Time-Consistent Strategies for Multi-Period Portfolio Optimization with/without the Risk-Free Asset

Author:

Zhou Zhongbao1ORCID,Liu Xianghui1,Xiao Helu2ORCID,Ren TianTian1,Liu Wenbin13

Affiliation:

1. School of Business Administration, Hunan University, Changsha 410082, China

2. Business School, Hunan Normal University, Changsha 410081, China

3. Kent Business School, University of Kent, Canterbury, CT2 7PE, UK

Abstract

The pre-commitment and time-consistent strategies are the two most representative investment strategies for the classic multi-period mean-variance portfolio selection problem. In this paper, we revisit the case in which there exists one risk-free asset in the market and prove that the time-consistent solution is equivalent to the optimal open-loop solution for the classic multi-period mean-variance model. Then, we further derive the explicit time-consistent solution for the classic multi-period mean-variance model only with risky assets, by constructing a novel Lagrange function and using backward induction. Also, we prove that the Sharpe ratio with both risky and risk-free assets strictly dominates that of only with risky assets under the time-consistent strategy setting. After the theoretical investigation, we perform extensive numerical simulations and out-of-sample tests to compare the performance of pre-commitment and time-consistent strategies. The empirical studies shed light on the important question: what is the primary motivation of using the time-consistent investment strategy.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

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