Benchmark, relative return, and asset pricing

Abstract

ABSTRACT In this note, we develop a simple asset pricing model using the relative return to a benchmark. The model makes no assumption on free-risk securities, equilibrium conditions, utility functions, diffusion processes, probability distributions, or return generating processes. Our main result indicates that the asset’s expected return is equal to the expected return of the lowest-risk asset, plus a risk premium directly proportional to the covariance between the asset’s excess return and the benchmark factor. This suggests that an asset pricing model can be built without restrictive assumptions. This also suggests that the classic CAPM can be viewed as a special case of our benchmark model.