Regularized hypervolume selection for robust portfolio optimization in dynamic environments

Abstract

This paper proposes a regularized hypervolume (SMetric) selection algorithm. The proposal is used for incorporating stability and diversification in financial portfolios obtained by solving a temporal sequence of multi-objective Mean Variance Problems (MVP) on real-world stock data, for short to longterm rebalancing periods. We also propose the usage of robust statistics for estimating the parameters of the assets returns distribution so that we are able to test two variants (with and without regularization) on dynamic environments under different levels of instability. The results suggest that the maximum attaining Sharpe Ratio portfolios obtained for the original MVP without regularization are unstable, yielding high turnover rates, whereas solving the robust MVP with regularization mitigated turnover, providing more stable solutions for unseen, dynamic environments. Finally, we report an apparent conflict between stability in the objective space and in the decision space.