Failing to Foresee the Updating of the Reference Point Leads to Time-Inconsistent Investment

The current literature on behavioral portfolio optimization with reference point updating assumes that the decision maker foresees how the reference point will evolve and thus solves a time-consistent problem formulation. Empirical findings on the other hand suggest that decision makers often fail to foresee the updating of the reference point and consequently make time-inconsistent decisions. We analyze and compare the optimal investment strategies for a discrete-time behavioral portfolio optimization problem with loss-aversion and time-varying reference points under both the time-consistent and time-inconsistent framework and for different updating rules for the reference point. There is only one framework predicting realistic investment behavior: the decision maker fails to foresee the updating of the reference point and thus faces a time-inconsistent problem, solves for a dynamically optimal strategy and updates the reference point in a non-recursive manner