We experimentally test a theory of risky choice in which the perception of a lottery payoff is noisy due to information processing constraints in the brain. We model perception using the principle of efficient coding, which implies that perception is most accurate for those payoffs that occur most frequently. Across two preregistered laboratory experiments, we manipulate the distribution from which payoffs in the choice set are drawn. In our first experiment, we find that risk taking is more sensitive to payoffs that are presented more frequently. In a follow-up task, we incentivize subjects to classify which of two symbolic numbers is larger. Subjects exhibit higher accuracy and faster response times for numbers they have observed more frequently. In our second experiment, we manipulate the payoff distribution so that efficient coding modulates the strength of valuation biases. As we experimentally increase the frequency of large payoffs, we find that subjects perceive the upside of a risky lottery more accurately and take greater risk. Together, our experimental results suggest that risk taking depends systematically on the payoff distribution to which the decision maker’s perceptual system has recently adapted. More broadly, our findings highlight the importance of imprecise and efficient coding in economic decision making.

We present a new model of asset prices in which investors evaluate risk according to prospect theory and examine its ability to explain 23 prominent stock market anomalies. The model incorporates all of the elements of prospect theory, accounts for investors' prior gains and losses, and makes quantitative predictions about an asset's average return based on empirical estimates of the asset's return volatility, return skewness, and past capital gain. We find that the model can help explain a majority of the 23 anomalies.

Using novel data from a crowdsourcing platform for ranking stocks, we investigate how investors form expectations about stock returns over the next week. We find that investors extrapolate from stocks’ recent past returns, with more weight on more recent returns, especially when recent returns are negative, salient, or from a dispersed cross-section. Such extrapolative beliefs are stronger among nonprofessionals and large stocks. Moreover, consensus rankings negatively predict returns over the next week, more so among stocks with low institutional ownership and a high degree of extrapolation. A trading strategy that sorts stocks on investor beliefs generates an economically significant profit.