The Sharpe ratio is used to compare portfolios, stocks or indices. This ratio is:

 

 

The Sharpe ratio is useful when assets are normally distributed or when the investor has a quadratic utility function. This means that the portfolio is completely described by its mean and volatility. As soon as the portfolio is invested in technology stocks, distressed companies, hedge funds or high yield bonds, this ratio is not anymore valid. In that case, the risk comes not only from volatility but from higher moments like skewness and kurtosis.

The Modified Sharpe ratio is the ratio of the excess return divided by the Modified Value-at-Risk. The modified Sharpe ratio is:

 

 

where the Modified VaR is equal to: