The beta coefficient is a key parameter in the (CAPM). It measures the part of the asset's statistical that cannot be mitigated by the provided by the portfolio of many risky assets, because it is 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 or correlated relative , and can be referred to as a measure of the asset's sensitivity of the 's returns to market returns, its non-diversifiable , its or market risk. On an individual asset level, measuring beta can give clues to and 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
stdx is the 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.
Calculation for Coefficient of Correlation:-
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.
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): -
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
Appendix 2: PTCL Prices & Rate of Returns Semi-Annually From 2002-2007
Appendix 3: JS-BSBF Equity Fund Prices & Rate of Returns Semi-Annually From 2002-2007
Appendix 4: 6-Month T-bill Rate of Returns from 2002-2007
Bibliography
Vice President, Js Investment
Head of Research, Invisor securities
Research Analysit; the Financial Daily
- www.thefinancialdaily.com
Official web-site for Financial Market Association
Pakistan Telecommunication Company Limited.
.
Institute of Business Management