Asset preference, skewness, and the measurement of expected utility

Abstract

This article shows that serious analytical errors may occur in expected utility theory when Taylor series approximation methods are used without careful attention to underlying mathematical assumptions. Recent studies have developed theory incorporating skewness of return into expected utility calculations based on a Taylor series approximation. It is apparent that this theory is invalid if assumptions for application of a Taylor series cannot be met. Errors may occur if returns fall outside the region of convergence of the utility function ot if the partial sums of the Taylor series provide poor approximations to the utility function. Stylized examples are presented to illustrate miscalculation of utility when the various assumptions are violated. These examples are motivated by the use of Taylor series approximations in current literature which deal with the new spectrum of financial securities.