Discrete time multi-period mean-variance model: Bellman type strategy and Empirical analysis

TL;DR

This paper introduces a Bellman principle-based dynamic strategy for discrete multi-period mean-variance models, enabling time consistency and improved risk-return trade-offs, with empirical validation of its advantages over traditional strategies.

Contribution

It develops a novel Bellman principle approach for dynamic, time-consistent strategies in multi-period mean-variance models, including varying investment periods.

Findings

Dynamic strategies outperform 1/n strategy in return and risk.

The model achieves higher returns with lower risk.

Optimal investment periods are effectively determined.

Abstract

In this paper, we attempt to introduce the Bellman principle for a discrete time multi-period mean-variance model. Based on this new take on the Bellman principle, we obtain a dynamic time-consistent optimal strategy and related efficient frontier. Furthermore, we develop a varying investment period discrete time multi-period mean-variance model and obtain a related dynamic optimal strategy and an optimal investment period. This paper compares the highlighted dynamic optimal strategies of this study with the 1/n equality strategy, and shows that we can secure a higher return with a smaller risk based on the dynamic optimal strategies.