Portfolio Management with Dual Robustness in Prediction and Optimization: A Mixture Model Based Learning Approach

Abstract

We develop in this paper a novel portfolio selection framework with a feature of dual robustness in both return distribution modeling and portfolio optimization. While predicting the return distributions of the future market always represents the most compelling challenge in investment, any underlying distribution can be always well approximated by using a mixture distribution, if we are able to ensure that the component list of a mixture distribution includes all distributions corresponding to scenario analysis of the potential market modes. Adopting a mixture distribution enables us not only to reduce the prediction problem for distributions to a parameter estimation problem of specifying the mixture weights of the component distributions using a Bayesian learning scheme and estimating the corresponding credible regions of the estimations, but also to harmonize information from different channels, such as historical data, market implied information and the investor subjective views. We establish further a robust mean-CVaR portfolio selection problem formulation to deal with the inherent probability uncertainty. By using duality theory, we show that the robust portfolio selection problem via learning with a mixture model can be reformulated as linear program or second-order cone program, which can be effectively solved in polynomial time. We present simulation analysis and some primary empirical results to illustrate the significance of the proposed approach and demonstrate the pros and cons of the method.