A Concave Security Market Line

We provide theoretical and empirical arguments in favor of a diminishing marginal premium for market risk. In capital market equilibrium with binding portfolio restrictions, investors with different risk aversion levels generally hold different sets of risky securities. Whereas the traditional linear relation breaks down, equilibrium can be described or approximated by a concave relation between expected return and market beta, and a concave relationship between market alpha and market beta. An empirical analysis of U.S. stock market data confirms the existence of a significant concave cross-sectional relation between average return and estimated market beta. We estimate that the market risk premium is at least four to six percent per annum, substantially above traditional estimates. A practical implication for active portfolio managers is that the alpha of ``betting against beta'' strategies seems dominated by the medium-minus-high-beta spread rather than the low-minus-medium-beta spread. The success of such strategies thus largely depends on underweighting or short selling high-beta stocks.