Erasmus university rotterdam

Criticism of beta

Beta has not been without criticism. Besides the well known criticism of Fama and French (1992) that other risk factors should be included in the risk and return relationship, beta was criticized because historical returns are used as a proxy for expected returns. The CAPM assumes that the expected return will be the same as the realized return.

A well known critique on the CAPM comes from Roll (1977). Roll argues that the CAPM may not be testable. The CAPM implies that the market portfolio is mean-variance efficient. A portfolio is called mean-variance efficient if it has a minimal variance for a certain amount of return. Roll (1977) criticized the CAPM because the market index was used as a proxy of the portfolio. He argued that the CAPM cannot test the true market portfolio since the true market portfolio cannot be measured. According to Roll, the true portfolio must include all assets, financial, real as well as human and not just stocks. Roll (1977) shows that the linearity test is a test of whether the portfolio used in the analysis is mean-variance efficient, rather than a test of the CAPM. Consequently the CAPM is not testable unless the true market portfolio composition is known and used in the test. When the proxy of the market portfolio is mean-variance efficient, the relationship between returns and beta could turn out to be linear. The opposite is also true, if the proxy is not mean-variance efficient, the relationship could be non-linear. Regardless of the returns being mean-variance efficient, most proxies of the market are very highly correlated with the true market portfolio and with each other according to Roll (1977). Nevertheless, the results differ depending on which proxy is used for the market.

The CAPM model can be sensitive to the return interval used to test beta, because beta can vary with the length of the interval used to measure returns. The beta of a company may change over time. Research has shown that beta is not stable over time. As a consequence the results of this study are only valid for the time interval used. A time varying beta could be a solution for this problem.

The CAPM measures risk by the beta of the asset. The upside moments and the downside moments of returns are treated equally by the CAPM. However, empirical studies have shown that return distributions typically have fat tails and are not symmetrical (Galagedera, 2006). Furthermore, the CAPM is a one-period model and does not have a time dimension. The assumption that returns are normally distributed over time is necessary in order to estimate the model through time. According to Pereiro (2001) the straight application of the classical CAPM is controversial when it is not clear whether the hypothesis of market efficiency holds. Moreover, the CAPM based models are not structure to deal with unavoidable, unsystematic risk arising from imperfect diversification.

Despite the criticisms of the CAPM it is still used by many professionals. Mainly because it offers a statistical framework that allows for an analysis of behavior in capital markets. Omran (2007) points out that inferences can be drawn about the realized returns and company characteristics like the market risk and investors’ preference for skewed distributions. These inferences that are made do not constitute tests of the CAPM but the provides useful insights into capital markets. Hereafter the versions of the CAPM that are used in this study are described.