A note on the CAPM with endogenously consistent market returns

I demonstrate that with the market return determined by the equilibrium returns of the CAPM, expected returns of an asset are affected by the risks of all assets jointly. Another implication is that the range of feasible market returns will be limited and dependent on the distribution of weights in the market portfolio. A large and well diversified market with no dominating asset will only return zero while a market dominated by a small number of assets will only return the risk-free rate. In the limiting case of atomistic assets, we recover the properties of the standard CAPM.