The Restrictions on Predictability Implied by Rational Asset Pricing Models

Motivation(s)

The use of regression analysis to predict asset returns has become commonplace because it is simple to implement and the resulting estimates of the slope coefficients and regression \(R^2\) have an appealing interpretation. Some argue that the ability to predict returns arises from market inefficiencies, while others point to rational variation in expected returns as the cause.

In frictionless markets, rational asset pricing models imply that some transformation of the equilibrium price process is a martingale with respect to the information that market participants use to form expectations. This martingale property establishes a direct link between the ability to predict returns and market efficiency. As a consequence, it imposes tight restrictions on the intercept, slope coefficients, and \(R^2\) of the linear models used to predict returns.

Prior research has not shown how rational models of asset pricing restrict the regression-based criteria used to measure predictability.

Proposed Solution(s)

The author builds off of the approach developed in Hansen and Jagannathan (1991) to characterize the restrictions on predictability. Standard no-arbitrage pricing arguments are used to infer the values of the coefficients in a regression of asset returns on a set of instrumental variables (see appendix). The restrictions make it possible to construct the linear specification for forecasting asset returns that is implied by the asset pricing model under consideration.

Evaluation(s)

The estimations and tests were done using Hansen’s (1982) generalized method of moments on portfolios constructed from CRSP and CITIBASE. The empirical investigation revealed the size portfolio returns are too predictable to be compatible with a number of well-known pricing models. These models include the consumption-based specifications of Lucas (1978), Abel (1990), and Epstein and Zin (1991), along with simple conditional versions of the Sharpe (1964) and Lintner (1965) CAPM and the Fama and French (1993) three-factor model.

Although none of the pricing models fully explains the ability to predict returns, the observed cross-sectional relation between market capitalization and return predictability appears consistent under circumstances where predictability is rational. If the factors that explain cross-sectional differences in average returns can be identified, then those factors may explain cross-sectional differences in predictability as well.

Future Direction(s)

• How would the proposed model perform when the signal is replaced with the cross-sectional differences in average returns?

Question(s)

• Why make the restriction sound so grandiose when it’s merely specifying a linear projection model?

Analysis

Perhaps this paper is too dated given the current machine learning curriculum, so the proposed model isn’t too impressive. The results and entire paper could have been written more succinctly. The argument for rational asset pricing models was not very convincing due to the lack of transactions costs.

References

Kir98

Chris Kirby. The restrictions on predictability implied by rational asset pricing models. Review of Financial Studies, 11(2):343–382, 1998.