Modified variance incorporating high-order moments in risk measure with Gram-Charlier returns

Abstract

This paper introduces a new risk measure for portfolio choice and compares its performance with two related metrics, namely the behavioral variance and the modified variance by using a Taylor’s expansion. The methodology for our proposal naturally incorporates investor attitudes to risk related to skewness and kurtosis by assuming a Gram-Charlier return distribution. The so-obtained risk measures represent a more reliable description of portfolio risk and encompass the cases where high-order moments are not relevant characteristics (i.e. under normality). Our results show the outperformance of our proposal for different risk tolerance parameters considering the minimum variance and Sharpe ratio criteria by employing random portfolio optimization technique for 11 sets of stocks.