Dynamic Factor Model-Based Multiperiod Mean-Variance Portfolio Selection with Portfolio Constraints

TL;DR

This paper develops a dynamic factor model-based approach for multi-period mean-variance portfolio optimization with practical constraints, providing semi-analytical solutions and demonstrating improved out-of-sample performance with real data.

Contribution

It introduces a semi-analytical dynamic programming solution for constrained multi-period portfolio selection under a broad class of dynamic factor models, including practical constraints.

Findings

Optimal policies are piecewise linear feedback functions of wealth and factors.

Portfolio policies depend on two stochastic processes derived from the model.

Incorporating factor structures can improve out-of-sample portfolio performance.

Abstract

Motivated by practical applications, we explore the constrained multi-period mean-variance portfolio selection problem within a market characterized by a dynamic factor model. This model captures predictability in asset returns driven by state variables and incorporates cone-type portfolio constraints that are crucial in practice. The model is broad enough to encompass various dynamic factor frameworks, including practical considerations such as no-short-selling and cardinality constraints. We derive a semi-analytical optimal solution using dynamic programming, revealing it as a piecewise linear feedback policy to wealth, with all factors embedded within the allocation vectors. Additionally, we demonstrate that the portfolio policies are determined by two specific stochastic processes resulting from the stochastic optimizations, for which we provide detailed algorithms. These processes reflect the investor's assessment of future investment opportunities and play a crucial role in characterizing the time consistency and efficiency of the optimal policy through the variance-optimal signed supermartingale measure of the market. We present numerical examples that illustrate the model's application in various settings. Using real market data, we investigate how the factors influence portfolio policies and demonstrate that incorporating the factor structure may enhance out-of-sample performance.