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

Zhongbao Zhou, Xianghui Liu, Helu Xiao, TianTian Ren and Wenbin Liu

Mathematical Problems in Engineering, 2018, vol. 2018, 1-20

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.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:7563093

DOI: 10.1155/2018/7563093

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