Prospect Theory, Partial Liquidation and the Disposition Effect

We solve the problem of an agent with prospect theory preferences who seeks to liquidate a portfolio of (divisible) claims.

Our methodology enables us to consider different formulations of prospect preferences in the literature (piecewise exponential or piecewise power) and various price processes. We find that these differences in specification matter - for instance, with piecewise power functions, the agent may liquidate at a loss relative to break-even, albeit the likelihood of liquidating at a gain is much higher than liquidating at a loss. This is consistent with the disposition effect documented in empirical and experimental studies. We find the agent does not choose to partially liquidate a position, but rather, if liquidation occurs, the entire position is sold. This is in contrast to partial liquidation when agents have standard concave utilities.