Is the CAPM a Biased Estimator of Market Risk?

Abstract

The Capital Asset Pricing Model (CAPM) is often used to determine an appropriate return on equity for regulated utilities. However, the CAPM will sometimes produce unrealistically high or low results during times of excess market volatility. I hypothesize that these results do not indicate a failure in the model itself. Instead, they are caused by the traditional implementation of the CAPM and the underlying definition of risk used by many financial theorists.My paper uses 1997-2001 data to provide an empirical comparison of betas generated in a manner consistent with the capital asset pricing model (CAPM betas) to betas generated using a method based on market losses (“Alternative Betas”). I use psychological literature and a mathematical example to suggest that when a loss-based notion of risk is used, only those observations in which the market declines constitute market risk; and that the CAPM is a systematically biased estimator of market risk because the variability of gains receive the same weight as the variability of losses.In the CAPM world, there are only two types of risk: market risk (measured by beta), and firm-specific risk; with the assumption that only market risk will be rewarded since firm specific risk can be diversified away. The CAPM assumes that the market is mean-variance efficient; predicts that the constant term will be 0; and predicts that a security's risk premium is proportional to both beta and the risk premium of the market portfolio (Bodie, 1996). Mathematically, the risk premium is equal to β[E(rM) − rf], where rM is the market return and rf is the risk-free rate.In the 30 years since the initial publication of the CAPM, there have been numerous criticisms of the model in the financial literature. Studies have suggested that the CAPM is not testable because the composition of the true market portfolio is unknown (Roll, 1977); the constant term is positive and significant (Miller and Scholes, 1972); the estimated risk premium is significantly lower than the actual risk premium (Black, Jensen, and Scholes, 1972); non-systematic risk has a significant effect on excess returns (Lintner, 1965b); and the expected return-beta relationship is not fully consistent with empirical observations (Fama and MacBeth, 1973).