Equilibrium "anomalies"

Many empirical "anomalies" are actually consistent with the single beta capital asset pricing model 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. Loadings on portfolios formed on relative leverage and relative distress completely subsume the powers of the Fama and French (1993) returns to small minus big market capitalization (SMB) portfolios and returns to high minus low book-to-market (HML) portfolios factors in explaining cross-sectional returns.