Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances
研究了分布鲁棒版本的Markowitz均值-方差投资组合模型，用Wasserstein距离定义分布不确定性区域，将问题转化为带正则项的经验方差最小化，并基于数据选择不确定性大小和鲁棒目标收益率，在标普500数据上回测表现优于Fama-French和Black-Litterman模型。
We revisit Markowitz’s mean-variance portfolio selection model by considering a distributionally robust version, in which the region of distributional uncertainty is around the empirical measure and the discrepancy between probability measures is dictated by the Wasserstein distance. We reduce this problem into an empirical variance minimization problem with an additional regularization term. Moreover, we extend the recently developed inference methodology to our setting in order to select the size of the distributional uncertainty as well as the associated robust target return rate in a data-driven way. Finally, we report extensive back-testing results on S&P 500 that compare the performance of our model with those of several well-known models including the Fama–French and Black–Litterman models. This paper was accepted by David Simchi-Levi, finance.