Effect of booms or disasters on the Sharpe Ratio

The purpose of this paper is to analyze the effect of either booms or disasters on the Sharpe Ratio. We provide a closed form expression of the Sharpe Ratio of an index whose log-return follows an arbitrary distribution. That is, besides variance, we allow for skewness, kurtosis and higher cumulants of the log-return to be non-zero. Our article has two main contributions. First, the Sharpe Ratio depends on all the cumulants and not just the mean and variance. Second, negatively skewed log-returns have a higher Sharpe Ratio than positively skewed returns. As a corollary, we explain why many hedge funds sell disaster insurance. Selling insurance by shorting options generates negative skewness, which in turn increases the Sharpe Ratio.