Is There a Relation Between Downside Risk and Expected Stock Returns?•

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 for several stock market indices. We find a positive and significant relation between downside risk and the portfolio returns on the NYSE/AMEX/Nasdaq stocks. This result also holds for the NYSE/AMEX, NYSE, Nasdaq, and S&P 500 index portfolios. Moreover, VaR remains to be a superior measure of risk even when it is compared to the traditional risk measures which have significant predictive power for market returns. These results are robust across different measures of downside risk, loss probability levels, and after controlling for macroeconomic variables associated with business cycle fluctuations.