Markowitz’s mean–variance portfolio model is widely used in the field of investment management. The changing dynamics of markets have resulted in higher uncertainties surrounding returns. Returns have often been found to be skewed and extreme events observed to be frequent. These characteristics are measured by skewness and kurtosis, which need to be accommodated in the definition of risk. They should also be included in the portfolio optimization process. The purpose of this paper is to investigate the impact of including higher moments in the estimation of risk in the process of international portfolio diversification. Our study is based on a sample of thirty-three globally traded stock market indexes, including emerging as well as developed markets, for the period between 2000 and 2012. Our inclusion of skewness and kurtosis makes portfolio optimization a nonlinear, nonconvex and multi-objective problem; this has been solved with the use of a genetic algorithm. Empirical results demonstrate that the higher moments model outperforms the traditional mean–variance model across the time period. The results of this study may be useful to fund managers, portfolio managers and investors, aiding them in understanding the behavior of the stock market and in selecting an optimal portfolio model among various alternative portfolio models.

中文翻译：

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基于遗传算法的投资组合优化在全球股市中具有较高的矩

马科维茨的均值-方差投资组合模型广泛应用于投资管理领域。不断变化的市场动态导致了更高的回报不确定性。人们经常发现回报是有偏差的，并且经常观察到极端事件。这些特征通过偏度和峰度来衡量，需要在风险定义中加以考虑。他们也应该包括在投资组合优化过程中。本文的目的是研究在国际投资组合多元化过程中将较高矩纳入风险估计的影响。我们的研究基于 2000 年至 2012 年期间 33 个全球交易的股票市场指数的样本，包括新兴市场和发达市场。我们包含的偏度和峰度使投资组合优化成为一个非线性、非凸和多目标的问题；这已经通过使用遗传算法解决了。实证结果表明，较高矩模型在整个时间段内优于传统的均值方差模型。这项研究的结果可能对基金经理、投资组合经理和投资者有用，帮助他们了解股票市场的行为并在各种替代投资组合模型中选择最佳投资组合模型。