Reference Dependence: Endogenous Anchors and Life-Cycle Investing

Abstract

In a complete market, we find optimal portfolios for an investor whose satisfaction stems from both a payoff's intrinsic utility and its comparison with a reference, as specified by Köszegi and Rabin. In the regular regime, arising when reference-dependence is low, the marginal utility of the optimal payoff is proportional to a twist of the pricing kernel. High reference-dependence leads to the anchors regime, whereby investors reduce disappointment by concentrating significant probability in one or few fixed outcomes, and multiple personal equilibria arise. If stocks follow geometric Brownian motion, the model implies that younger investors have larger stocks positions than older investors, suggesting that reference-dependence helps explain this typical recommendation of financial planners.