The Capital Asset Pricing Model Discussion

Capital asset pricing model (CAPM) is regarded as a superior model of security price behavior to others based on wealth maximization criteria. CAPM explicitly identifies the risk associated with an ordinary share as well as the future returns it is expected to generate. Until recent the empirical tests supported CAPM, but a test by Fama and French in 1992 did not, stating that it is useless for the precisely what it was developed for. Following the criticism of the model questions such as whether to abandon the model and develop a new one arose. In this essay I will describe the model and describe the researchers test, which justify the usefulness of the model.

Main concepts behind the problem and discussion

The CAPM was developed by Sharpe (1963) as a logical extension to the basic portfolio theory, followed by numerous academics, notably Lintner (1965). The model was developed to explain the difference in risk premium across assets. According to the model this differences are due to the differences in the riskiness of the expected returns. The model affirmers that the correct measure of risk is beta and that the risk premium of riskiness is same across all assets. Given the beta and the risk free rate, the model predicts the expected risk premium. There are several assumptions made. 1) The CAPM is a single-period model, which means that all investors make same decisions over the same period of time and thus expected returns arise from expectations over same period. 2) The CAPM is defined by random variables that are normally distributed, characterized by mean expected returns and covariance’s upon which all investors agree. 3) The CAPM is single index model as systematic risk is predicted entirely by beta factor. Further assumptions are made through Markowitz mean-variance efficiency criteria, based on perfect markets.

•All investor are rational and risk averse
•All investments are infinitely divisible.
•All investors are price takers.
•All investors can borrow-lend without restrictions, at the risk-free rate.
•Transaction costs are zero.
•All information is available and costless.

When the CAPM assumptions are satisfied, everyone in the economy will hold all risky assets in the same proportion. Thus the betas will be equal for everyone. Therefor the model predicts that the ratio of the risk premium to the beta of every asset is the same. More precisely, every investment provides the same compensation for a given level of risk, when beta is used as a measure of risk. The model had been supported for three decades by many notorious researchers; until in the first half of 1990’s the criticism and doubts in usefulness of the model arose. Critics of the model maintain that its assumptions are so restrictive as to invalidate its conclusions, such as investor rationality, perfect markets and linearity. Furthermore, the model is single period model, based on the estimates, which are difficult to be determined in practice. Moreover, it assumes that investors will hold a well-diversified portfolio that ignores unsystematic risk. Even though there is evidence by Black (1993) that suggests that the CAPM does not work accurately for investments with very high and low betas, most tests validate the CAPM for a broad spectrum of beta values.

As the expected returns and betas are unknown, in order to use them in empirical tests researchers had to estimate them. Black, Jensen and Scholes (1972) came up with a clever idea to create portfolios with estimated betas based on historical data. This foresaw grouping assets into portfolios with increasing historical betas, hold the portfolio for several years, and change the portfolio periodically. They analyzed the NYSE over 35 year period by dividing the listing into 10 portfolios. Their study revealed an almost straight-line relationship between portfolio’s beta and its average return. A very important point suggested by these three researchers is that the risk free rate does not necessarily need to be zero. This played an important role in development of the model. Thus they conclude that CAPM is an approximation to reality. After a decade in 1981 a study by Banz suggested that the model might be missing an important point. Banz tests the CAPM by checking if the size of a firm was involved in explaining residuals. The test suggests that size explains the variation of average returns better then beta. The procedure used by Banz is similar to Black, Jensen and Scholes (1972).

He divides the assets into different subgroups, totaling 25 portfolios. Banz concluded that because size effect is large and thus it is statistically significant. To prove the significance of his findings Banz did a further test constructing two portfolios, each with 20 assets. One portfolio consisted entirely by stocks of small firms, while the second portfolio consisted entirely by stocks of large firms. Banz concluded that small firms earned on average 1.5 percent more per month. Thus the model seems to be missing an important factor. But the model is sad to be an approximation of reality and thus the findings of Banz is not enough to reject the model. Even though Roll used his statement as criticism to the model I think it is a good counter argument to Banz’s findings. Roll (1977) noted:

“Most CAPM tests may be invalid because all stock exchange indices are only a partial measure of the true global market portfolio. Explained simply, by definition the market portfolio should include every security world-wide.”

In 1992 a study by Fama and French further challenges the view that the CAPM is an abstraction from reality. Eugene F. Fama and Kenneth R. French:

“Two easily measured variables, size and book-to-market equity, combine to capture the cross-sectional variation in average stock returns associated with market beta, size, leverage, book-to-market equity, and earnings-price ratios. Moreover, when the tests allow for variation in beta that is unrelated to size, the relation between market beta and average return is flat, even when beta is the only explanatory variable.”

They suggest that Banz’s findings may economically be so significant that it questions the validity of the model. They grouped stocks from NYSE, AMEX and NASDAQ into 10 beta classes and 10 size classes. They find that size is important with and without betas and conclude that beta has little ability to explain expected returns. The criticism can be summarized as follows. Relation between average return and beta is flat, and other variables such as firm size are more significant. The latter researchers suggested that the data used by Fama and French has been collected over shorter period of time and had significantly different macro-economical factors. I have looked up the data and found that there are notable differences.

The data collected by Fama and French has approximately 12% higher returns for small firms, and 4 % higher return for large firms. During same period the standard deviation has declined by 8% for small firms and 7% for large firms. This may well be the reason behind their findings. Furthermore Black in 1993 suggests that the findings of Fama and French are invalid according to the data they had used. It is important to briefly evaluate an alternative method to CAPM, the arbitrage pricing theory (APT) was introduced by Ross (1976,1977) as an alternative to CAPM. This method depends on the law of one price and categorizes the risk into two parts. Both systematic and unsystematic risks are taken into consideration. Moreover, with its multifactor return generating structure, APT is thought to be more efficient, but on it has a serious disadvantage in defining systematic risk factors.

Conclusions

Even though there was a lively discussion about the validity of the CAPM in my opinion it has passed all the counter arguments. The main challenge appeared to be Banz arguing about the size effect that has been successfully answered by latter researchers and pointed out that the data used in his study was the reason of his findings. The criticism by Fama and French regarding the ratio of book-to market equity, has been justified as wrong by Kothari, Shanken and Sloan (1995):

“Our examination of the cross-section of expected returns reveals economically and statistically significant compensation (about 6 to 9 percent per annum) for beta risk when betas are estimated from time-series regressions of annual portfolio returns on the annual return on the equally weighted market index. The relation between book-to-market equity and returns is weaker and less consistent than that in Fama and French (1992). We conjecture that past book-to-market results using COMPUS- TAT data are affected by a selection bias and provide indirect evidence.”

They point out another problem with the data used in their study; firms with high book-to-market equity ratio were less likely to survive. The lack of empirical support for the CAPM may be due to the inappropriateness of some assumptions made. Although the critics of the model make a persuasive case against CAPM the above mentioned responses justify the wrong doing of their studies. To summarize, modifying the model in 1972 by Black, Jensen and Scholes included more or less all-necessary aspects of asset pricing. In my opinion there is highly unlikely to develop a model that will perfectly capture and predict the asset pricing, thus CAPM is as close as we can get.