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Realization Utility with Path-Dependent Reference Points

In this paper, we propose a tractable model to study the impact of path-dependent reference points on optimal trading strategies of a realization utility investor. We find that when reference points are adaptive to prior paper gains and losses, two interesting effects arise endogenously: (a) Discount effect, i.e., a constant subjective discount factor in effect becomes a stochastic one; and (b) Mean-reverting effect, i.e., a constant investment opportunity in effect becomes a stochastic one with expected return being mean-reverting, which provides a new interpretation of belief in mean reversion. In addition, these two effects offset each other in the state of paper gains while get reinforced in the state of paper losses, leading to a more salient disposition effect. The model can be easily extended to incorporate other factors such as asymmetric adaptation of reference points, jump risks in the underlying stocks, and liquidation shocks, yielding new interesting trading behaviors.