Approximated Portfolio Choice - Do We Dance on a Pinhead?

Abstract

HARA-utility investors allocate their money to a risk-free fund and to a risky fund (two fund separation). The paper shows that under weak conditions, the risky fund can be approximated by the risky fund derived from exponential utility, without material effects on the certainty equivalent of the portfolio payoff. Also, effects of changes in asset return parameters on the risky fund can be approximated using the exponential utility function, thereby simplifying the analysis. The approximation is of high quality if extreme portfolio returns have a very small probability and if the investor's level of relative risk aversion exceeds 2.

Keywords: HARA-utility, portfolio choice, certainty equivalent, approximated choice

JEL Classification: G10, G11, D81