About Capital Asset Pricing Model - Case Study Example

Table of Contents Introduction: 2 Assumptions: 2 Portfolio Theory & CAPM: 3 Empirical Evidence: 6 Drawbacks of CAPM: 7 CAPM & Dividend Discount Model: 8 Conclusion: 9 Capital Asset Pricing Model (CAPM) Introduction: Capital Asset Pricing Model (CAPM) has been at the heart of finance and it is the centerpiece of courses pertaining to finance. It has an intuitive appeal and provides a simple way to measure the relationship between risk and return. Unfortunately, the empirical evidences collected over the period of time contradict with the model due to its simplifying assumptions but yet it provides a rational basis for pricing assets. Assumptions: CAPM works under a series of key assumptions. The first assumption is that there are no transaction costs which mean that investors are free to buy and sell assets in the market. CAPM holds that investors are operating in a perfectly capital market and all securities are valued accurately. If we plot the returns on the Security Market Line than none of the returns will be above or below the SML Line. A perfect capital market assumes that information is freely available to all the investors who have homogenous expectations. Figure 1: Security Market Line . Secondly, the model assumes that the assets are infinitely divisible. This assumption emphasizes that investors can take any position in investment. For instance, they can buy $1 worth of stock of Intel Corporation. The third assumption about CAPM is that personal taxes are not present which implies that returns generated in the form of dividends or capital gains are not taxed. The fourth assumption is that individual investors do not have power to affect the prices of stocks by the action of their buying and selling rather it is determined in total by their actions. The fifth assumption is that investors make decision based on expected returns or risk, the other factors such as behavioral finance is not accounted to it. The sixth assumption is that there is no restriction on amount of short sales; individuals are free to conduct as many short sales transaction as possible. The seventh and the most stringent assumption is that investors are given the choice to borrow or lend unlimited amount of money at the risk free rate. The eighth assumption deals with the homogeneity of the investors’ expectations which mean that all the investors have defined their relative period of investment in exactly the same manner. The final assumption withholds that all the assets are marketable whether they be financial or non-financial such as human capital. Portfolio Theory & CAPM: CAPM has its roots build on the model of portfolio developed by Markowitz in late 50’s. According to the Markowitz’s model of “Mean-Variance analysis”, the investors are risk averse and will prefer more return on the same level of risk (Elton & Gruber, 1997). The efficient frontier is the set of all values of expected returns which have a minimal value of risk represented by the standard deviation of assets. Figure 2 describes an efficient frontier for risky assets which starts from the point b and ends at point a. All the points below b are not efficient since they have a lower expected rate of return for the same level or risk. Figure 2: Mean-Variance Efficient Frontier If we assume that risk-free borrowing and lending is allowed than the efficient set turns into a straight line starting from Rf and extending to the point tangent to T. Now the understanding of CAPM is relatively simple. Assuming all the investors have homogenous expectations about returns and risk, than they will have an opportunity set similar to the diagram represented in Figure 2. The portfolio of risky assets at point T will be held by all the investors. If investors with same expectations are investing in the risky portfolio, than it must be the market portfolio. Furthermore, it is necessary that each investor will hold a combination of risk-free and risky asset in its portfolio. According to the portfolio theory, an asset’s systematic risk is measured by its contribution to the risk of the tangent portfolio βT. As an investor holds a completely diversified portfolio, therefore it eliminates his unsystematic risk and is left with only systematic risk. An implication of the portfolio theory is that an asset’s risk premium is directly proportional to its systematic risk. Ri – Rf = βt(Rt – Rf) Thus CAPM can be written in the form of; Ri = Rf +βt(Rt – Rf) The first term in the right hand side of the equation represents assets with zero risk or beta as they are uncorrelated with market. The second term denotes the beta times premium per unit of the beta. Beta represents the volatility of returns of an asset with respect to average market returns. For instance, if a stock has a beta of 2 and if the market moves down by 10% than the stock price reduces by 20% which shows the stock is highly volatile with respect to the market. The premium represents the beta times premium per unit of beta’s risk. CAPM is one of the most significant discoveries in the field of finance. It can determine the expected rate of return on any asset in the economy. The equation also asserts that only systematic risk is a vital factor in determining the expected rate of return. However, there is a serious error or misconception which should be corrected before we move into the next section. Invariably, we will find in the real world that a group of investors holding a security with higher betas have lower returns than a group of investor holding a portfolio of securities with a lower beta. This invalidates the concept of CAPM, since stocks with higher betas are supposed to provide a higher return compared with stocks of lower betas because they are less risky. However, CAPM validates the concept by stressing that the stocks with lower betas will not provide higher rate of return during all periodic intervals. Since they are more risky therefore they will provide a lower rate of return during some periods. But, if we take a longer horizon into account, than on average they will produce higher rate of returns. Empirical Evidence: Unfortunately, the empirical evidence does not validate the model of CAPM developed by Sharpe and Lintner despite its theoretical feasibility. Empirical evidence shows that the relationship between beta and average return is flatter in nature as opposed to the CAPM model developed by Sharpe and Lintner (Fama & French, 2003). The practical results show that CAPM exaggerates the rate of returns for high beta stocks and it underestimates the low beta stocks (Fama & French). Betas of individual stocks are highly dependent on three factors; cyclicality of revenues, financial leverage and operating leverage. Empirical evidence shows that financial leverage which is determined by the debt to equity ratio has a profound impact on the beta of the stock. This requires a further adjustment in estimating the cost of capital using CAPM for a stock which is highly leveraged. However, the traditional analysis more focused towards cross sectional analysis where a sample of firms from a specific country was taken and a regression model was developed to find the impact of financial leverage on the beta. The study conducted by (Faff, Brooks, & Kee) investigated the impact of financial leverage on the betas of firms using a time series analysis which had its own advantages over cross sectional analysis. The time series model delivers a higher level of statistical power which is not present in cross-sectional analysis. The findings revealed that the estimated unlevered beta produced by time-series approach is close to the theoretically implied unlevered beta but the mean difference across the sample of 348 US Stocks was statistically significant. Another principal finding of the study was that due care needs to be taken for high D/E ratio firms as they are over-penalized the beta while only firms with low D/E ratios seem to have the justified leverage adjustments. Another study conducted by (Morreli, 1997) aimed to understand what role does beta, size and and Book to Market ratio play as a contributor to risk and the realized returns on the securities. The article states that traditionally there has been no significant relationship found between realized returns and beta. However, according to Morelii (1997)if the technique adopted by Pettengil is adopted, than beta is considered to be the most significant factor associated with risk. Theoretically, we assume that expected excess returns are positive. However, a surprising result discovered from this study was that 39% of the sample had a negative excess market return which seriously puts the CAPM model in trouble. Drawbacks of CAPM: CAPM is a theoretical model build on a set of assumptions which are too stringent. These assumptions do not hold in the real investment world. For instance, we can’t assume that the capital markets are perfect and even empirical evidence proves that there are opportunities of abnormal returns. Another assumption that only systematic risk exists and unsystematic risk can be completely eliminated is although probable but it is not accomplished by the individual investors in the real world. The most criticized assumption is about borrowing and lending at the risk-free rate which is almost not possible because there is always a credit risk involved in borrowing and lenders will demand a premium to compensate for the additional risk. CAPM model is built upon certain variables such as the risk free rate, Average market rate of return and the beta of the stock. The yield on short-term government Treasury bond is often taken as a substitute for risk free rate which changes almost every year. Furthermore, beta of the stock changes over the period of time. The issue of concern here is that uncertainty arises in the value of the expected return because the values of the variables in the model are not constant but rather change over the period of time. CAPM & Dividend Discount Model: The CAPM plays a pivotal role in the dividend discount model which assumes that the value of a stock is the expected value of all future dividends incorporating the time value of money. It can be computed by the formula; V = D1/(1+k)1+ D2/(1+k)2+ D3/(1+k)3+………..+ D4/(1+k)4 V is the value of the stock Where D is the Dividend per share for the respective year k is the required rate of return on the stock Now, since an investor computes the expected or required rate of return mainly through CAPM model therefore it has to play a principal role in the valuation of the stock. Stocks with higher betas will have a higher required rate of return therefore they will discount the dividends heavily and provide a lower price or vice versa. The discount rate is a key factor in evaluating projects or stocks whether it be the dividend discount model or any cash flow discounting. A study conducted by (Graham & Harvey, 2001) revealed that NPV has been a key project evaluation method with discount factor calculated using the capital asset pricing model. The study also revealed that the large firms are keener to use CAPM than the small and less sophisticated firms. Perhaps, this can restore the confidence of academicians that CAPM is still valued by the large corporations. Conclusion: Empirical evidence has not supported Capital Asset Pricing Model but its theoretical and sound reasoning has attracted the financial engineers. Criticism has grown in the recent period but CAPM will stand until something better is presented. It is difficult to replace CAPM as it remains at the heart of financial toolkits due to its intuitive appeal. References Elton, E. J. & Gruber, M. J., 1997. Modern portfolio theory, 1950 to date, Journal of Banking & Finance, 21, pp.1743-1759 Faff, R.W., Brooks, R. D. & Kee, H. Y., 2002. New evidence on the impact of financial leverage on beta risk: A time-series approach, North American Journal of Economics and Finance, 13, pp.1–20 Fama E. F. & French K.R., 2003. The Capital Asset Pricing Model:Theory and Evidence, Journal of Economic Perspectives, 18(3), pp-25-46 Graham, J. R. & Harvey, C. R., 2001. The theory and practice of corporate finance: evidence from the field, Journal of Financial Economics, 60(187) Morelli D., 1997. Beta, size, book-to-market equity and returns: A study based on UK data, Journal of Multinational Financial Management, 17(3), pp-257-272 Read More