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.

摘要

本文介绍了一种新的投资组合选择风险度量，并将其性能与两个相关指标进行比较，即行为方差和使用泰勒展开的修正方差。通过假设 Gram-Charlier 回报分布，我们提案的方法自然地结合了投资者对与偏度和峰度相关的风险的态度。如此获得的风险度量代表了对投资组合风险的更可靠描述，并涵盖了高阶矩不相关的特征（即在正常情况下）的情况。我们的结果表明，通过对 11 组股票采用随机投资组合优化技术，考虑到最小方差和夏普比率标准，我们提出的不同风险承受能力参数的建议表现出色。