Asset Pricing Implications of Benchmarking : A Two-Factor CAPM

In this paper we consider the equilibrium effects of an institutional investor whose performance is benchmarked to an index. In a partial equilibrium setting, the objective of the institutional investor is modeled as the maximization of expected utility (an increasing and concave function, in order to accommodate risk aversion) of final wealth minus a benchmark. In equilibrium this optimal strategy gives rise to the two-beta CAPM in Brennan (1993): together with the market beta a new risk-factor (that we call active management risk) is brought into the analysis. This new beta is deffined as the normalized (to the benchmark's variance) covariance between the asset excess return and the excess return of the market over the benchmark index. Different to Brennan, the empirical test supports the model's predictions. The cross-section return on the active management risk is positive and signifficant especially after 1990, when institutional investors have become the representative agent of the market