Rationally Irrational? Learning and Short-Sale Restrictions in Dynamic Portfolio Decisions

Abstract

This paper examines the impact of learning on portfolio choice and asset pricing when there are short-sale constraints. Prior research on parameter uncertainty and learning shows that mildly risk averse investors always hold more extreme positions, short or long, than investors who never change their parameter estimates. Here, we show that short-sale constraints can reverse the conclusion. Namely, if an asset has a negative risk-premium (or a gamble's odds are unfair), an investor in a multiperiod world may still want to hold the asset (or take the gamble). Similarly, an in contrast to the extant literature on learning, assets with high risk premium (or gambles with great odds) may not be held at all. These results are driven by the possibility that the future will prove the investor's current beliefs wrong. We introduce implied risk aversion as a measure of the wedge that is being driven between investors and outside observers by the combination of short-sale constraints, parameter uncertainty, and learning. To an outsider, who does not account for parameter uncertainty, mildly risk averse investors always look less risk averse than they truly are. The converse is true for investors who actually are more risk averse. Their portfolio choices can even imply infinite levels of risk-aversion. When we solve for the equilibrium in a short-sale restricted economy with heterogeneity in investor risk aversion, we find that the market always appears to be more risk-averse than it really is. By contrast, learning without short-sale restrictions creates only a modest discrepancy between reality and inferences. Parameter uncertainty, learning, and constraints that inhibit short-sales may explain the equity premium puzzle.