Abstract 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.

Abstract A spurious positive relation between exponential generalized autoregressive conditional heteroskedasticity (EGARCH) estimates of expected month t idiosyncratic volatility and month t stock returns arises when the month t return is included in estimation of model parameters. We illustrate via simulations that this look-ahead bias is problematic for empirically observed degrees of stock return skewness and typical monthly return time series lengths. Moreover, the empirical idiosyncratic risk-return relation becomes negligible when expected month t idiosyncratic volatility is estimated using returns only up to month t − 1.

Hazard stocks are the opposite of lottery stocks. We proxy hazard stocks with the minimum daily idiosyncratic return over the past month, “IMIN,” and examine the relation between hazard stocks and expected returns. The literature on lottery stocks implies that investors should discount hazard stocks. Anomalously, we find a negative relation between IMIN and future returns. Hedge portfolios that are long high IMIN stocks and short low IMIN stocks generate monthly alphas of -0.52% to -0.76%. The results are robust after controlling for numerous firm characteristics and corporate events. The hazard stock anomaly is primarily driven by limits to arbitrage and, to a lesser degree, by firm-level information uncertainty. Via the Reg SHO pilot program, we provide causal evidence that the apparent asymmetric preferences across lottery and hazard stocks are due to arbitrage asymmetry as described by Stambaugh et al. (2015). This demonstrates that asymmetric arbitrage may yield what appear to be asymmetric preferences.