Taylor series approximations to expected utility and optimal portfolio choice

This paper revisits the subject of Taylor series approximations to expected utility and investigates the applicability of the technique to optimal portfolio choice problems. We first provide conditions under which the approximate expected utility of a given portfolio converges to its exact counterpart. We then extend the analysis to the optimal portfolio choice setting and provide conditions on the distribution of asset returns under which the solution to the approximate portfolio choice problem converges to its exact counterpart. Finally, we show that, when asset returns are skewed, one can improve the precision and efficiency of the Taylor expansion by applying a simple nonlinear transformation to asset returns designed to symmetrize the transformed return distribution and shrink its support.