Optimal stock investment decisions rely on assessments of the distribution of expected returns. Using a representative sample, we find over half the US population cannot answer simple questions on expected stock returns. Respondents who are unable to make any return prediction, who cannot answer questions on the distribution of expected returns, or who reveal unlikely distributional beliefs participate less in the stock market and have smaller stock investments. However, overoptimistic investors are more likely to participate in the stock market and have larger stock investments. These results persist after controlling for financial literacy, intelligence, education, and demographics. People who are ignorant about stock return distribution are more likely to invest in equities if they have higher levels of trust. Therefore, trust can substitute for cognition as a factor positively associated with individuals’ propensity to invest.

Individuals’ stock market participation depends on the risk-return trade-off they expect to achieve. We find that the expected economic benefits of investing are highly heterogeneous. We define the personal equity risk premium (PERP) as the difference between an individual's expectation of returns and personal opportunity cost of capital. Higher PERP is associated with greater stock market participation. Our results hold after we control for known factors, such as financial literacy, trust, and loss aversion, and are stronger for the level of stock investment. Disentangling PERP shows that both components help explain both stock market participation and the level of participation.