Time Consistent Behavioral Portfolio Policy for Dynamic Mean–Variance Formulation

14 Pages Posted: 24 Apr 2018

See all articles by Xiangyu Cui

Xiangyu Cui

Shanghai University of Finance and Economics - School of Statistics and Management

Xun Li

Hong Kong Polytechnic University

Duan Li

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering & Engineering Management

Yun Shi

Shanghai University

Date Written: March 2017

Abstract

When one considers an optimal portfolio policy under a mean-risk formulation, it is essential to correctly model investors’ risk aversion which may be time variant or even state dependent. In this paper, we propose a behavioral risk aversion model, in which risk aversion is a piecewise linear function of the current excess wealth level with a reference point at the discounted investment target (either surplus or shortage), to reflect a behavioral pattern with both house money and break-even effects. Due to the time inconsistency of the resulting multi-period mean–variance model with adaptive risk aversion, we investigate the time consistent behavioral portfolio policy by solving a nested mean–variance game formulation. We derive a semi-analytical time consistent behavioral portfolio policy which takes a piecewise linear feedback form of the current excess wealth level with respect to the discounted investment target. Finally, we extend the above results to time consistent behavioral portfolio selection for dynamic mean–variance formulation with a cone constraint.

Keywords: investment analysis, state-dependent risk aversion, dynamic mean–variance formulation, time consistency, behavioral portfolio policy

Suggested Citation

Cui, Xiangyu and Li, Xun and Li, Duan and Shi, Yun, Time Consistent Behavioral Portfolio Policy for Dynamic Mean–Variance Formulation (March 2017). Journal of the Operational Research Society, Vol. 68, Issue 12, 2017. Available at SSRN: https://ssrn.com/abstract=3161479 or http://dx.doi.org/10.1057/s41274-017-0179-6

Xiangyu Cui

Shanghai University of Finance and Economics - School of Statistics and Management ( email )

777 Guoding Road
Shanghai, Shanghai 200433
China

Xun Li

Hong Kong Polytechnic University ( email )

The Hong Kong Polytechnic University
Hung Hom, Kowloon
Hong Kong

Duan Li

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering & Engineering Management ( email )

Shatin, New Territories
Hong Kong
(852) 2609-8323 (Phone)
(852) 2609-5505 (Fax)

HOME PAGE: http://www.se.cuhk.edu.hk/~dli/

Yun Shi (Contact Author)

Shanghai University ( email )

SHANGDA ROAD 99
Shanghai, SHANGHAI 200444
China

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