w-MPS Risk Aversion and the CAPM

This paper establishes general conditions for the validity of mutual fund separation and the equilibrium CAPM. We use partial preference orders that display weak form mean preserving spread (w-MPS) risk aversion in the sense of Ma (2011). We derive this result without imposing any distributional assumptions on asset returns. The results hold even when the market contains an infinite number of securities and a continuum number of traders, and when each investor is permitted to hold some (arbitrary) finite portfolios. A proof of existence of equilibrium CAPM is provided for finite economies by assuming that when preferences are constrained on the market subspace spanned by the risk free bond, the market portfolios admit continuous utility representations.