Portfolio Selection in Quantile Utility Models
57 Pages Posted: 13 Dec 2019
Date Written: November 27, 2019
This paper develops a model for optimal portfolio allocation for an investor with quantile preferences. The investor chooses optimal allocation of weights to maximize the τ-quantile of the utility of the portfolio, for τ ∈ (0,1). A central characteristic of this model is that the portfolio choice is independent of the utility function and related exclusively to the risk attitude, which is captured by the quantile τ. We derive conditions under which the optimal portfolio decision has an interior solution that guarantees diversification vis-a-vis fully investing in a single risky asset. For some families of popular distribution functions the optimal portfolio decision is characterized by two regions: a first region given by the lower quantiles in which diversification is optimal and a second region given by the upper quantiles in which the optimal portfolio allocation is characterized by no diversification. The presence of a risk-free asset produces an all-or-nothing optimal response of the investor to the risky asset that depends on the investors' quantile preferences. This result entails a different interpretation of standard mutual fund separation theorem. In an empirical application we compare the optimal asset allocation of expected utility and quantile utility individuals for a tactical portfolio of stocks, bonds and a risk-free asset.
Keywords: Optimal asset allocation, Expected Utility, Quantile Utility, Portfolio Theory, Risk Attitude
JEL Classification: G11
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