On Reference-Regulated Multiperiod Mean-Variance Portfolio Optimization in High Dimensions

Abstract: The multiperiod mean-variance (MV) portfolio optimization serves as a vital expansion of Markowitz's static MV portfolio selection framework. Just like its static counterpart, the multiperiod MV portfolio remains susceptible to estimation errors. We propose a reference-regulated multiperiod mean-variance (RRMV) framework that penalizes deviations from a reference policy. Therefore, this new optimization successfully combines the advantages of dynamic strategies and reference portfolios. A key contribution of this paper is the characterization of the out-of-sample Sharpe ratio under high-dimensional asymptotics with estimation errors in both the mean vector and the covariance matrix. We show how the reference penalty and the investment horizon jointly affect the optimized portfolio performance, and how regularization operates differently from the single-period portfolio optimization. Extensive simulation and real data studies demonstrate that the proposed framework improves the stability and out-of-sample Sharpe ratios of multiperiod policies significantly.