Return expectations across the wealth distribution

This paper examines how a household’s expectation of asset returns varies with wealth. In the model, households face idiosyncratic investment risks and confront Knightian uncertainty about returns on the risky asset. Their return expectations are formed out of a dynamic zero-sum game with nature. We characterize the robust consumption–investment policies using a perturbation method. The model predicts a U-shaped relationship between expected risky returns and wealth, as nature is less incentivized to distort the perceptions of both poor and rich households. We confront this prediction with U.S. survey data.