Overconfident investors, Predictable Returns, and optimal consumption-portfolio rules

In a market characterized by partial information, we delve into the influence of overconfidence on individual optimal consumption and portfolio decisions. To address this, we tackle the max–min expected utility problem, which allows us to derive the optimal consumption and portfolio rules. Solving this problem yields two higher-order nonlinear partial differential equations that capture the scaled deterministic equivalent wealth − a key component for evaluating the value function and quantifying welfare loss. This paper presents an alternative theoretical perspective on the phenomena of underconsumption or overinvestment, attributing these behaviors to the overconfidence bias. Our model forecasts that overconfidence bias leads to an excessive allocation to risky assets and a reduction in consumption, thereby inevitably resulting in a certain degree of welfare loss. Moreover, it provides a cohesive theoretical framework to explain stock return puzzles, such as the momentum and reversal effects, within a structured model. Significantly, we discover that the conditional Sharpe ratio adheres to a mean-reverting process. These insights indicate that overconfidence bias significantly influences individual behavior, which in turn has a profound impact on return anomalies.