Introduction
wo of the major paradigms of portfolio theory are the one-period Capital Asset T Pricing Model (CAPM) and the intertemporal Consumption Capital Asset Pricing Model (CCAPM). Each has encountered empirical problems. The CAPM fails to explain many well-documented anomalies (e.g., the weekend effect, the January effect, the small firm effect), while the CCAPM is faced with strong empirical rejection from Hansen and Singleton (1982) in the stock market and Jagannathan (1985) in the futures market.' Despite these shortcomings, the models continue to find favor in the investments literature. Recent articles using the CAPM to model futures market returns include Chang, Chen, and Chen (CCC) (1990); Elam and Vaught (1988); Baxter, Conine, and Tamarkin (BCT) (1985); and Carter, Rausser, and Schmitz (CRS) (1983). Unfortunately, in an intertemporal setting, such as a futures market, one-period models may fail to capture important intertemporal elements of risk in their definition of risk premium.
In the stock market, attempts have been made to adapt the one-period CAPM to a time varying framework [e.g., Ferson and Gibbons (1985)l. However, it would be more natural to use a multi-period model to generate time varying asset pricing equations. A simple approach is through the CCAPM. However, given the previous rejections, it must first be documented that some specification of this model has empirical support.
This article adapts the methodology of Huang (1988Huang ( , 1989) ) to address problems in the empirical rejection of the CCAPM. This methodology relies on replacing the marginal rate of substitution with an index portfolio, avoiding the use of noise and infrequently reported consumption data. The index portfolio's return is identified by a multi-factor linearity assumption. Estimation is performed using the Generalized Method of Moments (GMM) [Hansen (1982); Hansen and Singleton (1982)l. Huang reports considerable success with this methodology in the foreign forward exchange markets.
This article extends Huang's methodology to more general settings and empirically estimates the model on the agricultural and foreign exchange futures markets. This This article is based on Chapters 2 and 3 of my dissertation. I would like to thank the members of my committee: Roger Huang, chairman; Hans Stoll; Cliff Huang; William Christie; Craig Lewis; Mark Cohen. I would also like to thank the seminar participants at Wayne State University, Virginia Polytechnic Institute, Loyola University, the University of Massachusetts-Boston, and the Commodity Futures Trading Commission. Futures data was provided by a grant from the Columbia Futures Center. The forward data was provided by Roger Huang.
'For examples of these anomalies, see Schwert (1983), Keim and Stambaugh (1984), Keim (1985). or many others.