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The Sharpe Ratio With Skewness

Journal: Sumerianz Journal of Economics and Finance (Vol.3, No. 8)

Publication Date:

Authors : ; ;

Page : 107-118

Keywords : Sharpe ratio; Sharpe ratio with skewness; portfolio skewness; Risk-adjusted performance measure; Portfolio analytics; Portfolio construction.;

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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.

Last modified: 2020-11-04 17:29:51