Portfolio Selection under Median and Quantile Maximization
63 Pages Posted: 20 Aug 2020 Last revised: 30 Mar 2021
Date Written: March 30, 2021
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: Suggested Citation