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# CAPM Model

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Term Report                                                                                                   Corporate Finance

Capital Asset Pricing Model (CAPM)

The Capital Asset Pricing Model (CAPM) is used in finance to determine a theoretically appropriate required rate of return (and thus the price if expected cash flows can be estimated) of an asset, if that asset is to be added to an already well-diversified portfolio, given that asset's non-diversifiable risk. The CAPM formula takes into account the asset's sensitivity to non-diversifiable risk (also known as systematic risk or market risk), often represented by the quantity beta (β) in the financial industry, as well as the expected return of the market and the expected return of a theoretical risk-free asset

The Formula

The CAPM is a model for pricing an individual security (asset) or a portfolio. For individual security perspective, we made use of the security market line (SML) and its relation to expected return and systematic risk (beta) to show how the market must price individual securities in relation to their security risk class. The SML enables us to calculate the reward-to-risk ratio for any security in relation to that of the overall market. Therefore, when the expected rate of return for any security is deflated by its beta coefficient, the reward-to-risk ratio for any individual security in the market is equal to the market reward-to-risk ratio, thus:

Individual security’ / beta        =       Market’s securities (portfolio)

Reward-to-risk ratio                          Reward-to-risk ratio

The market reward-to-risk ratio is effectively the market risk premium and by rearranging the above equation and solving for (Ri), we obtain the Capital Asset Pricing Model (CAPM).

Where:

• Ri - is the expected return on the capital asset
• Rf - is the risk-free rate of interest
• β - (the beta coefficient) the sensitivity of the asset returns to market returns, or also ,
• Rm - is the expected return of the market
• (Rm – Rf) - is sometimes known as the market premium or risk premium.

Assumptions of CAPM

• All investors have rational expectations.
• There are no arbitrage opportunities.
• Returns are distributed normally.
• Fixed quantity of assets.
• Perfectly efficient capital markets.
• Investors are solely concerned with level and uncertainty of future wealth
• Separation of financial and production sectors.
• Thus, production plans are fixed.
• Risk-free rates exist with limitless borrowing capacity and universal access.
• The Risk-free borrowing and lending rates are equal.
• No inflation and no change in the level of interest rate exists.
• Perfect information, hence all investors have the same expectations about security returns for any given time period.

CAPM is the theory of the relationship between risk and return which states that the expected risk premium on any security equals its beta times the market risk Premium.

Expected Risk Premium=Beta X Market Risk Premium

Ri   =   beta x (Rm – Rf)

Where

Ri is the risk-adjusted discount rate (also known as the Cost of Capital);
Rf is the rate of a "risk-free" investment.
Rmis the return rate of a market benchmark.

The CAPM assumes that the Stock market is dominated by well diversified investors who are concerned only with market risk. That makes sense in a stock market where trading is dominated by large institutions and even small investor can diversify at very low cost. The Security Market Line shows that how expected rate of return depends upon Beta. According to CAPM, expected rates of return for all securities and all portfolios lie on this line.

Beta

The Beta coefficient, in terms of finance and investing, is a measure of a stock (or portfolio)’s volatility in relation to the rest of the market. Beta is calculated for individual companies using regression analysis.

The beta coefficient is a key parameter in the capital asset pricing model (CAPM). It measures the part of the asset's statistical variance that cannot be mitigated by the diversification provided by the portfolio of many risky assets, because it is correlated with the return of the other assets that are in the portfolio.

The Formula for the Beta of an asset within a portfolio is

βA = Cov(ra,rp) / Var (rp)

Where ra measures the rate of return of the asset, rp measures the rate of return of the portfolio of which the asset is a part and Cov(ra,rp) is the covariance between the rates of return. In the CAPM formulation, the portfolio is the market portfolio that contains all risky assets, and so the rp terms in the formula are replaced by rm, the rate of return of the market.

Beta is also referred to as financial elasticity or correlated relative volatility, and can be referred to as a measure of the asset's sensitivity of the asset's returns to market returns, its non-diversifiable risk, its systematic risk or market risk. On an individual asset level, measuring beta can give clues to volatility and liquidity in the marketplace. On a portfolio level, measuring beta is thought to separate a manager's skill from his or her willingness to take risk.

Investing

By definition, the market itself has an underlying beta of 1.0, and individual stocks are ranked according to how much they deviate from the macro market. A stock that swings more than the market (i.e. more volatile) over time has a beta above 1.0. If a stock moves less than the market, the stock's beta is less than 1.0.

Higher-beta stocks mean greater volatility and are therefore considered to be riskier, but are in turn supposed to provide a potential for higher returns; low-beta stocks pose less risk but also lower returns. In the same way a stock's beta shows its relation to market shifts, it also is used as an indicator for required returns on investment (ROI). If the market with a beta of 1 has an expected return increase of 8%, a stock with a beta of 1.5 should increase return by 12%.

Extreme and Interesting Cases

• Beta has no upper or lower bound, and betas as large as 3 or 4 will occur with highly volatile stocks.
• Beta can be zero. Some zero-beta securities are risk-free, such as treasury bonds and cash. However, simply because a beta is zero does NOT mean that it is risk free. A beta can be zero simply because the correlation between that item and the market is zero
• A negative beta simply means that the stock is inversely correlated with the market.
• A negative beta might occur even when both the benchmark index and the stock under consideration have positive returns. It is possible that lower positive returns of the index coincide with higher positive returns of the stock, or vice versa. The slope of the regression line, i.e. the beta, in such a case will be negative.

Coefficient of Correlation

The coefficient of correlation indicates an association between two variables.

The formula is:

Where

rxy is the correlation between X and Y

COV(X, Y) the covariance between X and Y

stdxis the standard deviation of X

The value of rxy is always between -1 and 1.

• The value -1 represents a perfect negative correlation (when one increases, the other decreases in exactly the same proportion.
• The value +1 represents a perfect correlation (when one increases, the other increases in exactly the same proportion.
• The value 0 represents a lack of correlation.

You can find an illustration of the correlation in the above graphs.

PAKISTAN TELECOMMUNICATION COMPANY LIMITED

Calculation of Beta: -

Graph:-

Explanation: -

The Company Stock that we have used in our research is PTCL (Pakistan Telecommunication Company Limited). It has a beta of 0.75. This suggests that change of 1% in market return will lead to change of 0.75% in stock (PTCL) return. The beta of stock (PTCL) is high because there is more risk is involved in it & there is no portfolio diversification available.

Capital Asset Pricing Model (CAPM): -

By making an analysis of the actual return on the stock and mutual fund with these respective returns derived through Capital Asset Pricing Model, we come to the conclusion that CAPM can be applied in our stock market only if we consider investing in stocks.

 Period Years Months Market Return (Rm) T-bill(Rf) Beta(B) Actual Returns PTCL CAPM ReturnsRf + B(Rm-Rf) 1 2002 1st January 33.89% 1.54% 0.75 26.10% 25.80% 2 2002 1st July 51.33% 1.97% 0.75 51.60% 38.99% 3 2003 1st January 27.60% 2.15% 0.75 9.42% 21.24% 4 2003 1st July 30.27% 1.93% 0.75 28.82% 23.19% 5 2004 1st January 18.02% 2.25% 0.75 15.01% 14.08% 6 2004 1st July 16.28% 2.47% 0.75 4.86% 12.83% 7 2005 1st January 19.77% 4.03% 0.75 49.21% 15.84% 8 2005 1st July 28.03% 7.91% 0.75 -0.83% 23.00% 9 2006 1st January 3.28% 8.31% 0.75 -37.92% 4.54% 10 2006 1st July 4.74% 8.54% 0.75 9.11% 5.69% 11 2007 1st January 36.82% 8.00% 0.75 28.67% 29.61% 12 2007 1st July 0.49% 8.94% 0.75 -22.02% 2.61%

Calculation for Coefficient of Correlation:-

 Actual Returns PTCL CAPM Returns 26.10% 25.80% 51.60% 38.99% 9.42% 21.24% 28.82% 23.19% 15.01% 14.08% 4.86% 12.83% 49.21% 15.84% -0.83% 23.00% -37.92% 4.54% 9.11% 5.69% 28.67% 29.61% -22.02% 2.61%

Coefficient of Correlation = 0.736178

Explanation:

Here we see that the correlation is strong here. The conclusion will be that although Beta is a very important function to measure the market risk and it provides with a good picture about the expected return on the stock but sometimes there is a lack of clear air in the estimated model. It is very important to mention here that the expected and the actual returns always differ. There is no such thing as a perfect measure of returns. Market uncertainty is always there.

We have come to this conclusion after analyzing it through coefficient of correlation between actual return and return through CAPM for stock is 0.736. As per our knowledge the coefficient of correlation ranges between -1 and +1. As the correlation is 0.736, it means that there is a strong relation between actual return and CAPM return on stock.

JS-BSBF EQUITY FUND

Fund Performance

The net income of the Fund for the year ended June 30, 2007, including unrealized gain on investment, was Rs. 658.483 million, which works out to Rs. 5.55 per share (2006: Rs. 4.42 per share) of the par value of Rs. 10.

The net assets of the Fund as on June 30, 2007 were Rs. 2.152 billion compared to Rs. 1.789 billion on June 30, 2006. The increase in net assets, including the cash dividends of Rs. 296.437 million paid during the year, comes to Rs. 659.62 million or 36.9%.

The Fund has paid two interim cash dividends during the year aggregating Rs. 2.50 (or 25%) per share. The interim cash dividends of Rs. 296.437 million comes to 45% of the net income for the year including the unrealized capital gain. As this dividend is more than 90% of the Fund’s net income excluding the realized capital gains for the year; therefore, the income of the Fund will not be subject to income tax under Clause 99 of Part 1 of the 2nd Schedule of the Tax Ordinance, 2001.

Non-Banking Finance Companies (Establishment & Regulation) Rules, 2003 provides that “a security listed on a stock exchange shall be valued at its last sale price on such exchange on the date on which it is valued or if such exchange is not open on such date, then at its last sale price on the next preceding date on which such exchange was open and if no sale is reported for such date the security shall be valued at an amount neither higher than the closing asked price nor lower than the closing bid price”.

TFCs quoted on the stock exchange are neither actively traded on the exchange nor the quotes available are indicative of fair value of the underlying security. According to the guidelines of IAS-39, to reflect the reliable measure of fair value to Term Finance Certificates, the Management Company has adopted policy of valuation of TFCs based on the average quotes available from reputable brokerage houses dealing in money market transactions.

Investment Objective and Strategy

The Fund maintains a mix of equities and debt instruments. Earnings comprise of capital appreciation, dividend income, and interest income. The portfolio seeks capital growth through investments in marketable securities with better-than-average appreciation potential and liberal dividend policies.

Fund and Investment Adviser Rating

The Pakistan Credit Rating Agency (PACRA) has assigned a 5-Star fund rating to BSJS Balanced Fund Limited, which reflects a good performance relative to its peers. The rating is a composite measure of two factors namely a) returns, and b) risk associated with the returns measured by Sharpe Ratio.

PACRA has awarded an “AM2+” asset manager rating to JS ABAMCO Limited (JS ABAMCO) to “AM2+”. The rating denotes the company’s very strong capacity to manage the risks inherent in asset management and the asset manager meets very high investment management industry standards and benchmarks.

 Period Year Month Market Rate Return (KSE 100) JS-BSBF Rate Return 1 2002 1st January 33.89% 1% 30th June 2 2002 1st July 51.33% 41% 31st December 3 2003 1st January 27.60% 77% 30th June 4 2003 1st July 30.27% -33% 31st December 5 2004 1st January 18.02% 4% 30th June 6 2004 1st July 16.28% -12% 31st December 7 2005 1st January 19.77% -19% 30th June 8 2005 1st July 28.03% 64% 31st December 9 2006 1st January 3.28% -10% 30th June 10 2006 1st July 4.74% -6% 31st December 11 2007 1st January 36.82% 13% 30th June 12 2007 1st July 0.49% 7% 30th November

Calculation for Beta:

Graph: -

Explanation: -

The well diversified portfolio of closed ended mutual fund used in our research is JS-BSBF Equity Fund. The Beta of the Mutual fund is 0.38. This suggests that change of 1% in market return will lead to change of 0.38% in stock (JS-BSBF) return. The Beta of Mutual Fund (JS-BSBF) is lower than PTCL stock because mutual fund is a pool of money invested by many investors. These are investments wide variety of securities and therefore the portfolio is diversified. The risk attached to mutual fund is low relatively to that of stock.

Capital Asset Pricing Model (CAPM): -

 Period Years Months Market Return (Rm) T-bill(Rf) Beta(B) JS-BSBF Actual Returns CAPM ReturnsRf + B(Rm-Rf) 1 2002 1st January 33.89% 1.54% 0.38 1.12% 13.83% 2 2002 1st July 51.33% 1.97% 0.38 40.55% 20.73% 3 2003 1st January 27.60% 2.15% 0.38 76.52% 11.82% 4 2003 1st July 30.27% 1.93% 0.38 -32.58% 12.70% 5 2004 1st January 18.02% 2.25% 0.38 4.07% 8.24% 6 2004 1st July 16.28% 2.47% 0.38 -11.82% 7.72% 7 2005 1st January 19.77% 4.03% 0.38 -18.72% 10.01% 8 2005 1st July 28.03% 7.91% 0.38 63.64% 15.55% 9 2006 1st January 3.28% 8.31% 0.38 -10.00% 6.40% 10 2006 1st July 4.74% 8.54% 0.38 -6.17% 7.09% 11 2007 1st January 36.82% 8.00% 0.38 13.16% 18.95% 12 2007 1st July 0.49% 8.94% 0.38 7.36% 5.73%

Calculation for Coefficient of Correlation:-

Explanation:

Here we see that the correlation is not strong at all. The conclusion will be that although Beta is a very important function to measure the market risk and it provides with a good picture about the expected return on the stock but sometimes there is a lack of clear air in the estimated model. It is very important to mention here that the expected and the actual returns always differ. There is no such thing as a perfect measure of returns. Market uncertainty is always there.

As per our findings the coefficient of correlation of actual return and CAPM return of JS-BSBF balanced mutual fund is 0.445. This suggests that both the returns have a weak correlation therefore our findings suggest that CAPM model dose not work as efficiently for the mutual fund as it does stocks.

Conclusion

The data and findings given in the report suggests that the beta for stock/shares is higher the beta for investments in well diversified portfolio such as mutual funds. The stock is more sensitive to changes in the stock market. The return on stock varies greatly with the variations in the market returns.

For instance if there are two  investors, Investor A and Investor B. Investor A wishes to invest in a stock (PTCL) and investor B wants to invest in mutual fund, a closed ended mutual fund      (JS-BSBF). By looking at the best fit line on the scattered plots the investor A finds that the beta of its stock is 0.75 this suggests to him that his stock is a risky stock and hence the investor A will demand a higher rate of return suggested by CAPM. Investor B by looking at its best fit line finds out that his mutual fund has a beta of 0.38, which is relatively low than that of investor A’s PTCL stock. This beta suggests to investor B that his mutual fund is not as risky as the PTCL’s stock, and therefore will demand a lower rate of return.

The security with a higher beta will have a higher risk premium and the security with a lower beta will have a lower risk premium.

The data and findings in the report suggest that the beta for stocks/shares is higher then beta for investment in well diversified portfolio such as mutual funds. The stocks are more sensitive to changes in the stock market. The return on stock varies greatly with the variation in the market returns.

Appendix 1: Market Returns Semi-Annually From 2002-2007

 Market Rate of Return Period Year Month Index Points Rate of Return 1 2002 1st January 1322.06 33.89% 30th June 1770.11 2 2002 1st July 1785.14 51.33% 31st December 2701.41 3 2003 1st January 2666.53 27.60% 30th June 3402.47 4 2003 1st July 3432.55 30.27% 31st December 4471.60 5 2004 1st January 4473.02 18.02% 30th June 5279.18 6 2004 1st July 5347.72 16.28% 31st December 6218.40 7 2005 1st January 6220.28 19.77% 30th June 7450.12 8 2005 1st July 7464.60 28.03% 31st December 9556.61 9 2006 1st January 9672.47 3.28% 30th June 9989.41 10 2006 1st July 9603.65 4.74% 31st December 10058.46 11 2007 1st January 10066.32 36.82% 30th June 13772.46 12 2007 1st July 13929.70 0.49% 30th November 13998.52

Appendix 2: PTCL Prices & Rate of Returns Semi-Annually From 2002-2007

 PTCL Rate of Return Period Year Month Price Return 1 2002 1st January 13.60 26.10% 30th June 17.15 2 2002 1st July 17.15 51.60% 31st December 26.00 3 2003 1st January 26.00 9.42% 30th June 28.45 4 2003 1st July 28.45 28.82% 31st December 36.65 5 2004 1st January 36.65 15.01% 30th June 42.15 6 2004 1st July 42.15 4.86% 31st December 44.20 7 2005 1st January 44.20 49.21% 30th June 65.95 8 2005 1st July 65.95 -0.83% 31st December 65.40 9 2006 1st January 65.40 -37.92% 30th June 40.60 10 2006 1st July 40.60 9.11% 31st December 44.30 11 2007 1st January 44.30 28.67% 30th June 57.00 12 2007 1st July 57.00 -22.02% 30th November 44.45

Appendix 3: JS-BSBF Equity Fund Prices & Rate of Returns Semi-Annually From 2002-2007

 JS-BSBF Equity Rate of Return Period Year Month Price Return 1 2002 1st January 6.54 1.12% 30th June 6.61 2 2002 1st July 6.61 40.55% 31st December 9.29 3 2003 1st January 9.29 76.52% 30th June 16.40 4 2003 1st July 16.40 -32.58% 31st December 11.06 5 2004 1st January 11.06 4.07% 30th June 11.51 6 2004 1st July 11.51 -11.82% 31st December 10.15 7 2005 1st January 10.15 -18.72% 30th June 8.25 8 2005 1st July 8.25 63.64% 31st December 13.50 9 2006 1st January 13.50 -10.00% 30th June 12.15 10 2006 1st July 12.15 -6.17% 31st December 11.40 11 2007 1st January 11.40 13.16% 30th June 12.90 12 2007 1st July 12.90 7.36% 30th November 13.85

Appendix 4: 6-Month T-bill Rate of Returns      from 2002-2007

 T-bill Rate Period Year Month Rate 1 2002 1st January 1.54 2 2002 1st July 1.97 3 2003 1st January 2.15 4 2003 2nd July 1.93 5 2004 1st January 2.25 6 2004 2nd July 2.47 7 2005 1st January 4.03 8 2005 2nd July 7.91 9 2006 3rd January 8.31 10 2006 3rd July 8.54 11 2007 3rd January 8.00 12 2007 3rd July 8.94 10.72

Bibliography

• Mr. Kashif Rafi

Vice President, Js Investment

• Asif Ali Qureshi

Head of Research, Invisor securities

• Qazi Waqas Ahmed

Research Analysit; the Financial Daily

• www.thefinancialdaily.com
•  www.fma.com

Official web-site for Financial Market Association

• www.berecorder.com
• www.jsil.com
• www.ptcl.com.pk

Pakistan Telecommunication Company Limited.

.

Institute of Business Management

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