Multi-period portfolio choice under loss aversion with dynamic reference point in serially correlated market

Abstract

This paper explores a novel multi-period portfolio decision model for loss-averse investors with dynamically adapted reference points in a market with serially correlated returns. We demonstrate that the optimal policy is a piecewise linear function of the deviation between current wealth and reference level, and its slopes are a path-dependent function of the historical returns, in sharp contrast to the constant slopes generated by the simplified model that ignores the diminishing sensitivity and assumes independent returns. This distinctive characteristic significantly departs from the conventional V-shaped pattern of the risky position, leading to a more intricate nonlinear functional mapping. Our study underscores the potential pitfalls of relying on the simplified model and offers valuable insights for investors and practitioners seeking to formulate effective portfolio strategies under realistic market conditions. Furthermore, our simulation analysis indicates that the predictability of returns, coupled with a slight degree of diminishing sensitivity, may amplify the disposition effect. Lastly, we establish that the new policy also effectively addresses the multi-period mean-conditional-value-at-risk (CVaR) portfolio optimization problem in the context of correlated returns, thereby expanding the practical applications of our findings.