
2
1
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3
6
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
This article has been cited by:
1. Carlos A. Ulibarri. 2013. Multivariate GARCH analysis of Fannie Mae, Freddie Mac, and American
International Group: Did the short-selling ban reduce systemic return-risk?. The North American Journal
of Economics and Finance 25, 60-69. [CrossRef]
2. Michael Devaney, William L. Weber. 2013. Short?sell moratorium effects on regional bank performance.
Journal of Financial Economic Policy 5:2, 92-110. [Abstract] [Full Text] [PDF]
3. Michael Devaney. 2012. Financial crisis, REIT short-sell restrictions and event induced volatility. The
Quarterly Review of Economics and Finance 52, 219-226. [CrossRef]
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doc_976785154.pdf