Effect of Booms and Busts on the Sharpe Ratio

Abstract

This article analyzes the effect of booms and busts on the Sharpe ratio. The authors provide a closed-form expression for the Sharpe ratio of an index whose log return follows an arbitrary distribution. The article has two main contributions. First, the Sharpe ratio—the ratio of the mean and the volatility of the simple (excess) return—depends on all the cumulants of the log return. Second, returns subject to busts (negatively skewed) have a higher Sharpe ratio than returns subject to booms (positively skewed). This explains why hedge funds sell disaster insurance. Selling insurance by shorting options leads to negatively skewed returns, which in turn increase the Sharpe ratio.