Linear Beta Pricing with Inefficient Benchmarks
Forthcoming, Quarterly Journal of Finance
44 Pages Posted: 29 Mar 2006 Last revised: 17 Apr 2013
Date Written: March 11, 2013
Current asset pricing models require mean-variance efficient benchmarks, which are generally unavailable because of partial securitization and free float restrictions. We provide a pricing model that uses inefficient benchmarks, a two-beta model, one induced by the benchmark and one adjusting for its inefficiency. While efficient benchmarks induce zero-beta portfolios of the same expected return, any inefficient benchmark induces infinitely many zero-beta portfolios at all expected returns. These make market risk premiums empirically unidentifiable and explain empirically found dead betas and negative market risk premiums. We characterize other misspecifications that arise when using inefficient benchmarks with models that require efficient ones. We provide a space geometry description and analysis of the specifications and misspecifications. We enhance Roll (1980), Roll and Ross’s (1994), and Kandel and Stambaugh’s (1995) results by offering a “Two Fund Theorem,” and by showing the existence of strict theoretical “zero relations” everywhere inside the portfolio frontier.
Keywords: Linear beta pricing, CAPM, expected returns, incomplete information, zero relation
JEL Classification: G10, G12
Suggested Citation: Suggested Citation