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

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... s 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) . I. Introduction The cotiditional tnean and variance of return on the market portfolio play central roles in Merton's ( 1973) intertemporal capital asset pricing model (IC APM). Although theoretical models suggest a positive relation between risk and return for the aggregate stock market, the existing empirical literature fails to agree on the intertemporal relation between expected return and volatility. There is a long literature that has tried to identify the existence of such a tradeoff between risk and return, but the results are far from being conclusive (see the recent article by Guo and Whitelaw (2006) and the references therein).