Description
Financial risk is an umbrella term for multiple types of risk associated with financing, including financial transactions that include company loans in risk of default.
CASE STUDY ON OPTIMIZATION OF PORTFOLIO RISK AND RETURN
CONTENTS
CHAPTER – I : : : : CHAPTER – II : * * * * * Introduction Objective of Study Methodology Limitations Portfolio and Holding period returns ` Sharpe’s Performance Measure Treynor’s Performance Measure CHAPTER – III : * Analysis and Interpretations 6 13 14 15 16 21 32 44 49 54 55
Conclusion & Suggestions Bibliography
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CHAPTER - I
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INTRODUCTION
Combination of individual assets or securities is a portfolio. Portfolio includes investment in different types of marketable securities or investment papers like shares, debentures stock and bonds etc., from different companies or institution held by individuals firms or corporate units and portfolio management refers to managing securities. Portfolio management is a complex process and has the following seven broad phases. 1. Specification of investment objectives and constraints. 2. Choice of asset mix. 3. Formulation of portfolio strategy. 4. Selection of securities. 5. Portfolio execution. 6. Portfolio rebalancing. 7. Portfolio performance.
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Portfolio Diversification:
An important way to reduce the risk of investing is to diversify your investments. Diversification is akin to “not putting all your eggs in one basket”. For example, if your portfolio only consisted of stocks of technology companies. It would likely face a substantial loss in value if a major event adversely affected the technology industry. There are different ways to diversify a portfolio whose holding are concentrated in one industry. You might invest in the stocks of companies belonging to other industry groups. You might allocate to different categories of stocks, such as growth, value, or income stocks. You might include bonds and cash investments in your asset allocation decisions. Potential bond categories include government, agency municipal and corporate bonds. You might also diversity by investing in foreign stocks and bonds. Diversification requires you to invest din securities whose investment returns do not move together. In other words, their investment returns have a low correlation. The correlation coefficient is used to measure the degree that returns of two securities are related. For example, two stocks whose returns move in lockstep have a coefficient of +1.0. Two stocks whose returns move in exactly the opposite direction have a correlation of -1.0. To
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effectively diversity, you should aim to find investments that have a low or negative correlation. As you increase the number of securities in your portfolio, you reach a point where you’ve likely diversified as much as reasonably possible. Financial planners vary in their views on how many securities you need to have a fully diversified portfolio. Some say it is 10 to 20 securities. Others say it is closer to 30 securities. Mutual funds offer diversification at a lower cost. You can buy no-load mutual funds from an online broker. Often, you can buy shares fund directly from the mutual fund, avoiding a commission altogether.
Asset allocation:
Asset allocation is the process of spreading your investment across the three major asset classes of stocks, bonds and cash. Asset allocation is a very important part of your investment decisionmaking. Professional financial planner frequently point out that asset allocation decisions are responsible for must of your investment return. Asset allocation begins with setting up an initial allocation. First, you should determine your investment profile. Specially, this requires you to assess you investment horizon, risk tolerance, and financial goals: Investment horizon, Also called time horizon your investment horizon is the number of years you to save for a financial goal. Since you’re likely to have more than goal, this means you will have more than one investment horizon. For example, saving for your give-year-daughter’s college has an investment horizon of 12 years. Saving for your retirement in 30 tears has an investment horizon of 30 years. When you retire, you will want to have
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saved a lump sum that is large enough to generate earnings every year until you die risk tolerance. Your risk tolerance is a measure of your willingness to accept a higher degree of risk in exchange for the chance to earn a higher rate or return. This is called the risk-return trade-off. Some of us, naturally, are consevatyi9ve investor, while other are aggressive investors. As a general rule, the younger your are, the higher your risk tolerance and the more aggressive you can be. As a result, you can afford to allocate a higher percentage of your investment to securities with more risk. These include aggressive growth stocks and the mutual funds that invest ion them. A more aggressive allocation is viable because you have more time to recover form a poor year of invest6ment returns. Financial goal, younger and aggressive investor’s allocation, as a general rule, younger and aggressive investors allocate 70% to 100% of their portfolios to stocks, with the remainder in bonds and cash. Conservative investors allocate 40% to 60% in bonds, and the remainder in cash. Moderate investors allocate somewhere between the allocation of aggressive and conservative, to make an initial allocation, you need to build a portfolio of individual securities, mutual funds, or both. In general, mutual funds provide more diversification benefit for the buck. How you choose to precisely allocate among the major asset classes depends, in part, on other factors. For example, if example, if interest rates are expected to rise, you might allocate a greater percentage to money market mutual funds, CDs, or other bank deposits. If rates are headed lower, you may choose to allocate more to stocks or bonds. Financial planners suggest that you rebalance, or reallocate, your portfolio from time to time. They differ in their views on how often you
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should reallocate. It may be once a year or it may be every three to six months. At a minimum, reallocation lets you up date any changes in your investment profile, or to take advantage of a change in interest rates. Rebalancing often involves nothing more than a “fine-tuning” of your current6 allocations. For example, a conservative investor may decide to shift 5% of her portfolio form stocks to cash to take advantage of higher rates that money market funds may be offering.
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-Need -Objective -Methodology
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SPECIFIC INVESTMENT OBJECTIVE AND CONSTRAINS
The first step in the portfolio management process is to specify the one’s investment objectives and constraints. The commonly stated investment goals are:INCOME - To provide a steady income through the regular interest or divided payment. GROWTH -To increase the value of the principal amount through capital appreciation. STABILITY – Since income and growth represent two ways by which return is generated and investment objectives may be expressed in terms of return and risk. An investor will be interested in higher return and lower level risk. However the risk and return go hand to hand, so an investor has to bear a higher level of risk in order to earn a higher return. CONSTRAINTS – An investor should bear in mind the constraints arising our of the following factor. -Liquidity -Taxes -Time horizon -Unique preferences and circumstances
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OBJECTIVES
To construct three portfolios of public sector units, public limited companies and foreign collaboration and fine their ex-post returns and risk for the period of three year. To make a comparative study of the risk-adjusted measure of portfolio performance using the shapre’s and Treynor’s performance indeed under total risk and market risk and market risk situations, by taking ex-post returns for a period of three years.
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METHODOLOGY Using a model consisting of two modules has carried out the work. The first module involves the section of portfolio and the second module involved evaluation of portfolio’s performance. MODULE-1 Securities selection and portfolio construction has been made by taking scripts Public Sector Units, public limited companies and foreign collaboration units. Equal weigtage has been given to industries like shipping, oil&gas and power growth oriented industries like pharmaceuticals, banking and FMCG and technology oriented industries like software and telecommunications.
MODULE – 2 Portfolio performance was evaluated by ranking holding period’s returns under total risk and market risk situation (measured by standard deviation and Beta coefficient) for the period of three years.
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LIMITATIONS
The work has been carried out under the following limitations:
? The all portfolio consist of riskly assets there no risk-free assets. ? Riskly assets consist of equity shares and where as risk-free assets consists of investments in the saving bank account, deposits, treasury bills, bonds etc. ? The holding period for risky assets was for I yr i.e. shares were assumed to be purchased at the first day and sold at the second consecutive day and average return for I yr is considered. ? An equal no of shares i.e. I (one) share of each script is assumed to be purchased form the secondary market. ? Return on the saving bank account is considered as benchmark rate of return. ? All the portfolio has been held constant for the whole period of the three years.
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CHAPTER - II
PORTFOLIOS
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PORTFOLIOS I
NSE CODE BANK OF INDA BHEL HLL M&M SCI SATYAM COMPUTER VSNL GLAXO IBP SAIL BANKINDIA HEL HINDLEVER M&M SCI SATYAMCOMPUTER VSNL GLAXO IBP SAIL
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PORTFOLIO II
NSE CODE UTI BANK TATA POWER ITC ESCORTS VARUNSHIPING WIPRO BHRATI DRREDDYS IPCL TISCL UTIBANK TATAPOWER ITC ESCORTS VARUNSHIP WIPRO BHRATI DRREDDY IPCL TISCO
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PORTFOLIO III
NSE CODE ING VYSYA ABB CADILA MICO BOSH GESHIPPING HUGHES SOFTWARE TATA TELECOM NICOLAS PHARMA ONGC ESSAR STEEL VYSYA BANK ABB CADILA MICO GESHIP HUGHESSOFT TATA TELECOM NICOLASPIR ONGC ESSARGUJ
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HOLDING PERIODS RETURNS:
All the investment is made at a certain period of time. Holding period returns enables an investor to know his returns during that period of time. It can be computed by using the formula:Holding period returns (HPR) = Today’s closing price – Yesterday’s closing price Yesterday’s closing price Holding period returns are used for comparative criterion. Holding period returns can be compared for making an assessment of relative returns.
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MODULE I
HOLDING PERIOD RETURNS
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Portfolio I for 2004-05
Name of the script Face value Dividen d declare d BANK OF INDIA BHEL HLL M&M SCI SATYAM COMP VSNL GLAXO IBP SAIL 10 10 1 10 10 2 10 10 10 10 0 40 300 0 0 0 0 0 100 0 0 4 3 0 0 0 0 7 10 0 Dividen d amount Market price when purchase d 10.5 128.7 222.2 119.2 30.0 243.7 286.2 417.8 294.3 5.7 0 3.11 1.35 0.00 0.00 0.00 0.00 1.68 3.40 0.00 -17.42 40.62 5.84 8.11 98.11 41.24 -20.27 -3.18 119.95 -3.98 -17.42 43.729 7.1901 8.11 98.11 41.24 -20.27 -1.504 123.35 -3.98 %Return on dividend %Return on security Total return
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Return
27.855
Portfolio I for 2005-06
Name of the script Face value Dividend declared Dividend amount Market price when purchased BANK OF INDIA BHEL HLL M&M SCI SATYAM COMP VSNL GLAXO IBP SAIL 10 10 1 10 10 2 10 10 10 10 30 40 300 55 0 110 85 70 140 0 3 4 3 5.5 0 2.2 8.5 7 14 0 26.5 180.8 227.25 112.8 72.55 257 188.5 34.7 891.35 5.65 %Return on dividend 11.32 2.21 1.32 4.88 6.00 0.86 4.51 2.04 1.57 0.00 89.32 24.99 -39.47 -6.52 -20.9 -28.55 -88.61 -6.5 -13.95 71.74 100.6 27.2 -38.14 -1.644 -20.9 -27.69 -84.1 -4.457 -12.38 71.74 %Return on security Total return
Return 1.026
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Portfrolio I for 2006-07
Name of the script Face value Dividend declared Dividend amount Market price when purchased BANK OF INDIA BHEL HLL M&M SCI SATYAM COMP VSNL GLAXO IBP SAIL 10 10 1 10 10 2 10 10 10 10 10 30 300 90 0 140 45 100 0 0 1 3 3 9 0 2.8 45.5 10 0 0 39.35 223.65 149.15 99.1 51.25 173.65 74.3 294.7 199.8 9.05 %Return on dividend 2.541 1.341 2.011 9.082 0.000 1.612 6.057 3.393 0.000 0.000 49.06 107.1 8.43 164.23 109.51 67.29 59.51 77.02 123.8 153.06 51.601 108.44 10.441 173.31 109.51 68.902 65.567 80.413 123.8 153.0 %Return on security Total return
Return 94.505
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PORTFOLIO II FOR 2004-05
Name of the script Face value Dividend declared Dividend amount Market price when purchased UTIBANK TATAPOWER ITC ESORTS VARUNSHIPING WIPRO BHARTI DRREDDY IPCI TISCO 10 10 10 10 10 2 10 5 10 10 0 0 0 10 0 50 0 0 0 0 0 0 0 1 0 1 0 0 0 0 23.7 103.1 625 77.1 11.55 1268.45 44.35 914.95 54.15 115.75 %Return on dividend 0.000 0.000 0.000 1.297 0.000 0.079 0.000 0.000 0.000 0.000 63.82 18.92 -10.19 -10.17 6.63 58.71 -13.12 22.24 52.26 -7.8 63.82 18.92 -10.19 -8.873 6.63 58.789 -13.12 22.24 52.26 -7.8 %Return on security Total return
Return 18.268
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PORTFOLIO II FOR 2005-06
Name of the script Face value Dividend declared Dividend amount Market price when purchased UTIBANK TATAPOWER ITC ESORTS VARUNSHIPING WIPRO BHARTI DRREDDY IPCI TISCO 10 10 10 10 10 2 10 5 10 10 22 65 0 10 0 50 20 100 22.5 80 2.2 6.5 0 1 0 1 2 5 2.25 8 40.7 114.05 706.3 61.15 11.7 1690 38.9 1096.1 87.5 97.85 %Return on dividend 5.40541 5.69925 0 1.63532 0 0.05917 5.14139 0.45616 2.57143 8.17578 2.23 2.27 -8.61 -48.74 -21.4 -22.58 -23.04 -13.5 8.47 35.9 7.6354 7.9693 -8.61 -47.105 -21.4 -22.521 -17.899 -13.044 11.041 44.076 %Return on security Total return
Return
-5.9856
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PORTFOLIO II FOR 2006-07
Name of the script Face value Dividend declared Dividend amount Market price when purchased UTIBANK TATAPOWER ITC ESORTS VARUNSHIPING WIPRO BHARTI DRREDDY IPCI TISCO 10 10 10 10 10 2 10 5 10 10 25 70 200 0 6 200 60 100 25 100 2.5 7 20 0 0.6 4 6 5 2.5 10 39.9 114.1 625.9 35.25 9.2 1231.2 29.1 914.95 83.85 135.1 %Return on dividend 6.26566 6.13497 3.1954 0 6.52174 0.32489 20.6186 0.54648 2.98151 7.40192 150.6 128.11 54.68 76.54 105.49 21.35 183.36 14.92 89.2 112.82 156.83 134.24 57.875 76.54 112.01 21.675 203.98 15.466 92.182 120.22 %Return on security Total return
Return 99.102
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PORT6FOLIO III FOR 2004-05
Name of the script Face value Dividend declared Dividend amount Market price when purchased ING VYSA ABB CADILA MICOBOSH GESHIPPING HUGHES TATATELECOM NICOLAS PHARMA ONGC ESSAR STEEL 10 10 5 100 10 5 10 10 10 10 35 0 0 0 0 40 0 0 140 0 3.5 0 0 0 0 2 0 0 14 0 112.2 238.9 124 2709 25.3 593.25 56.4 295.75 125.65 125.65 %Return on dividend 3.11943 0 0 0 0 0.33713 0 0 11.1421 0 89.95 16.72 11.282 -4.06 22.45 -40.45 139.1 -0.047 87.97 87.97 93.069 16.72 11.28 -4.06 22.45 -40.113 139.1 -0.047 99.112 87.97 %Return on security Total return
Return 42.548
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PORTFOLIO III FOR 2005-06
Name of the script Face value Dividend declared Dividend amount Market price when purchased ING VYSA ABB CADILA MICOBOSH GESHIPPING HUGHES TATATELECOM NICOLAS PHARMA ONGC ESSAR STEEL 10 10 5 100 10 5 10 10 10 10 40 60 70 40 40 40 25 105 130 0 3.5 6 3.5 40 4 2 2.5 10.5 13 0 247.25 263.9 129.55 2387.35 30.75 277.7 171.9 271.05 329.6 329.6 %Return on dividend 1.41557 2.27359 2.70166 1.6755 13.008 0.7202 1.45433 3.87382 3.94417 0 4.77 12.77 -3.31 47.45 25.99 -28.22 47.45 -24.88 13.43 13.43 6.1856 15.044 -0.6083 49.125 38.998 -27.5 48.904 -21.006 17.374 13.43 %Return on security Total return
Return
13.995
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PORTFOLIO III FOR 2006-07
Name of the script Face value Dividend declared Dividend amount Market price when purchased ING VYSA ABB CADILA MICOBOSH GESHIPPING HUGHES TATATELECOM NICOLAS PHARMA ONGC ESSAR STEEL 10 10 5 100 10 5 10 10 10 10 40 60 70 40 40 40 25 105 130 0 3.5 6 3.5 40 4 2 2.5 10.5 13 0 247.25 263.9 129.55 2387.35 30.75 277.7 171.9 271.05 329.6 329.6 %Return on dividend 1.41557 2.27359 2.70166 1.6755 13.0081 0.7202 1.45433 3.87382 3.94417 0 76.28 106.67 144.09 138.36 135.6 117.65 96.37 -24.88 95.26 95.26 77.696 108.94 146.04 140.04 148.61 118.37 97.824 -21.006 99.204 95.26 %Return on security Total return
Return
101.1727
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EX-POST PORTFOLIO RETURNS
YEAR 2005 2006 2007 Ri
PORTFOLIO PORTFOLIO PORTFOLIO I II III 27.85 18.26 42.54 1.02 -5.98 13.99 94.5 99.1 101.17 41.1233333 37.12666667 52.567
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MODULE – II
RISK ADJUSTED MEASUREMENT OF PORTFOLIO PERFORMANCE SHARPE’S PERFORMANCE MEASURE CALCULATIONS OF STANDARD DEVIATION
Risk
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Risk in holding securities is generally associated with the possibility that realized return will be less than returns were expected. The source of such disappointment is the failure of dividends or the fail in security’s prices. Forces that contribute to variation in return, price or dividend const6itures elements of risk. Some influences that are external to the firm, cannot be controlled and affect large number of securities. Other influences are internal to the firm are controllable to all large degree.
Systematic Risk
The systematic risk affects the entire market. Those forces that are uncontrollable external and board in the effect are called sources of systematic risk. Economic, political and sociological changes are sources of systematic risk.
Systematic risk further divided into
-Market Risk -Interest -Purchasing power Risk
Market Risk
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J.C. Francis defined Market risk as that portion of total variability of returned caused by the alternating farces of bull and bear market. When the security index moves upwards haltingly for a significant period of time, it is known as bull market. In the bull market the indeed moves form a low level to the peak. Bear market is just reverse to the bull market. During the bull and bear market more than 80 percent of the securities prices rise or fall along with the stock market indices.
Interest Rate Risk
The rise or fall in the interest rate affects the cost borrowing. When the call money market rate changes. Interest rates not only affect the security traders but also corporate bodies who carry their business on borrowed funds. The cost of borrowing would. Increase and a heavy out flow of profit would take place in the form of interest to the capital borrowed. This lead a reduction in earning per share and a consequent fall in the price of share.
Purchasing power Risk
Variations in the returns are caused also by the loss of purchasing power of currency. Inflation is the reason behind the loss of purchasing power the rise in price penalizes the returns to the investors, and every potential rise in price a risk to the investor.
Unsystematic Risk
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Unsystematic risk is the unique risk, which will be different to different firms. Unsystematic risk stems form managerial inefficiency, technological change in production process, availability of raw material mentioned factors differ form industry to industry, and company to company. They have to be analyzed separately for each industry and firm. Broadly Unsystematic risk can be classified into: -Business risk -Financial risk
Business Risk
It is the portion of the unsystematic risk caused by the operat6in environment of the business.
Financial Risk
Financial risk in a company is associated with the capital structure the company. It refers to the variability of the income to the equity capital to debt capital.
Measurement of Risk
The risk of a portfolio can be measured by using the following measure of risk.
Variability
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Investment risk is associated with the variability of rates of return. The more variable is the return, the more risky the investment. The total variance is the rate of return on a stock around the expected average, which includes both systematic and unsystematic risk. The total risk can be calculated by using the standard deviation. The standard deviation of a set of numbers is the squares root of the square of deviation around the arithmetic average. Ymbolically, the standard deviation can be expressed asð = ? (rit-ri) n-1 Where, ri is the mean return of the portfolio and rit is the return form the portfolio for a particular year
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SHARPE’S PERFORMANCE INDEX:William Sharpe’s of portfolio performance is also known as reward to variability ratio (RVAR). It is simply the ratio of reward, which defined as realized portfolio returns in excess of the risk free rate, to the variability of return measured by the standard deviation relation to total risk assumed by the investor. The measure can be defined follows:RVAR = rp-rf ð Where, rp= the average return for the portfolio (P) during it HPR rf= risk free rate of return during JHPR ð = the standard deviation of the portfolio (P) during HPR
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CAPITAL MARKET LINE
Capital market shows the conditions prevailing in the capital market in terms of expected return and risk. It depicts the equilibrium condition that prevails in the market for efficient portfolio’s consisting of the portfolio of risky asset or risk free asset or both. All combination of risky and risk free portfolio are bounded by the capital market line, and all investors will end up with portfolio somewhere on the capital market line. The capital market is usually derived under the assumptions that there exists a risk a risk-less asset available for investment. It is further assumed that6 investor can borrow or lend as much as desired at the risk free assets with a portfolio or risky assets to obtain the desired risk return combination. Using the capital market line can graphically represent Sharpe’s measure for portfolios. The vertical axis represents the return on the portfolios and the the horizontal axis represents the standard deviation for returns. The vertical intercept is rf. RVAR measures the slope of the line form rf to the portfolio being evaluated. The steeper the line, the higher the slope (RVAR) and the better performance.
TREYNOR’S PERFORMANCE INDEX
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The measure is also referred to as reward to volatility ratios (RVOL). Treynor sough to relate return on a portfolio to its risk. He distinguished between total risk and systematic risk assuming that6 the portfolio is well diversified. In measuring the portfolio performance Treynor introduced the concept of characteristic line. The slope of the characteristics measures the relative volatility of the portfolio’s returns. The slope of this line is the beta co-efficient which is measure of the volatility (or responsiveness) of the portfolio’s returns in relation to those of the market index. Treynors’s ratio is the realized portfolio’s return in excess of the risk-free to the volatility of return as measured by the portfolio beta. RVOT = rp-rf Bp = Average excess return of portfolio (P) Systematic risk for portfolio
SECURITY MAEKET LINE
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The security market line indicates the risk-return trade-off for portfolio and individual securities. Treynor extended his analysis to identify the component of risk that will be compensated by the market. It is known as systematic risk and is commonly measured by the beta. Beta is a measure of risk that applies to all assets and portfolio whether efficient or inefficient. Security market line specifies the relationship between expected return and risk for all assets and portfolios whether efficient or inefficient. The security market is obtained by taking the risk (beta) on the horizontal axis and portfolio return on the vertical axis. The Security market line can be graphically.
E (rm)
SML
rf Beta 1.00
Beta
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Beta is a market risk measure employed primarily in the equity. It measures the systematic risk of a single instrument or an entire portfolio. William Sharp (1964) used the notion in his landmark paper introducing the capital asset pricing model (CAPM). The name “beta” was applied later. Beta describes the sensitivity of an instrument or portfolio to broad market movements. The stock market (represented by an index such s the S&P 500 or 100) is assigned a beta of 1.0. By comparison, a portfolio (or instrument) with a beta of 2.0 will tend to benefit or suffer form broad market moves twice as much as the market overall. The formula for beta is ?XY-(?XY) (?Y) N?X-(?X) Where X is the market return And Y is the security return Both quantities are calculated using simple returns. Beta is generally estimated form historical price time series. For example, 60 trading of simple returns might be used with sample estimators for covariance and variance. It is possible to construct negative beta portfolio beta portfolios. Approaches include. Beta is sometimes used as a measure of a portfolio’s mark risk. This can be misleading because beta does not capture specific risk. Because of specific risk. A portfolio can have a low beta, but still be highly volatile. Ti price fluctuations would simply have a low correlation with those of the overall market. It is said that a security or portfolio having higher beta will perform well provided market has to go up i.e., market indeed.
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Calculation of standard deviation of returns
PORTFOLIO I
Year 2005 2006 2007 Ri= Return 27.85 1.02 94.5 41.123 Di=r-ri -13.273 -40.103 53.377 Di*Di 176.18 1608.3 2849.1 4633.5 S.D 48.133
PORTFOLIO II
Year
2005 2006 2007 Ri=
Return
18.26 -5.98 99.1 37.127
Di=r-ri
-18.867 -43.973
Di*Di
355.95 1858.2 3840.7 6054.8
S.D
55.022
PORTFOLIO III
Year 2005 2006 2007 Return 45.54 13.99 101.17 Di=r-ri -8.0267 -39.577 47.603 Di*Di 64.427 1566.3 2266.1 S.D 44.141
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Ri=
53.567
3896.8
SHARPE PERFORMANCE MEASURE
Avg portfolio Portfolios I II III Return (;p) in % 41.128 37.128 52.57 Risk free Rate
% 5.25 5.25 5.25 Excess return (rp-ri) 35.878 31.878 47.32 Standard Deviation 48.13 55.02 44.14 Sharpe’s Ratio rprt\ 0.745 0.579 1.072 Ranking 2 3 1
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TREYNOR’S PERFORMANCE MEASURE CALCULATION OF BETA
Beta for portfolio I
Year Avg Avg
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Market Return X
X2
Stock Return Y
XY
2004-05 2005-06 2006-07
5.683 -8.827 72.886
32.296 77.916 5890.8
27.855 1.025 123.38
158.3 -9.0477 7334.4
Beta =1.05261
Beta portfolio II
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Year
Avg Market Return X X2
Avg Stock Return Y XY
2004-05 2005-06 2006-07
5.683 -8.827 76.03 72.886
32.296 77.916 5780.6 5890.8
18.267 -5.985 99.102 111.38
103.81 52.83 7534.7 7691.4
Beta =1.210018
Beta for portfolio III
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Year
Avg Market Return X X2
Avg Stock Return Y XY
2004-05 2005-06 2006-07
5.683 -8.827 76.03 72.886
32.296 77.916 5780.6 5890.8
42.548 13.99 101.17 157.71
Beta =0.965732
241.8 -123.49 7692.1 7810.4
TREYNORS PERFOMANCE INDEDX
Portfolio Portfolios Avg Return (rp) Risk free Rate (rf) Beta Risk Premimum Tn Rp-rf ß Ranking
I
41.128
5.25
1.052
35.878
34.1046
2
44
II III
37.128 52.57
5.25 5.25
1.21 0.965
31.878 47.32
26.3455 49.0363
3 1
CHAPTER - III
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ANALYSIS
AND
INTERPRETATIONS
HOLDING PERIOD RETURNS
In THE YEAR 2004 NSE INDEX gained 5.58% returns during the same year portfolio I, II and III has registered a growth of 27.85, 94.50 respectively. Return wise portfolio III emerges as best portfolio subsequently PI and PII During the year 2005 the NSE INDEX registered a negative growth rate of -8.82 during the same year portfolio I II and III has registered return
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of 18.26, -5.98 and 99.10 respectively. Return wise portfolio III performs well and portfolio I and II occupying subsequent position. In the year 2006 he NSE INDEX shows a fabulous growth rate of 76.88 and portfolio I, II and III performed by 42.54, 13.29 and 101.17 and portfolio III emerged as best portfolio subsequently portfolio I and II
OVERALL PERFOMANCE C The overall performance of the market and the portfolios can be shown by taking the arithmetic average of return. For the previously said of three years market has registered growth rate of 24.58. Arithmetic of portfolio I II and III are 41.128, 37.12 and 52.57 respectively. Portfolio III emerges as best performer.
SHARPE’S PERFORMANCE MEASURE Sharpe’s performance measure gives the appropriate return per unit of risk as measured by standard deviation. The reward of variability ratios computed has shown the ex-post return of per unit of risk for the three portfolio’s for the period of three years. The rate of risk of portfolio II is high deviation by 55.02 by an average return of 37.12, similarly the portfolio I has a deviation of 48.13
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with a return or 41.128 and portfolio III with a deviation of 44.14 with an average return of 55.57. Using 5.25 as return on saving bank account as a proxy for the risk free rate and substuting there value in Sharpe’s evaluation portfolio I gives a slope of 0.745, in portfolio I gives a reward of 35.87(41.128-4.25) for bearing a risk of 48.13 making the sharpe’s ratio to 0.745. For every additional 1% risk and investor has as additional pf 0.745 returns for above portfolio. Portfolio II gives a return or 37.12 while the standard deviation was 55.02 using 5% return on the saving account as proxy market shares ratios to 0.579. Therefore for every additional 1% risk investor will earn an additional 0.579 of return. And portfolio II with a return of 52.57 with an standard deviation making Sharpes ratios to 1.072 as additional return.
OVERALLPERFORMANCE
Overall performances of the portfolios are 41.12, 37, 12 and 52.57 respectively. The risk free rate was 5.25. Investing in three portfolios during the same period provide an risk premium of 35.87, 31.87, one 47.32 respectively. For every 1% of additional risk an investor will earn 0.745,
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0.579 and 1.07 of return. Portfolio III outperformed by 1.072 compared with other two portfolios. The investor will earn on return per unit of beta of 34.120, 26.34 and 49.036 by ranking the portfolio shows that portfolio III performs well as compared with other two portfolios.
TREYNOR’S PERFORMANCE MEASURE
Treynor’s performance measure gives appropriate return per unit or firsk as measured by the beta coefficient. Portfolio I,II and II provided a return of 41.12% 37.12% and 52.57% with 1.05% 1.21% and 0.965% as beta coefficient respectively. Treynor’s
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ratios for the three portfolios above the risk free rate of 5.25% were 34.16%26.34%, 49.036% respectively. Investing in portfolio I II and III provides risk premium of 35.87, 31.87 and47.32 for bearing a risk of beta of 1.052% 1.21% and 0.965% receptively. Thus an investor will earn a return per unit of beta of 34.16% 26.34% and 49.03% receptively. Portfolio III emerging as the best performer, portfolio I and II was occupying the subsequent position.
CONCLUSIONS AND SUGGESTIONS
1. Among the three portfolios I II and III, portfolio III gives a highest return with a proportionate risk ( ) of 44% with a return of 52.57%. 2. Portfolio III has outperformed in both sharpe’s and Treynor’s measure.
50
3. It is advisable to invest in portfolio III i.e. foreign collaboration securities in long run and portfolio II i.e. public limited companies in short run because the later is more correlated with the market index. 4. Diversification of portfolios in various projects or securities may reduce high risk and it provides the high wealth to the shareholders. 5. Beta is used to evaluate the risk proper measurement of beta may reduce the high risk and it gives the high risk premium.
Bibliograpohy
? Prasanna Chandra Management) (Security Analysis and Portfolio
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? Avadhani Management) ? Francis and Taylor
(Security Analysis and Portfolio
(Investment Management)
? Graham and Dodd Security Analysis, McGraw Hill
INTERNET SITES: www.nseindia.com www.wikipedia.com www.bseindia.com SEARCH ENGINES: www.google.com
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doc_352504945.doc
Financial risk is an umbrella term for multiple types of risk associated with financing, including financial transactions that include company loans in risk of default.
CASE STUDY ON OPTIMIZATION OF PORTFOLIO RISK AND RETURN
CONTENTS
CHAPTER – I : : : : CHAPTER – II : * * * * * Introduction Objective of Study Methodology Limitations Portfolio and Holding period returns ` Sharpe’s Performance Measure Treynor’s Performance Measure CHAPTER – III : * Analysis and Interpretations 6 13 14 15 16 21 32 44 49 54 55
Conclusion & Suggestions Bibliography
1
CHAPTER - I
2
INTRODUCTION
Combination of individual assets or securities is a portfolio. Portfolio includes investment in different types of marketable securities or investment papers like shares, debentures stock and bonds etc., from different companies or institution held by individuals firms or corporate units and portfolio management refers to managing securities. Portfolio management is a complex process and has the following seven broad phases. 1. Specification of investment objectives and constraints. 2. Choice of asset mix. 3. Formulation of portfolio strategy. 4. Selection of securities. 5. Portfolio execution. 6. Portfolio rebalancing. 7. Portfolio performance.
3
Portfolio Diversification:
An important way to reduce the risk of investing is to diversify your investments. Diversification is akin to “not putting all your eggs in one basket”. For example, if your portfolio only consisted of stocks of technology companies. It would likely face a substantial loss in value if a major event adversely affected the technology industry. There are different ways to diversify a portfolio whose holding are concentrated in one industry. You might invest in the stocks of companies belonging to other industry groups. You might allocate to different categories of stocks, such as growth, value, or income stocks. You might include bonds and cash investments in your asset allocation decisions. Potential bond categories include government, agency municipal and corporate bonds. You might also diversity by investing in foreign stocks and bonds. Diversification requires you to invest din securities whose investment returns do not move together. In other words, their investment returns have a low correlation. The correlation coefficient is used to measure the degree that returns of two securities are related. For example, two stocks whose returns move in lockstep have a coefficient of +1.0. Two stocks whose returns move in exactly the opposite direction have a correlation of -1.0. To
4
effectively diversity, you should aim to find investments that have a low or negative correlation. As you increase the number of securities in your portfolio, you reach a point where you’ve likely diversified as much as reasonably possible. Financial planners vary in their views on how many securities you need to have a fully diversified portfolio. Some say it is 10 to 20 securities. Others say it is closer to 30 securities. Mutual funds offer diversification at a lower cost. You can buy no-load mutual funds from an online broker. Often, you can buy shares fund directly from the mutual fund, avoiding a commission altogether.
Asset allocation:
Asset allocation is the process of spreading your investment across the three major asset classes of stocks, bonds and cash. Asset allocation is a very important part of your investment decisionmaking. Professional financial planner frequently point out that asset allocation decisions are responsible for must of your investment return. Asset allocation begins with setting up an initial allocation. First, you should determine your investment profile. Specially, this requires you to assess you investment horizon, risk tolerance, and financial goals: Investment horizon, Also called time horizon your investment horizon is the number of years you to save for a financial goal. Since you’re likely to have more than goal, this means you will have more than one investment horizon. For example, saving for your give-year-daughter’s college has an investment horizon of 12 years. Saving for your retirement in 30 tears has an investment horizon of 30 years. When you retire, you will want to have
5
saved a lump sum that is large enough to generate earnings every year until you die risk tolerance. Your risk tolerance is a measure of your willingness to accept a higher degree of risk in exchange for the chance to earn a higher rate or return. This is called the risk-return trade-off. Some of us, naturally, are consevatyi9ve investor, while other are aggressive investors. As a general rule, the younger your are, the higher your risk tolerance and the more aggressive you can be. As a result, you can afford to allocate a higher percentage of your investment to securities with more risk. These include aggressive growth stocks and the mutual funds that invest ion them. A more aggressive allocation is viable because you have more time to recover form a poor year of invest6ment returns. Financial goal, younger and aggressive investor’s allocation, as a general rule, younger and aggressive investors allocate 70% to 100% of their portfolios to stocks, with the remainder in bonds and cash. Conservative investors allocate 40% to 60% in bonds, and the remainder in cash. Moderate investors allocate somewhere between the allocation of aggressive and conservative, to make an initial allocation, you need to build a portfolio of individual securities, mutual funds, or both. In general, mutual funds provide more diversification benefit for the buck. How you choose to precisely allocate among the major asset classes depends, in part, on other factors. For example, if example, if interest rates are expected to rise, you might allocate a greater percentage to money market mutual funds, CDs, or other bank deposits. If rates are headed lower, you may choose to allocate more to stocks or bonds. Financial planners suggest that you rebalance, or reallocate, your portfolio from time to time. They differ in their views on how often you
6
should reallocate. It may be once a year or it may be every three to six months. At a minimum, reallocation lets you up date any changes in your investment profile, or to take advantage of a change in interest rates. Rebalancing often involves nothing more than a “fine-tuning” of your current6 allocations. For example, a conservative investor may decide to shift 5% of her portfolio form stocks to cash to take advantage of higher rates that money market funds may be offering.
.
7
-Need -Objective -Methodology
8
SPECIFIC INVESTMENT OBJECTIVE AND CONSTRAINS
The first step in the portfolio management process is to specify the one’s investment objectives and constraints. The commonly stated investment goals are:INCOME - To provide a steady income through the regular interest or divided payment. GROWTH -To increase the value of the principal amount through capital appreciation. STABILITY – Since income and growth represent two ways by which return is generated and investment objectives may be expressed in terms of return and risk. An investor will be interested in higher return and lower level risk. However the risk and return go hand to hand, so an investor has to bear a higher level of risk in order to earn a higher return. CONSTRAINTS – An investor should bear in mind the constraints arising our of the following factor. -Liquidity -Taxes -Time horizon -Unique preferences and circumstances
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OBJECTIVES
To construct three portfolios of public sector units, public limited companies and foreign collaboration and fine their ex-post returns and risk for the period of three year. To make a comparative study of the risk-adjusted measure of portfolio performance using the shapre’s and Treynor’s performance indeed under total risk and market risk and market risk situations, by taking ex-post returns for a period of three years.
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METHODOLOGY Using a model consisting of two modules has carried out the work. The first module involves the section of portfolio and the second module involved evaluation of portfolio’s performance. MODULE-1 Securities selection and portfolio construction has been made by taking scripts Public Sector Units, public limited companies and foreign collaboration units. Equal weigtage has been given to industries like shipping, oil&gas and power growth oriented industries like pharmaceuticals, banking and FMCG and technology oriented industries like software and telecommunications.
MODULE – 2 Portfolio performance was evaluated by ranking holding period’s returns under total risk and market risk situation (measured by standard deviation and Beta coefficient) for the period of three years.
11
LIMITATIONS
The work has been carried out under the following limitations:
? The all portfolio consist of riskly assets there no risk-free assets. ? Riskly assets consist of equity shares and where as risk-free assets consists of investments in the saving bank account, deposits, treasury bills, bonds etc. ? The holding period for risky assets was for I yr i.e. shares were assumed to be purchased at the first day and sold at the second consecutive day and average return for I yr is considered. ? An equal no of shares i.e. I (one) share of each script is assumed to be purchased form the secondary market. ? Return on the saving bank account is considered as benchmark rate of return. ? All the portfolio has been held constant for the whole period of the three years.
12
CHAPTER - II
PORTFOLIOS
13
PORTFOLIOS I
NSE CODE BANK OF INDA BHEL HLL M&M SCI SATYAM COMPUTER VSNL GLAXO IBP SAIL BANKINDIA HEL HINDLEVER M&M SCI SATYAMCOMPUTER VSNL GLAXO IBP SAIL
14
PORTFOLIO II
NSE CODE UTI BANK TATA POWER ITC ESCORTS VARUNSHIPING WIPRO BHRATI DRREDDYS IPCL TISCL UTIBANK TATAPOWER ITC ESCORTS VARUNSHIP WIPRO BHRATI DRREDDY IPCL TISCO
15
PORTFOLIO III
NSE CODE ING VYSYA ABB CADILA MICO BOSH GESHIPPING HUGHES SOFTWARE TATA TELECOM NICOLAS PHARMA ONGC ESSAR STEEL VYSYA BANK ABB CADILA MICO GESHIP HUGHESSOFT TATA TELECOM NICOLASPIR ONGC ESSARGUJ
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HOLDING PERIODS RETURNS:
All the investment is made at a certain period of time. Holding period returns enables an investor to know his returns during that period of time. It can be computed by using the formula:Holding period returns (HPR) = Today’s closing price – Yesterday’s closing price Yesterday’s closing price Holding period returns are used for comparative criterion. Holding period returns can be compared for making an assessment of relative returns.
17
MODULE I
HOLDING PERIOD RETURNS
18
Portfolio I for 2004-05
Name of the script Face value Dividen d declare d BANK OF INDIA BHEL HLL M&M SCI SATYAM COMP VSNL GLAXO IBP SAIL 10 10 1 10 10 2 10 10 10 10 0 40 300 0 0 0 0 0 100 0 0 4 3 0 0 0 0 7 10 0 Dividen d amount Market price when purchase d 10.5 128.7 222.2 119.2 30.0 243.7 286.2 417.8 294.3 5.7 0 3.11 1.35 0.00 0.00 0.00 0.00 1.68 3.40 0.00 -17.42 40.62 5.84 8.11 98.11 41.24 -20.27 -3.18 119.95 -3.98 -17.42 43.729 7.1901 8.11 98.11 41.24 -20.27 -1.504 123.35 -3.98 %Return on dividend %Return on security Total return
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Return
27.855
Portfolio I for 2005-06
Name of the script Face value Dividend declared Dividend amount Market price when purchased BANK OF INDIA BHEL HLL M&M SCI SATYAM COMP VSNL GLAXO IBP SAIL 10 10 1 10 10 2 10 10 10 10 30 40 300 55 0 110 85 70 140 0 3 4 3 5.5 0 2.2 8.5 7 14 0 26.5 180.8 227.25 112.8 72.55 257 188.5 34.7 891.35 5.65 %Return on dividend 11.32 2.21 1.32 4.88 6.00 0.86 4.51 2.04 1.57 0.00 89.32 24.99 -39.47 -6.52 -20.9 -28.55 -88.61 -6.5 -13.95 71.74 100.6 27.2 -38.14 -1.644 -20.9 -27.69 -84.1 -4.457 -12.38 71.74 %Return on security Total return
Return 1.026
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Portfrolio I for 2006-07
Name of the script Face value Dividend declared Dividend amount Market price when purchased BANK OF INDIA BHEL HLL M&M SCI SATYAM COMP VSNL GLAXO IBP SAIL 10 10 1 10 10 2 10 10 10 10 10 30 300 90 0 140 45 100 0 0 1 3 3 9 0 2.8 45.5 10 0 0 39.35 223.65 149.15 99.1 51.25 173.65 74.3 294.7 199.8 9.05 %Return on dividend 2.541 1.341 2.011 9.082 0.000 1.612 6.057 3.393 0.000 0.000 49.06 107.1 8.43 164.23 109.51 67.29 59.51 77.02 123.8 153.06 51.601 108.44 10.441 173.31 109.51 68.902 65.567 80.413 123.8 153.0 %Return on security Total return
Return 94.505
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PORTFOLIO II FOR 2004-05
Name of the script Face value Dividend declared Dividend amount Market price when purchased UTIBANK TATAPOWER ITC ESORTS VARUNSHIPING WIPRO BHARTI DRREDDY IPCI TISCO 10 10 10 10 10 2 10 5 10 10 0 0 0 10 0 50 0 0 0 0 0 0 0 1 0 1 0 0 0 0 23.7 103.1 625 77.1 11.55 1268.45 44.35 914.95 54.15 115.75 %Return on dividend 0.000 0.000 0.000 1.297 0.000 0.079 0.000 0.000 0.000 0.000 63.82 18.92 -10.19 -10.17 6.63 58.71 -13.12 22.24 52.26 -7.8 63.82 18.92 -10.19 -8.873 6.63 58.789 -13.12 22.24 52.26 -7.8 %Return on security Total return
Return 18.268
22
PORTFOLIO II FOR 2005-06
Name of the script Face value Dividend declared Dividend amount Market price when purchased UTIBANK TATAPOWER ITC ESORTS VARUNSHIPING WIPRO BHARTI DRREDDY IPCI TISCO 10 10 10 10 10 2 10 5 10 10 22 65 0 10 0 50 20 100 22.5 80 2.2 6.5 0 1 0 1 2 5 2.25 8 40.7 114.05 706.3 61.15 11.7 1690 38.9 1096.1 87.5 97.85 %Return on dividend 5.40541 5.69925 0 1.63532 0 0.05917 5.14139 0.45616 2.57143 8.17578 2.23 2.27 -8.61 -48.74 -21.4 -22.58 -23.04 -13.5 8.47 35.9 7.6354 7.9693 -8.61 -47.105 -21.4 -22.521 -17.899 -13.044 11.041 44.076 %Return on security Total return
Return
-5.9856
23
PORTFOLIO II FOR 2006-07
Name of the script Face value Dividend declared Dividend amount Market price when purchased UTIBANK TATAPOWER ITC ESORTS VARUNSHIPING WIPRO BHARTI DRREDDY IPCI TISCO 10 10 10 10 10 2 10 5 10 10 25 70 200 0 6 200 60 100 25 100 2.5 7 20 0 0.6 4 6 5 2.5 10 39.9 114.1 625.9 35.25 9.2 1231.2 29.1 914.95 83.85 135.1 %Return on dividend 6.26566 6.13497 3.1954 0 6.52174 0.32489 20.6186 0.54648 2.98151 7.40192 150.6 128.11 54.68 76.54 105.49 21.35 183.36 14.92 89.2 112.82 156.83 134.24 57.875 76.54 112.01 21.675 203.98 15.466 92.182 120.22 %Return on security Total return
Return 99.102
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PORT6FOLIO III FOR 2004-05
Name of the script Face value Dividend declared Dividend amount Market price when purchased ING VYSA ABB CADILA MICOBOSH GESHIPPING HUGHES TATATELECOM NICOLAS PHARMA ONGC ESSAR STEEL 10 10 5 100 10 5 10 10 10 10 35 0 0 0 0 40 0 0 140 0 3.5 0 0 0 0 2 0 0 14 0 112.2 238.9 124 2709 25.3 593.25 56.4 295.75 125.65 125.65 %Return on dividend 3.11943 0 0 0 0 0.33713 0 0 11.1421 0 89.95 16.72 11.282 -4.06 22.45 -40.45 139.1 -0.047 87.97 87.97 93.069 16.72 11.28 -4.06 22.45 -40.113 139.1 -0.047 99.112 87.97 %Return on security Total return
Return 42.548
25
PORTFOLIO III FOR 2005-06
Name of the script Face value Dividend declared Dividend amount Market price when purchased ING VYSA ABB CADILA MICOBOSH GESHIPPING HUGHES TATATELECOM NICOLAS PHARMA ONGC ESSAR STEEL 10 10 5 100 10 5 10 10 10 10 40 60 70 40 40 40 25 105 130 0 3.5 6 3.5 40 4 2 2.5 10.5 13 0 247.25 263.9 129.55 2387.35 30.75 277.7 171.9 271.05 329.6 329.6 %Return on dividend 1.41557 2.27359 2.70166 1.6755 13.008 0.7202 1.45433 3.87382 3.94417 0 4.77 12.77 -3.31 47.45 25.99 -28.22 47.45 -24.88 13.43 13.43 6.1856 15.044 -0.6083 49.125 38.998 -27.5 48.904 -21.006 17.374 13.43 %Return on security Total return
Return
13.995
26
PORTFOLIO III FOR 2006-07
Name of the script Face value Dividend declared Dividend amount Market price when purchased ING VYSA ABB CADILA MICOBOSH GESHIPPING HUGHES TATATELECOM NICOLAS PHARMA ONGC ESSAR STEEL 10 10 5 100 10 5 10 10 10 10 40 60 70 40 40 40 25 105 130 0 3.5 6 3.5 40 4 2 2.5 10.5 13 0 247.25 263.9 129.55 2387.35 30.75 277.7 171.9 271.05 329.6 329.6 %Return on dividend 1.41557 2.27359 2.70166 1.6755 13.0081 0.7202 1.45433 3.87382 3.94417 0 76.28 106.67 144.09 138.36 135.6 117.65 96.37 -24.88 95.26 95.26 77.696 108.94 146.04 140.04 148.61 118.37 97.824 -21.006 99.204 95.26 %Return on security Total return
Return
101.1727
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EX-POST PORTFOLIO RETURNS
YEAR 2005 2006 2007 Ri
PORTFOLIO PORTFOLIO PORTFOLIO I II III 27.85 18.26 42.54 1.02 -5.98 13.99 94.5 99.1 101.17 41.1233333 37.12666667 52.567
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MODULE – II
RISK ADJUSTED MEASUREMENT OF PORTFOLIO PERFORMANCE SHARPE’S PERFORMANCE MEASURE CALCULATIONS OF STANDARD DEVIATION
Risk
29
Risk in holding securities is generally associated with the possibility that realized return will be less than returns were expected. The source of such disappointment is the failure of dividends or the fail in security’s prices. Forces that contribute to variation in return, price or dividend const6itures elements of risk. Some influences that are external to the firm, cannot be controlled and affect large number of securities. Other influences are internal to the firm are controllable to all large degree.
Systematic Risk
The systematic risk affects the entire market. Those forces that are uncontrollable external and board in the effect are called sources of systematic risk. Economic, political and sociological changes are sources of systematic risk.
Systematic risk further divided into
-Market Risk -Interest -Purchasing power Risk
Market Risk
30
J.C. Francis defined Market risk as that portion of total variability of returned caused by the alternating farces of bull and bear market. When the security index moves upwards haltingly for a significant period of time, it is known as bull market. In the bull market the indeed moves form a low level to the peak. Bear market is just reverse to the bull market. During the bull and bear market more than 80 percent of the securities prices rise or fall along with the stock market indices.
Interest Rate Risk
The rise or fall in the interest rate affects the cost borrowing. When the call money market rate changes. Interest rates not only affect the security traders but also corporate bodies who carry their business on borrowed funds. The cost of borrowing would. Increase and a heavy out flow of profit would take place in the form of interest to the capital borrowed. This lead a reduction in earning per share and a consequent fall in the price of share.
Purchasing power Risk
Variations in the returns are caused also by the loss of purchasing power of currency. Inflation is the reason behind the loss of purchasing power the rise in price penalizes the returns to the investors, and every potential rise in price a risk to the investor.
Unsystematic Risk
31
Unsystematic risk is the unique risk, which will be different to different firms. Unsystematic risk stems form managerial inefficiency, technological change in production process, availability of raw material mentioned factors differ form industry to industry, and company to company. They have to be analyzed separately for each industry and firm. Broadly Unsystematic risk can be classified into: -Business risk -Financial risk
Business Risk
It is the portion of the unsystematic risk caused by the operat6in environment of the business.
Financial Risk
Financial risk in a company is associated with the capital structure the company. It refers to the variability of the income to the equity capital to debt capital.
Measurement of Risk
The risk of a portfolio can be measured by using the following measure of risk.
Variability
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Investment risk is associated with the variability of rates of return. The more variable is the return, the more risky the investment. The total variance is the rate of return on a stock around the expected average, which includes both systematic and unsystematic risk. The total risk can be calculated by using the standard deviation. The standard deviation of a set of numbers is the squares root of the square of deviation around the arithmetic average. Ymbolically, the standard deviation can be expressed asð = ? (rit-ri) n-1 Where, ri is the mean return of the portfolio and rit is the return form the portfolio for a particular year
33
SHARPE’S PERFORMANCE INDEX:William Sharpe’s of portfolio performance is also known as reward to variability ratio (RVAR). It is simply the ratio of reward, which defined as realized portfolio returns in excess of the risk free rate, to the variability of return measured by the standard deviation relation to total risk assumed by the investor. The measure can be defined follows:RVAR = rp-rf ð Where, rp= the average return for the portfolio (P) during it HPR rf= risk free rate of return during JHPR ð = the standard deviation of the portfolio (P) during HPR
34
CAPITAL MARKET LINE
Capital market shows the conditions prevailing in the capital market in terms of expected return and risk. It depicts the equilibrium condition that prevails in the market for efficient portfolio’s consisting of the portfolio of risky asset or risk free asset or both. All combination of risky and risk free portfolio are bounded by the capital market line, and all investors will end up with portfolio somewhere on the capital market line. The capital market is usually derived under the assumptions that there exists a risk a risk-less asset available for investment. It is further assumed that6 investor can borrow or lend as much as desired at the risk free assets with a portfolio or risky assets to obtain the desired risk return combination. Using the capital market line can graphically represent Sharpe’s measure for portfolios. The vertical axis represents the return on the portfolios and the the horizontal axis represents the standard deviation for returns. The vertical intercept is rf. RVAR measures the slope of the line form rf to the portfolio being evaluated. The steeper the line, the higher the slope (RVAR) and the better performance.
TREYNOR’S PERFORMANCE INDEX
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The measure is also referred to as reward to volatility ratios (RVOL). Treynor sough to relate return on a portfolio to its risk. He distinguished between total risk and systematic risk assuming that6 the portfolio is well diversified. In measuring the portfolio performance Treynor introduced the concept of characteristic line. The slope of the characteristics measures the relative volatility of the portfolio’s returns. The slope of this line is the beta co-efficient which is measure of the volatility (or responsiveness) of the portfolio’s returns in relation to those of the market index. Treynors’s ratio is the realized portfolio’s return in excess of the risk-free to the volatility of return as measured by the portfolio beta. RVOT = rp-rf Bp = Average excess return of portfolio (P) Systematic risk for portfolio
SECURITY MAEKET LINE
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The security market line indicates the risk-return trade-off for portfolio and individual securities. Treynor extended his analysis to identify the component of risk that will be compensated by the market. It is known as systematic risk and is commonly measured by the beta. Beta is a measure of risk that applies to all assets and portfolio whether efficient or inefficient. Security market line specifies the relationship between expected return and risk for all assets and portfolios whether efficient or inefficient. The security market is obtained by taking the risk (beta) on the horizontal axis and portfolio return on the vertical axis. The Security market line can be graphically.
E (rm)
SML
rf Beta 1.00
Beta
37
Beta is a market risk measure employed primarily in the equity. It measures the systematic risk of a single instrument or an entire portfolio. William Sharp (1964) used the notion in his landmark paper introducing the capital asset pricing model (CAPM). The name “beta” was applied later. Beta describes the sensitivity of an instrument or portfolio to broad market movements. The stock market (represented by an index such s the S&P 500 or 100) is assigned a beta of 1.0. By comparison, a portfolio (or instrument) with a beta of 2.0 will tend to benefit or suffer form broad market moves twice as much as the market overall. The formula for beta is ?XY-(?XY) (?Y) N?X-(?X) Where X is the market return And Y is the security return Both quantities are calculated using simple returns. Beta is generally estimated form historical price time series. For example, 60 trading of simple returns might be used with sample estimators for covariance and variance. It is possible to construct negative beta portfolio beta portfolios. Approaches include. Beta is sometimes used as a measure of a portfolio’s mark risk. This can be misleading because beta does not capture specific risk. Because of specific risk. A portfolio can have a low beta, but still be highly volatile. Ti price fluctuations would simply have a low correlation with those of the overall market. It is said that a security or portfolio having higher beta will perform well provided market has to go up i.e., market indeed.
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Calculation of standard deviation of returns
PORTFOLIO I
Year 2005 2006 2007 Ri= Return 27.85 1.02 94.5 41.123 Di=r-ri -13.273 -40.103 53.377 Di*Di 176.18 1608.3 2849.1 4633.5 S.D 48.133
PORTFOLIO II
Year
2005 2006 2007 Ri=
Return
18.26 -5.98 99.1 37.127
Di=r-ri
-18.867 -43.973
Di*Di
355.95 1858.2 3840.7 6054.8
S.D
55.022
PORTFOLIO III
Year 2005 2006 2007 Return 45.54 13.99 101.17 Di=r-ri -8.0267 -39.577 47.603 Di*Di 64.427 1566.3 2266.1 S.D 44.141
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Ri=
53.567
3896.8
SHARPE PERFORMANCE MEASURE
Avg portfolio Portfolios I II III Return (;p) in % 41.128 37.128 52.57 Risk free Rate
% 5.25 5.25 5.25 Excess return (rp-ri) 35.878 31.878 47.32 Standard Deviation 48.13 55.02 44.14 Sharpe’s Ratio rprt\ 0.745 0.579 1.072 Ranking 2 3 140
TREYNOR’S PERFORMANCE MEASURE CALCULATION OF BETA
Beta for portfolio I
Year Avg Avg
41
Market Return X
X2
Stock Return Y
XY
2004-05 2005-06 2006-07
5.683 -8.827 72.886
32.296 77.916 5890.8
27.855 1.025 123.38
158.3 -9.0477 7334.4
Beta =1.05261
Beta portfolio II
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Year
Avg Market Return X X2
Avg Stock Return Y XY
2004-05 2005-06 2006-07
5.683 -8.827 76.03 72.886
32.296 77.916 5780.6 5890.8
18.267 -5.985 99.102 111.38
103.81 52.83 7534.7 7691.4
Beta =1.210018
Beta for portfolio III
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Year
Avg Market Return X X2
Avg Stock Return Y XY
2004-05 2005-06 2006-07
5.683 -8.827 76.03 72.886
32.296 77.916 5780.6 5890.8
42.548 13.99 101.17 157.71
Beta =0.965732
241.8 -123.49 7692.1 7810.4
TREYNORS PERFOMANCE INDEDX
Portfolio Portfolios Avg Return (rp) Risk free Rate (rf) Beta Risk Premimum Tn Rp-rf ß Ranking
I
41.128
5.25
1.052
35.878
34.1046
2
44
II III
37.128 52.57
5.25 5.25
1.21 0.965
31.878 47.32
26.3455 49.0363
3 1
CHAPTER - III
45
ANALYSIS
AND
INTERPRETATIONS
HOLDING PERIOD RETURNS
In THE YEAR 2004 NSE INDEX gained 5.58% returns during the same year portfolio I, II and III has registered a growth of 27.85, 94.50 respectively. Return wise portfolio III emerges as best portfolio subsequently PI and PII During the year 2005 the NSE INDEX registered a negative growth rate of -8.82 during the same year portfolio I II and III has registered return
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of 18.26, -5.98 and 99.10 respectively. Return wise portfolio III performs well and portfolio I and II occupying subsequent position. In the year 2006 he NSE INDEX shows a fabulous growth rate of 76.88 and portfolio I, II and III performed by 42.54, 13.29 and 101.17 and portfolio III emerged as best portfolio subsequently portfolio I and II
OVERALL PERFOMANCE C The overall performance of the market and the portfolios can be shown by taking the arithmetic average of return. For the previously said of three years market has registered growth rate of 24.58. Arithmetic of portfolio I II and III are 41.128, 37.12 and 52.57 respectively. Portfolio III emerges as best performer.
SHARPE’S PERFORMANCE MEASURE Sharpe’s performance measure gives the appropriate return per unit of risk as measured by standard deviation. The reward of variability ratios computed has shown the ex-post return of per unit of risk for the three portfolio’s for the period of three years. The rate of risk of portfolio II is high deviation by 55.02 by an average return of 37.12, similarly the portfolio I has a deviation of 48.13
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with a return or 41.128 and portfolio III with a deviation of 44.14 with an average return of 55.57. Using 5.25 as return on saving bank account as a proxy for the risk free rate and substuting there value in Sharpe’s evaluation portfolio I gives a slope of 0.745, in portfolio I gives a reward of 35.87(41.128-4.25) for bearing a risk of 48.13 making the sharpe’s ratio to 0.745. For every additional 1% risk and investor has as additional pf 0.745 returns for above portfolio. Portfolio II gives a return or 37.12 while the standard deviation was 55.02 using 5% return on the saving account as proxy market shares ratios to 0.579. Therefore for every additional 1% risk investor will earn an additional 0.579 of return. And portfolio II with a return of 52.57 with an standard deviation making Sharpes ratios to 1.072 as additional return.
OVERALLPERFORMANCE
Overall performances of the portfolios are 41.12, 37, 12 and 52.57 respectively. The risk free rate was 5.25. Investing in three portfolios during the same period provide an risk premium of 35.87, 31.87, one 47.32 respectively. For every 1% of additional risk an investor will earn 0.745,
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0.579 and 1.07 of return. Portfolio III outperformed by 1.072 compared with other two portfolios. The investor will earn on return per unit of beta of 34.120, 26.34 and 49.036 by ranking the portfolio shows that portfolio III performs well as compared with other two portfolios.
TREYNOR’S PERFORMANCE MEASURE
Treynor’s performance measure gives appropriate return per unit or firsk as measured by the beta coefficient. Portfolio I,II and II provided a return of 41.12% 37.12% and 52.57% with 1.05% 1.21% and 0.965% as beta coefficient respectively. Treynor’s
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ratios for the three portfolios above the risk free rate of 5.25% were 34.16%26.34%, 49.036% respectively. Investing in portfolio I II and III provides risk premium of 35.87, 31.87 and47.32 for bearing a risk of beta of 1.052% 1.21% and 0.965% receptively. Thus an investor will earn a return per unit of beta of 34.16% 26.34% and 49.03% receptively. Portfolio III emerging as the best performer, portfolio I and II was occupying the subsequent position.
CONCLUSIONS AND SUGGESTIONS
1. Among the three portfolios I II and III, portfolio III gives a highest return with a proportionate risk ( ) of 44% with a return of 52.57%. 2. Portfolio III has outperformed in both sharpe’s and Treynor’s measure.
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3. It is advisable to invest in portfolio III i.e. foreign collaboration securities in long run and portfolio II i.e. public limited companies in short run because the later is more correlated with the market index. 4. Diversification of portfolios in various projects or securities may reduce high risk and it provides the high wealth to the shareholders. 5. Beta is used to evaluate the risk proper measurement of beta may reduce the high risk and it gives the high risk premium.
Bibliograpohy
? Prasanna Chandra Management) (Security Analysis and Portfolio
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? Avadhani Management) ? Francis and Taylor
(Security Analysis and Portfolio
(Investment Management)
? Graham and Dodd Security Analysis, McGraw Hill
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