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.

ABSTRACT We analyze a simple model of bank lending in order to ascertain what can be inferred from relative denial and default rates about lending discrimination. We show that if minority applicants are of lower average creditworthiness than majority applicants, then, contrary to a popular argument, a uniform, nondiscriminatory credit policy cannot simultaneously produce (i) higher denial rates for minority applicants, and (ii) equal default rates for minority and majority applicants. Moreover, we show that equality of denial or default rates always implies discrimination. In particular, equal denial (default) rates imply discrimination against majority (minority) applicants.

We analyze a simple model of bank lending in order to ascertain what can be inferred from relative denial and default rates about lending discrimination. We show that if minority applicants are of lower average creditworthiness than majority applicants, then, contrary to a popular argument, a uniform, nondiscriminatory credit policy cannot simultaneously produce (i) higher denial rates for minority applicants, and (ii) equal default rates for minority and majority applicants. Moreover, we show that equality of denial or default rates always implies discrimination. In particular, equal denial (default) rates imply discrimination against majority (minority) applicants.

The authors analyze a simple model of bank lending in order to ascertain what can be inferred from relative denial and default rates about lending discrimination. They show that if minority applicants are of lower average creditworthiness than majority applicants, then, contrary to a popular argument, a uniform, nondiscriminatory credit policy cannot simultaneously produce higher denial rates for minority applicants and equal default rates for minority and majority applicants. Moreover, the authors show that equality of denial or default rates always implies discrimination. In particular, equal denial (default) rates imply discrimination against majority (minority) applicants.