Discrete-Time Mean-CVaR Portfolio Selection and Time-Consistency Induced Term Structure of the CVaR

25 Pages Posted: 22 Sep 2017

See all articles by Moris Simon Strub

Moris Simon Strub

Southern University of Science and Technology - Division of Information Systems and Management Engineering

Duan Li

Chinese University of Hong Kong; City University of Hong Kong

Xiangyu Cui

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

Jianjun Gao

Shanghai University of Finance and Economics; Shanghai Jiao Tong University

Date Written: September 21, 2017

Abstract

We investigate a discrete-time mean-risk portfolio selection problem, where risk is measured by the conditional value-at-risk (CVaR). By embedding this time-inconsistent problem into a family of expected utility maximization problems with a piecewise linear utility function, we solve the problem analytically. In contrast to the case of a complete, continuous-time market, the mean-CVaR efficient frontier in this generally incomplete, discrete-time setting is a straight line in the mean-CVaR plane and there is in particular a constant trade-off between risk and return. The cumulated amount invested in the risky assets under the optimal strategy is of a V -shaped pattern as a function of the current wealth. We further solve an inverse investment problem, where we investigate how mean-CVaR preferences need to adapt such that the pre-commited optimal strategy remains optimal at any point in time. Our result shows that, although conceptually distinct, a pre-commited mean-CVaR investor behaves like a naive mean-CVaR investor with a time-increasing confidence level for the CVaR, who revises her investment decision at every point in time. Finally, an empirical application of our results suggests that risk measured by the CVaR might help to understand the long-standing equity premium puzzle.

Keywords: Mean-Risk Portfolio Choice, Conditional Value-At-Risk, Optimal Investment Strategies, Time-Inconsistency, Time-Consistency Induced Risk Measure, Equity Premium Puzzle

JEL Classification: C61, G11

Suggested Citation

Strub, Moris Simon and Li, Duan and Cui, Xiangyu and Gao, Jianjun, Discrete-Time Mean-CVaR Portfolio Selection and Time-Consistency Induced Term Structure of the CVaR (September 21, 2017). Available at SSRN: https://ssrn.com/abstract=3040517 or http://dx.doi.org/10.2139/ssrn.3040517

Moris Simon Strub

Southern University of Science and Technology - Division of Information Systems and Management Engineering ( email )

1088 Xueyuan Ave
Shenzhen, Guangdong
China

HOME PAGE: http://sites.google.com/view/morisstrub/home

Duan Li (Contact Author)

Chinese University of Hong Kong ( email )

Shatin, New Territories
Hong Kong

City University of Hong Kong

Tat Chee Avenue
Kowloon Tong
Kowloon
Hong Kong
852 3442 8591 (Phone)

Xiangyu Cui

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

777 Guoding Road
Shanghai, Shanghai 200433
China

Jianjun Gao

Shanghai University of Finance and Economics ( email )

No. 100 Wudong Road
Shanghai, Shanghai 200433
China

Shanghai Jiao Tong University ( email )

800 Dongchuan Road
Shanghai
China
+86-18201925139 (Phone)
+86 34205004 (Fax)

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