The paper presents a computationally efficient method to solve overlapping gener- ations models with asset choice. The method is used to study an OLG economy with many cohorts, up to 3 different assets, stochastic volatility, short-sale constraints, and subject to rather large technology shocks. On the methodological side, the main findings are that global projection methods with polynomial approximations of degree 3 are sufficient to provide a very precise solution, even in the case of large shocks. Globally linear approximations, in contrast to local linear approximations, are sufficient to capture the most important financial statistics, including not only the average risk premium, but also the variation of the risk premium over the cycle. However, global linear approximations are not sufficient to reliably pin down asset choices. With a risk aversion parameter of only 4, the model generates a price of risk, measured as the Sharpe ratio, that is almost half of what it is for US stocks. However, the asset price fluctuations and the equity premium are much smaller than in US data.