We develop a model of portfolio selection with subjective uncertainty and learning in order to explain why some people hold stocks while others don’t. We model heterogeneity in information directly, which is an alternative to the existing explanations that emphasized heterogeneity in transaction costs of investment. We plan to calibrate the model to survey data (when available) on people’s perception about the distribution of stock market returns. Our approach also leads to a model of learning with new implications such as zero optimal risky assets, or ex post correlation of uncorrelated labor income and optimal portfolio composition. It also points to two factors in probabilistic thinking that should have a major impact on stock ownership. These are the level and the precision of expectations. We construct proxy measures for the two parameters from the 1992-2000 waves of the Health and Retirement Study (HRS). We use a large battery of the subjective probability questions administered in each wave of HRS to construct an overall “index of optimism” (the correlated factor between all subjective probabilities) and “index of precision” (the fraction of nonfocal probability answers, following Lillard and Willis, 2001). We also construct measures for how people forecast the weather, their cognitive capacity, wealth, and basic demographics. Our results indicate that stock ownership and the probability of becoming a stockholder are strongly positively correlated with the indices of the level and precision of expectations. Interpretation of the former is quite challenging and further research is needed to understand its full content.