Prospect Theory, Liquidation, and the Disposition Effect

There is a well-known intuition linking prospect theory with the disposition effect, the tendency of investors to sell assets that have risen in value rather than fallen. Recently, several authors have studied rigorous models in an attempt to formalize the intuition. However, some have found it difficult to predict a disposition effect while others produce a more extreme prediction where investors never voluntarily sell at a loss. We solve a model of asset liquidation where investors realize utility over gains and losses, and utility is concave over gains and convex over losses. Under the preferences of Tversky and Kahneman (Tversky, A., D. Kahneman. 1992. Advances in prospect theory: Cumulative representation of uncertainty. <i>J. Risk Uncertainty</i> <b>5</b>(4) 297-323) and lognormal asset prices, investors exhibit a disposition effect as gains are realized at a greater rate than losses. Nonetheless, in contrast to the extant literature, we find that the investor will "give up" and sell at a loss when the asset has a sufficiently low Sharpe ratio. <i>This paper was accepted by Brad Barber, Teck Ho, and Terrance Odean, special issue editors.</i>