Reference dependence and endogenous anchors

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 an endogenous reference as modeled by Kőszegi 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, or “anchors.” Multiple equilibria arise because anchors may not be unique. If stocks follow geometric Brownian motion, the model implies that investors with longer horizons choose larger stocks holdings.