Bayesian nonparametric portfolio selection with rolling maximum drawdown control

Abstract

We present a novel approach to the portfolio selection problem for a multiperiod investor facing multiple risky assets, trading constraints, and return predictability. Our objective is to maximize mean-variance utility while addressing the computational challenges arising from the curse of dimensionality associated with dynamic programming in the presence of trading constraints. To overcome this, we employ model predictive control, a computationally efficient method for solving the problem. Additionally, we propose the use of a non-parametric Bayesian model, specifically the hierarchical Dirichlet process based Hidden Markov Model (HDP-HMM), to predict the multiperiod mean and covariance of returns. Then, we consider a time-varying maximum drawdown to adjust the risk aversion, which can effectively cope with the limit loss problems. Through extensive simulation studies and empirical analysis, we demonstrate that trading strategies based on our proposed method outperform existing approaches in out-of-sample performance.