Portfolio Selection under Median and Quantile Maximization

71 Pages Posted: 20 Aug 2020

See all articles by Xue Dong He

Xue Dong He

The Chinese University of Hong Kong - Department of Systems Engineering and Engineering Management

Zhao Li Jiang

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering and Engineering Management; National University of Singapore (NUS) - Risk Management Institute

Steven Kou

Boston University

Date Written: July 22, 2020

Abstract

In this paper, we study a portfolio selection problem in which an agent trades a risk-free asset and multiple risky assets with deterministic mean return rates and volatility and wants to maximize the alpha-quantile of her wealth at some terminal time. Because of the time inconsistency caused by quantiles, we consider intra-personal equilibrium strategies. We find that among the class of time-varying, affine portfolio strategies, the intra-personal equilibrium does not exist when alpha>1/2, leads to zero investment in the risky assets when alpha<1/2, and is a portfolio insurance strategy when alpha=1/2. We then compare the intra-personal equilibrium strategy in the case of alpha=1/2, namely under median maximization, to some other strategies and apply it to explain why more wealthy people invest more precentage of wealth in risky assets. Finally, we extend our model to account for multiple terminal time.

Keywords: quantiles, median, portfolio selection, intra-persional equilibrium, portfolio insurance

JEL Classification: G11

Suggested Citation

He, Xue Dong and Jiang, Zhao Li and Kou, Steven, Portfolio Selection under Median and Quantile Maximization (July 22, 2020). Available at SSRN: https://ssrn.com/abstract=3657661 or http://dx.doi.org/10.2139/ssrn.3657661

Xue Dong He (Contact Author)

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

505 William M.W. Mong Engineering Building
The Chinese University of Hong Kong, Shatin, N.T.
Hong Kong
Hong Kong

HOME PAGE: http://https://sites.google.com/site/xuedonghepage/home

Zhao Li Jiang

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

Hong Kong
China

National University of Singapore (NUS) - Risk Management Institute ( email )

21 Heng Mui Keng Terrace
Level 4
Singapore, 119613
Singapore

Steven Kou

Boston University ( email )

595 Commonwealth Avenue
Boston, MA 02215
United States
6173583318 (Phone)

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