This study extends the classic Capital Asset Pricing Model (CAPM) by relaxing the assumptions that all assets are perfectly divisible and liquid, and that investors face the same set of investment opportunities. It is assumed that investors can invest in two types of assets: perfectly divisible, and perfectly indivisible (or discrete). Also, investors may face different sets of investment opportunities in risky indivisible assets. The paper focuses on the following subjects: single investor's equilibrium and his demand for risky assets; market equilibrium and risk-return relationships; and optimal decision rules for evaluating single risky projects. The modifications that the single investor and the market as a whole make in the equilibrium conditions due to the presence of investment opportunities in risky indivisible assets, are identified, studied, and interpreted. It is shown that the theoretical implications of the present extended model are more consistent with empirical findings, and that the relaxation of the assumption that all assets are perfectly divisible eliminates some of the most unattractive and disturbing implications of the classic CAPM, while preserving the more attractive properties of that model.