Skewness risk premium: Theory and empirical evidence

Using an equilibrium asset and option pricing model in a production economy under jump diffusion, we derive an analytical link between the equity premium, risk aversion and the systematic variance and skewness risk premium. In an empirical application of the model using more than 20 years of data on S&P500 index options, we find that, in line with theory, risk-averse investors demand risk-compensation for holding equity when the systematic skewness risk premium is high. However, when we differentiate between market conditions proxied by investor sentiment, we find that in up-markets (high sentiment) risk aversion is low, while in down-markets (low sentiment) risk aversion is high. We show that in line with theory, the skewness-risk-premium-return relationship only holds when risk aversion is high. In periods of low risk aversion, investors demand lower risk compensation, thus substantially weakening the skewness-risk premium-return trade off. Therefore, we also provide new evidence that helps to disentangle sentiment from risk aversion.