The cost of a short-selling constraint – welfare implications for investors under uncertainty

Abstract

In this article, I analyse investors' welfare losses from being restricted from short-selling. To measure those losses, I use the concept of the proportionate opportunity cost along with various Constant Relative Risk Aversion (CRRA) utility functions. Two sets of asset returns are used with a Vector Autoregressive process for generating joint returns distributions: the original historical asset returns data set and the historical asset returns with extreme values exaggerated. In each case, 1000 alternative sets of assets, including one with a risk-free nominal return, are randomly made available for investment. I show that the optimal portfolio strategy with the short-selling constraint performs almost as well as the unconstrained portfolio strategy for investors with medium and high levels of risk aversion. The results, derived from the original historical asset returns data set, show that investors' welfare losses reach 12.8% of initial wealth when risk aversion is low and reach 13.5% of initial wealth with extreme returns exaggerated. The results in both cases indicate that less risk-averse investors experience greater welfare losses and that the short-selling constraint reduces the cost of sub-optimal diversification.