Portfolio Selection under Median and Quantile Maximization

63 Pages Posted: 20 Aug 2020 Last revised: 30 Mar 2021

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: March 30, 2021

Abstract

Although maximizing median and quantiles is intuitively appealing and has an axiomatic foundation, it is difficult to study the optimal portfolio strategy due to the discontinuity and time inconsistency in the objective function. We use the intra-personal equilibrium approach to study the problem. Interestingly, we find that the only viable outcome is from the median maximization, because for other quantiles either the equilibrium does not exist or there is no investment in the risky assets. The median maximization strategy gives a simple explanation to why wealthier people invest more percentage of their wealth in risky assets.

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 (March 30, 2021). 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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