Portfolio Selection under Median and Quantile Maximization

TL;DR

This paper investigates optimal portfolio strategies under median and quantile maximization, revealing that only median maximization yields viable equilibrium strategies and explaining wealthier individuals' higher risky asset investments.

Contribution

It introduces an intra-personal equilibrium approach to portfolio optimization under median and quantile objectives, highlighting the unique viability of median maximization.

Findings

Median maximization yields viable equilibrium strategies.

Quantile objectives other than median often lack equilibrium or lead to no risky investment.

Median maximization explains why wealthier individuals invest more in risky assets.

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.