Benchmark, relative return, and asset pricing

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.

KEYWORDS:

• Asset pricing
• benchmark
• relative return
• CAPM

JEL CLASSIFICATION:

• G11
• G12

Acknowledgments

I wish to thank John Y. Campbell, from Harvard University, for his very helpful comments and references.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

¹ In this manuscript, the tilde (~) indicates a random variable. Operators E_t, V_t, and Cov_t refer respectively to mathematical expectations, variance and covariance, where index t implies that we consider the available information at time t (index k refers to investor k).