Optimal positive thinking and decisions under risk

We examine a static one-riskfree-one-risky asset portfolio choice when the investor’s well-being is affected by the anticipatory feelings associated to potential capital gains and losses. These feelings can be manipulated by the choice of subjective beliefs on the distribution of returns. However, the bias of these endogeneous subjective beliefs induces the choice of a portfolio that is suboptimal with respect to the objective expected utility of final wealth. We characterize the structure of these optimal beliefs. We show that the subjective probability distribution must be degenerated at the lower and upper bounds of feasible returns. When the intensity of anticipatory feelings is small, the formation of beliefs must be biased in favor of optimism, which implies an increase in the equilibrium demand for the risky asset. We also show that the optimal beliefs are approximately independent of the investor’s degree of risk aversion.