Asymmetries and Portfolio Choice

Asset returns have asymmetric distributions and their correlations change in market up and downturns. Also, investors' attitudes towards risk show an asymmetric treatment of losses versus gains. Motivated by these facts, we examine the portfolio choice problem of an investor with generalized disappointment aversion utility, who faces a set of asset returns described by a multivariate extended skew-normal distribution. We derive an analytical solution for the proposed setup, and show that it leads to three fund separation: the investor allocates wealth to the risk-free asset, the standard mean-variance efficient portfolio, and an additional portfolio reflecting the asymmetry in asset returns. In our framework, the optimal portfolio can be characterized by the investor's effective risk aversion and implicit asymmetry aversion. We demonstrate that disappointment aversion is associated with much larger asymmetry aversion than standard preferences. Our model offers an explanation to patterns in popular portfolio advice that are puzzles to standard models.