Equilibrium 'Anomalies'

Abstract

Many empirical "anomalies" are actually consistent with the single beta CAPM if the empiricist utilizes an equity-only proxy for the true market portfolio. Equity betas estimated against this particular inefficient proxy will be understated, with the error increasing with the firm's leverage. Thus, firm-specific variables that correlate with leverage (such as book-to-market and size) will appear to explain returns after controlling for proxy beta simply because they capture the missing beta risk.

We demonstrate this by constructing a hypothetical economy where the single-beta CAPM prices all assets and where firms are allowed to have simple capital structures. This framework allows us to compare the true betas of the economy's financial assets with the proxy betas generated from any market proxy.

Our model provides a specific roadmap for recovering CAPM expected returns for use in applications of the static CAPM (like performance measurement and the corporate cost of capital). The model implies that if the single-factor CAPM holds, factors formed on relative leverage and relative distress should provide the best complements to the equity market index for explaining the cross-section of returns. In fact, we find that loadings on portfolios formed on relative leverage and relative distress completely subsume the powers of the Fama and French (1993) SMB and HML factors in explaining cross-sectional returns.

Keywords: CAPM, asset pricing, anomalies, beta, HML, SMB, leverage, financial distress

JEL Classification: G11, G12, G14