Myopic Portfolio Choice with Higher Cumulants

This paper explores analytically the implications of higher order moments in the distribution of returns for the myopic optimal portfolio of an expected utility maximizer. The use of cumulant generating functions and entropy is crucial to find these solutions. With constant absolute risk aversion (CARA) utility, I find in closed form the optimal amount of risky asset for many distributions. My focus is in the problem with one risky asset but the results can be extended to multivariate returns. When possible, I set up a simple equilibrium model and solve for the equilibrium price, analyzing the effect of higher cumulants on the risk premium. My approach also provides new intuition about the effect of higher order events with constant relative risk aversion (CRRA). In that case, with a traditional budget constraint, the model stills need to be evaluated numerically, but I introduce a new formulation to obtain analytical results. The main practical conclusion of this paper is that tail events can matter for portfolio choice when departures from normality are large. ∗I would like to thank very helpful comments from John Campbell, Emmanuel Farhi, Leonid Kogan, Luis Viceira and participants in Harvard/HBS Finance Lunch.