Is there an intertemporal relation between downside risk and expected 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. We find a positive and significant relation between downside risk and the portfolio returns on NYSE/AMEX/Nasdaq stocks. VaR remains a superior measure of risk when compared with the traditional risk measures. These results are robust across different stock market indices, different measures of downside risk, loss probability levels, and after controlling for macroeconomic variables and volatility over different holding periods as originally proposed by Harrison and Zhang (1999).