The Sharpe Ratio With Skewness

We propose an investment choice model to improve existing risk-adjusted performance measures by incorporating portfolio skewness. Building on a partial differential equation analysis, we demonstrate that a risk-adjusted performance measure maximizes investor expected utility. To evaluate the Sharpe ratio with skewness adjustment for all investors, we price second-order returns using first-order returns and show that the resulting ratio is the sum of the Sharpe ratio due to first-order returns and the Sharpe ratio due to second-order returns. We further show that the Sharpe ratio with skewness adjustment increases with return mean, decreases with volatility, and non-decreases with skewness. Finally, we test the Sharpe ratio with skewness using 299 market indexes including country indexes such as the MSCI China a index and S and P 500. The test reveals that the Sharpe ratio with skewness can accurately assess performance of wide-range assets. Our model anchors a risk-adjusted performance measure to an investment choice.