On the validity of the Capital Asset Pricing Model

One of the most important developments of modern finance is the Capital Asset Pricing Model (CAPM) of Sharpe, Lintner and Mossin. Although the model has been the subject of several academic papers, it is still exposed to theoretical and empirical criticisms. The CAPM is based on Markowitz’s (1959) mean variance analysis. Markowitz demonstrated that rational investors would hold assets, which offer the highest possible return for a given level of risk, or conversely assets with the minimum level of risk for a specific level of return. Building on Markowitz’s work, Sharpe and Lintner after making a number of assumptions, developed an equilibrium model of exchange showing the return of each asset as a function of the return on the market portfolio. This model and its underlying assumptions are reviewed in section 1. This model known as the Capital Asset Pricing Model has since been the focus of a number of empirical tests, and as shown in sections 3 and 5 the majority of these tests deny the validity of the model. However, as discussed in sections 4 and 6 these tests have not been free of criticism. Section 2 briefly presents a framework under which the empirical tests of the CAPM can be carried out. Section 7 provides a conclusion. 1. The CAPM and its assumptions Sharpe and Lintner assumed that there are no transaction costs and no income taxes. Further, they assumed that assets are infinitely divisible and there are no restrictions to short selling and that investors can lend and borrow unlimited amounts at the risk free rate of interest. More importantly they assumed the homogeneity of expectations and that individuals hold mean variance efficient portfolios. Another implicit assumption of the CAPM is that all assets including human capital are marketable. Moreover the CAPM is essentially a single period model. It is clear that these assumptions do not hold in the real world and thus, not surprisingly, the model’s validity has been suspect from the outset. * The author has an M.Sc. in Finance and Economics from the London School of Economics. He is currently a Lecturer in Economics at the University College, Lahore. The Lahore Journal of Economics, Vol.5, No.1 74 However, on closer examination the assumptions underlying the CAPM are not as stringent as they first appear to be. Exactly the same results would obtain if short sales were disallowed. Since in equilibrium no investor sells any security short, prohibiting short selling will not change the equilibrium. More formally the derivative of the Langrangian with respect to each security will have a Kuhn-Tucker multiplier added to it, but since each security is contained in the market portfolio, the value of the multiplier will be zero and hence the solution will remain unaffected. Further, Fama (1970) and Elton and Gruber (1974 and 1975) give a set of conditions under which the multi-period problem reduces to a single period CAPM, where all individuals maximise a single period utility function. The conditions are that firstly consumers act as if the one-period returns are not state dependent, i.e. the distribution of one-period returns on all the assets are known at the beginning of the period. Secondly, the consumption opportunities are not state dependent and lastly consumers’ tastes are independent of future events. Fama further shows that given these conditions the derived one period utility is equivalent to a multi-period utility function given nonsatiation and risk aversion. However, it is argued by many that the above conditions are rather restrictive. Merton (1973) has shown that a necessary and sufficient condition for individuals to behave as if they were single-period maximisers and for the equilibrium return relationship of CAPM to hold is that the investment opportunity set is constant. Furthermore, the main results of the model hold if income tax and capital gains taxes are of equal sizes. If the assumption of riskless lending or borrowing is violated, then Black (1972) has shown that we still obtain a linear relationship between an asset’s returns and its risk as measured by the covariance of the assets returns with the market. This model as distinct from the standard CAPM is known as the zero beta CAPM. Thus, even though the assumptions underlying the Capital Asset Pricing Model are demanding and have been the basis for much of the criticism against the model, nevertheless these assumptions are not altogether inflexible. More importantly, the final test of the model is not how reasonable the assumptions underlying it seem to be, but rather how well the model conforms with reality. Indeed, many proponents of the CAPM argue that due to technological advances, capital markets operate as if these assumptions are satisfied.