Portfolio management with robustness in both prediction and decision: A mixture model based learning approach

We develop in this paper a novel portfolio selection framework with a feature of double robustness in both return distribution modeling and portfolio optimization. While predicting the future return distributions always represents the most compelling challenge in investment, any underlying distribution can be always well approximated by utilizing a mixture distribution, if we are able to ensure that the component list of a mixture distribution includes all possible distributions corresponding to the scenario analysis of potential market modes. Adopting a mixture distribution enables us to (1) reduce the problem of distribution prediction to a parameter estimation problem in which the mixture weights of a mixture distribution are estimated under a Bayesian learning scheme and the corresponding credible regions of the mixture weights are obtained as well and (2) harmonize information from different channels, such as historical data, market implied information and investors׳ subjective views. We further formulate a robust mean-CVaR portfolio selection problem to deal with the inherent uncertainty in predicting the future return distributions. By employing the duality theory, we show that the robust portfolio selection problem via learning with a mixture model can be reformulated as a linear program or a second-order cone program, which can be effectively solved in polynomial time. We present the results of simulation analyses and primary empirical tests to illustrate a significance of the proposed approach and demonstrate its pros and cons.