^aCollege of Business and Technology, Western Illinois University, 1 University Circle, Macomb, IL 61455-1390, USA. E-mail: AA-Melkumian@wiu.edu

Abstract

A restriction on portfolio size results in welfare losses for investors. To measure these welfare losses, we compare n-asset optimal portfolios with 26-asset optimal portfolios using the concept of proportionate opportunity cost. The original historical asset returns data are used with a VAR in generating joint returns distributions for the portfolio formation period. We find that suboptimal diversification imposes substantial costs on investors with low levels of relative risk aversion. Investors with high levels of risk aversion incur very small or no cost at all diversifying sub-optimally. We show that investors with high levels of risk aversion place most of their initial wealth in the safe asset and, therefore, few stocks are needed to achieve optimal diversification.