# A critical analysis of the merits of the Capital Asset Pricing Model

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Critically Analyse the Relative Merits of Capital Asset Pricing Model (CAPM) and empirical approaches to asset pricing such as Fama and French model. People always search for new tools or better techniques that allow a job to be completed faster and better. It applies to every field including the finance field. Capital Asset Pricing Model (CAPM) is used to calculate the cost of capital and measure portfolio performance since 1970s. In 1990s, Fama and French show the CAPM is wrong and they proposed a better three-factor model. One would expect practitioners switching to the new better asset pricing model immediately. However, in a survey conducted by Graham and Harvey (2001), 73.5% of 392 U.S. CFOs relies to some extent on the CAPM when estimating the cost of equity. Brounen, Abe de Jong and Koedijk (2004) conducted a similar survey for 313 European firms and around 45% of on average relied on the CAPM. Why practitioners do not use the three-factor model as Fama and French (2004) claimed? There may be some possible answers. The practitioners may not know the three-factor model; or it is not cost effective to collect the extra information required by the three-factor model; or the practitioners think the three-factor model does not help much, i.e. the Fama-French three-factor model is not always better than the CAPM. Now let us see what CAPM model really is and what are its main properties , its relative merits and demerits and its practical implication with respect to another famous model the Fama and French Model. The CAPM is concerned with the pricing of assets in equilibrium. The CAPM tells us how investors determine expected returns, and asset prices, as a function of risk. The model bases on the idea that not all risks should affect asset prices. In particular, a risk that can be diversified away when held along with other investments in a portfolio is not a risk at all. Only those "systematic risk" is counted when determining the price. The CAPM model is the extension of one period mean- variance portfolio models of Markowitz (1959) and Tobin (1958) .CAPM is based on numerous assumption and these assumptions become to some sort of basis for criticism by many people as they claim them to unrealistic. The assumptions are as follows and must be kept in mind. Investors choose their investment portfolios on the basis of expected return and variance of return over single period; It is assumed that the diversified portfolio is held by Investors Investors have the same estimates of mean, variance and covariance of all assets; The capitals markets have no transaction costs; Perfect capital market. All assets are perfectly divisible; Single-period transaction horizon. No restriction on short sales; It is also assumed as Investors can borrow and lend at the risk-free rate of return . ( means that a holding period of almost one year is required) No Taxes No commission Basically the assumptions made by the CAPM focuses on the relationship between the risk ( systematic Risk) and return is not as what happens in the real world in which all these decisions are made by companies and individuals. Well if we have a look at capital markets of the world which are not perfect but still this is a point of argument that efficient stock markets which are in developed countries are efficient enough, still there lies some chance of stock market to be priced incorrectly and which further prevents returns not to be plotted on security Market line. We can therefore see that the assumption we took for the single period transaction therefore seems reasonable enough. Investors want to hold a portfolio that reflects the whole stock market. It is very easy for the investors to diversify risk ( specific and Unsystematic) and to make portfolios which track up the stock market. Is it possible to have at a risk free rate in today's world? but in this case it is assumed that such is the case and because the investors to borrow at risk free rate because the individual investor involves more risk as compared to the risk associated with government and resultantly if we are not able to borrow at a risk free rate then the security Market line will be shallower than what we studied in the theory. Regarding the assumption of investors only receiving compensation for systematic risk seems to be very fair to me and is practically acceptable. In my view the assumptions of the CAPM seem to be idealised slightly than the real view and i think there might be some chances of existence of relationship between required return and Risk. The equation for CAPM to find the expected rate of return is mentioned below. E(ri) = Rf + Î²i(E(rm) - Rf) Explaining the equation . 1) Rf = Estimate the risk free rate, generally treasury bill rate. 2) Bi = Estimate the stock's beta coefficient, b, which is an index of systematic ( or non-diversifiable market) risk. 3) rm = Estimate the rate of return on market portfolio, such as standaed & poor's 500 stock composite index. 4) Example : Treasury bill rate ( risk free) = 8% , Bi = 1.5 & market portfolio = 12% = E(ri) = 8% = 1.5 ( 12% - 8%) = 14% 14% = { 8% ---> risk free rate { 6% ---> risk premium, stock price is 1.5 times more volatile than the market portfolio

## ADVANTAGES OF THE CAPM

The CAPM has several advantages over other methods: It considers only systematic risk, reflecting a reality in which most investors have diversified portfolios from which unsystematic risk has been essentially eliminated. It generates a theoretically-derived relationship between required return and systematic risk which has been subject to frequent empirical research and testing. Another advantage which makes it superior than others is that it calculates cost of equity by taking into account level of risk with respect to stock market. Discount rates are used in investment appraisal which makes it a better model then weighted average cost of capital.

## DISADVANTAGES OF THE CAPM

Besides advantages it also has some disadvantages like in order to compute CAPM we need to assign values to risk free rate of return, the equity risk premium, beta and return on market. The risk free rate of return for which we use yield on short term Government debt changes on daily basis according to different conditions prevailing. Proxy beta for the investments must be different from the companies equity beta. If the proxy for the market portfolio isn't mean-variance efficient then we wont identify the correct CML and the expected returns estimated using CAPM are unlikely to match actual returns. Similarly using a broad stock market index as proxy for the market portfolio may be inappropriate. Another difficulty is that proxy company betas uses information that may not be readily available. More over other issues regarding estimating the expected returns for individual stocks based on Capital Asset Pricing model are Do dividend adjustments in the index matter? It is assumed in CAPM that Market portfolio returns includes dividends. It is therefore relevant to ask that number of indexes constructed without dividends do matter in obtaining a best estimate to see whether or not dividends are included in the index used. So where it is possible that the indexes with or without the dividends are considered here. What data frequency and time period should be used? As we know regarding estimation that the more observations we take the better the results are. If we follow this then we should be using long time periods as possible. Similarly if we take long estimation period for the beta and it is possible that the value of the actual beta will change over time and the consequential estimate for beta will be prejudiced. Naturally when this happens we will have to shorten the period. Now as we have to collect more observations over shorter time we can do this by increasing the sampling frequency. What index should be used? As we know CAPM is very precise about the index. Value weighted index which consist of all assets in world should be used. As we know that very limited and small portion of assets are traded on the stock exchanges so its not possible to make such a index so we make a proxy instead. Regarding proxy the most commonly used are equal weighted and value weighted index. There are many of its anomalies which were later on discovered in the 80s and 90s, they in fact became a challenge to the CAPM as the market beta does not suffice to explain expected stock returns. The anomalies were Earning price ratio. Size Leverage Book to Market equity ratio. Basu (1977) shows that when common stocks are sorted on earning price ratio , earning price future return on high EP stocks are higher than those predicted by CAPM. Banz (1981) documented about a size effect that stock of small i.e low market value stocks earned a higher return the predicted by CAPM.small stocks have higher betas and higher returns then large stocks but the difference was more than what was predicted by CAPM. Bhandari ( 1988) illustrated that leverage is positively related to stocks expected returns. As we know that leverage is measured by book value of debt over market value of equity. Therefore Fama and French (1992) state the earlier findings of other researchers like , higher book to market equity ratios , ratio of book value to market value , have higher returns that are not captured by market beta which is why Fama and French launched a challenge.

## The Fama-French three-factor model

This Model as previously discussed was put forward by Fama and French in response to the CAPM in which they think had flaws or deficiencies which were therefore overcome in their model. Fama & French ( 1992) discussed about the book to market equity ratio, leverage, size and earning to price ratio and according to them the book to market equity has a greater and stronger power then the size but on the other hand, book to market equity ratio cannot be replaced by size in explaining the average returns. A three factor model was therefore proposed by Fama and French for expected returns to show more factors which could be involved and influence the expected returns which the CAPM was not able to include according to them. Variables include the return on stock index, excess returns on portfolio of small stocks over a portfolio of large stocks and excess return on portfolio of high book to market stocks over a portfolio of low book to market stocks. Following is the equation for computation put forward by them. (Rit - Rft) = Î±i + Î²1i (Rmt - Rft)+ Î²2i SMBt + Î²3i HMLt + Îµit In the equation, as discussed before SMB (small minus big) is the difference of the returns on small and big stocks, HML(high minus low) is the difference of the returns on high and low book-to-market equity ratio (B/M) stocks, and the betas are the factor sensitivities of the state variables. Fama and French argue if asset pricing is rational, size and BE/ME must proxy for risk. SMB captures the risk factor in returns related to size, HML captures the risk factor in returns related to the book-to-market equity and the excess market return, Rm - R captures the market factor in stock returns. However, Fama and French (1992) show that it is unlikely as they find market betas alone has no power to explain average returns. They also find the averages of the monthly cross-sectional correlations between market betas and the values of these two state variables for individual stocks are all within 0.15. According to Fama and French (1995) the weaker firms which show a continuous trend of less earning over time and having high book to Market value and have positive slopes on the High minus Low , similarly the firms with a consistent trend of higher earning tend to have lower book to market value and show negative slopes on the HML. According to them, the variation in the risk factor which is relevant to earning performance is captured by HML. Similarly stocks with the property of lower returns over long term which we may refer as the losers tend to have a positive SMB and HML slopes the reason being as they are smaller and financially distressed and resultantly higher future returns. On the other hand stocks with the property of higher long term returns which we may refer to as the winners tend to have negative slopes and low future returns. Fama and French also say that market beta is not able to capture the co variation in the returns of small stocks and which is compensated in average returns. Fama and French also show the existence of co variation in the returns on small stocks that is not captured by the market betas and is compensated in average returns. Fama and French (1993, 1996) have interpreted their three- factor model as evidence for a "distress premium". Small stocks with high book- to-market ratios are firms that have performed poorly and are vulnerable to financial distress, and hence investors command a risk premium. However, the model cannot explain the momentum effect. The Fama-French three-factor model predicts the reversal of future returns for short-term winners and losers. Hence, the continuation of short-term returns is left unexplained by the model.

## CONCLUSION

As we have been through both CAPM and Fama and French models to help investors understand the risk/reward trade-off which they face when making investments. We first introduced the CAPM, with its inherent simplicity, linking market covariance risk to expected returns. Its simplicity helps to build intuition around the concept of modelling return as a function of risk. The CAPM's simplicity is also its greatest shortcoming, as the underlying assumptions limit its ability to explain and predict actual returns. The Fama-French Three-Factor Model expands the capabilities of the model by adding two company specific risk factors - SMB and HML. The three factors in concert explain most of the returns due to risk exposure, but it has its own limitations too. CAPM has stood up well against all the attacks and criticisms against it , although these criticisms have increased in the recent years , but in my view CAPM remains a very useful tool in the financial management. In my view with these Models investors are able to make more informed investment decisions with respect to personal preference regarding the risk/reward trade-off. REFERENCING Bartholdy.J and Peare.P, (2004) , Estimation of expected return: CAPM vs Fama and French, page 1-8. Banz, R.W, (1981), The Relationship between Return and Market Value of Common Stocks, Journal of Financial Economics 9. 3-18. (http://thefinanceworks.net/Workshop/1002/private/3_Asset%20pricing/Articles/Banz%20on%20small%20firm%20effect%201981%20JFE.pdf) French.R and Fama.F (2003), The CAPM: Theory and Evidence, Centre for Research in Security Prices (CRSP) University of Chicago. French.R and Fama.F ( 1996), The CAPM is Wanted, Dead or Alive, The Journal of Finance, Vol. 51, No. 5. Lam Kenneth ,( 2005), Is The Fama-French Three Factor Model Better Than The CAPM,. Page 1-6. Megginson W L,( 1996.) Corporate Finance Theory, Addison-Wesley, p10, Project-specific discount rates, student accountant, April 2008. Russo. Francesco ( 2005) , CAPM : The challenges of globalization. International Financial Management. Available at ( http://people.hbs.edu/mdesai/IFM05/Russo.pdf) Shapiro Alex, The Capital Asset Pricing Model (CAPM), Foundations of Finance Note 9, (pp 1-5). Watson D and Head A, 2007, Corporate Finance: Principles and Practice, 4th edition,FT Prentice Hall, pp222-3. Available at ( http://accounting-financial-tax.com/2010/06/more-advance-with-cost-of-capital-analysis/)