Dynamic portfolio selection under quantile maximization

Abstract

Although maximizing quantiles is intuitively appealing and has an axiomatic foundation, it is difficult to find the optimal portfolio strategy because of time inconsistency. Using an intrapersonal equilibrium approach and focusing on the class of time-varying affine strategies, 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 risky assets. We also prove that maximizing the median endogenizes the use of portfolio insurance. The calibration of the model uncovers a new empirical phenomenon: “portfolio share smile.”