An Intertemporal Equilibrium Beta Pricing Model

Gregory Connor, Robert A. Korajczyk
1989 The Review of financial studies  
This article develops an intertemporal, discrete-time, competitive equilibrium version of the arbitrage pricing theory (APT) and explores the econometric implications of this model under various restrictions on investor preferences and on the dynamic behavior of dividends. We describe conditions under which the econometric techniques typically used for estimating and testing the APT can be shown to be consistent with our economic model. We relate our intertemporal version of the APT to the
more » ... the APT to the static APT and to Merton's intertemporal capital asset pricing model. The original arbitrage pricing theory of Ross (1976) is a static asset pricing theory. This means that one views the pricing equilibrium as occurring only once, followed by a terminal realization of investor wealth. Of course, the model is usually tested by relying on time-series data-that is, the observation of the repeated price setting process that occurs in security markets. The time-series data must be assumed to have various stationarity properties to render the model estimable. Since the asset pricing model is static (it has no time dimension), the appropriateness of these stationarity assumptions cannot be addressed within the pricing model. In this case, the economic model provides little guidance about the appropriate specification for the time-series properties of the statistical model. Lucas (1978) suggests an integrated approach in which the statistical model used for estimation (a time-stationary relationship) is derived endogenously in a time-stationary, infinite-horizon asset pricing model. This approach was extended by Prescott and Mehra (1980) , who named the approach a recursive competitive equilibrium (RCE) approach. We apply the RCE approach to the APT, using a model that is similar to the RCE model that Bossaerts and Green (1988) developed in their intertemporal extension of the CAPM. We analyze whether the econometric assumptions needed to estimate the model can be derived endogenously within the model. This general version of the intertemporal APT produces the APT pricing relationship at each point in time, but its time-series properties may not be consistent with the econometric assumptions generally used to estimate various versions of the model. Most, if not all, APT empirical tests require that asset returns obey a strict or approximate factor model with timeconstant betas [e.g., Roll and Ross (1980), Chen (1983), Connor and Korajczyk (1988) , and Lehmann and Modest (1988) ]. Many of the econometric procedures used in these empirical tests also require that returns be inter-temporally homoskedastic. The general version of the intertemporal APT we present is not necessarily consistent with these econometric assumptions. Requiring consistency between the pricing model and the econometric assumptions makes the economic modeling problem more difficult and the necessary assumptions stricter. We believe our RCE model is a useful complement to recent empirical studies that present evidence of time-varying risk premia [e.g., Keim and Stambaugh (1986); Fama and French (1988); French, Schwert, and Stambaugh (1987) ]. The concept of time-varying risk premia cannot be properly explored within a static model such as the CAPM or static APT. Our competitive equilibrium approach has the potential to provide closed-form derivations of some of the econometric specifications for time-varying premia that these papers employ. In particular, we describe two special cases of our model that provide simple closed-form solutions and are consistent with estimation techniques that assume time-invariant parameters. One of the special cases predicts time-varying risk premia that behave in a manner
doi:10.1093/rfs/2.3.373 fatcat:vyhhemlskzejrmyszjlgz37diq