This paper examines the intertemporal relation between downside risk and expected stock returns. Value at risk (VaR), expected shortfall, and tail risk are used as measures of downside risk to determine the existence and significance of a risk-return tradeoff. We find a positive and significant...

Asness et. al. (2018) recently resurrect the size effect, concluding that it “…should be restored as one of the central cross-sectional empirical anomalies for asset pricing theory to explain”. We suggest a theoretical explanation for the size effect, based on the observation that many...

The Black-Scholes model and many of its extensions imply a log-normal distribution of stock returns. However, for holding periods of up to a year, the empirical return distribution (both conditional and unconditional) is not log-normal, but rather much closer to the logistic distribution. This...