Higher-Moment Risk

We use a new method to estimate ex ante higher order moments of stock market returns from option prices. Even and odd number higher order moments are strongly negatively correlated, creating periods where the return distribution is riskier because it is more left-skewed and fat tailed. The higher-moment risk increases in good times when variance is lower and prices are higher. This time variation is inconsistent with disaster-based models where disaster risk, and thus higher-moment risk, peaks in bad times. The variation in higher-moment risk also has important implications for investors as it causes the probability of a three-sigma loss on the market portfolio to vary from 0.7% to 1.9% percent over the sample, peaking in calm periods such as just before the onset of the financial crisis.