We derive asset-pricing and portfolio-choice implications of a dynamic incomplete-markets model in which consumers are heterogeneous in several respects: labor income, asset wealth, and preferences. In contrast to earlier papers, we insist on at least roughly matching the model's implications for heterogeneity — notably, the equilibrium distributions of income and wealth — with those in U.S. data. This approach seems natural: Models that rely critically on heterogeneity for explaining asset prices are not convincing unless the heterogeneity is quantitatively reasonable. We find that the class of models we consider here is very far from success in explaining the equity premium when parameters are restricted to produce reasonable equilibrium heterogeneity. We express the equity premium as a product of two factors: the standard deviation of the excess return and the market price of risk. The first factor, as expected, is much too low in the model. The size of the market price of risk depends crucially on the constraints on borrowing. If substantial borrowing is allowed, the market price of risk is about one one-hundredth of what it is in the data (and about 15% higher than in the representative-agent model). However, under the most severe borrowing constraints that we consider, the market price of risk is quite close to the observed value.