This Excel spreadsheet calculates the Modified Sharpe Ratio.
The standard Sharpe Ratio is only appropriate for normally-distributed returns, where the entire distribution can be summarized through the mean and the variance.
But many modern investment vehicles, such as hedge funds and bonds, display fat-tailed returns, in which there is the potential for extreme losses. In these situations, the standard Sharpe Ratio underestimates risk and should not be used.
The potential for extreme losses can be quantified through the modified Value at Risk, which takes into account the skew and kurtosis of the returns distribution.
The standard Sharpe Ratio is the effective return (μ – rf) divided by the variance (σ2). However, the modified Sharpe Ratio is the effective return divided by the modified Value at Risk, and is defined by the following equations.
μ and σ are the mean and standard deviation, S is skew, K is kurtosis, zc is the quantile of the distribution and Z is the Cornish-Fisher asymptotic expansion for the quantile of a non-gaussian distribution.