Choice under uncertainty may be viewed as choice between alternative probability distributions of returns. Under Von Neumann and Morgenstern's assumptions, an individual's optimal choice is a distribution that maximizes the expected utility of returns. In the theoretical analysis, the distribution functions are assumed to be known However, in most realistic cases, the distributions of returns are unknown and are estimated using available economic data. The traditional mode of analysis is to neglect the estimation risk and use the estimated distribution (in lieu of the true distribution) in determining the optimal choice under uncertainty. In this paper, we consider the portfolio choice problem and determine the effect of estimation risk on an individual's optimal choice under uncertainty.