The Effect of Higher Moments of Risky Asset Return on Portfolio Choice

Abstract

This paper studies the effect of higher moments of risky asset return on portfolio choice. It builds the model of portfolio choice problem and approximates its optimal solution as a function of the mean, variance, skewness, and kurtosis of the excess return by applying a Taylor expansion to the Euler equation, which maximizes the expected utility of next period portfolio wealth; based on the daily data of Shanghai Exchange Composite Index from January 2nd, 1991 to December 29th, 2006, it does an empirical study on the property of return distribution and the effect of higher moments on portfolio choice. Results show: the distribution of risky asset return is non-normality; the optimal allocation to the risky asset increases (decreases) with positive (negative) skewness and decreases with excess kurtosis, at the same time, the magnitude of increasing and decreasing increases with the degree of investor's relative risk aversion; time aggregation reduces the magnitude of non-normality, but does not change the effect of higher moments on portfolio choice; positive skewness in the Chinese stock market is different from negative skewness in the U.S. stock market. The study demonstrates that the effect of higher moments of risky asset return should be considered in the context of portfolio choice.