A Semiautoregression Approach to the Arbitrage Pricing Theory



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    • Department of Finance, Stern School, New York University. I am greatly indebted to John Campbell for his comments and encouragement, to Douglas Holtz-Eakin for providing me with part of the program for the autoregression, and to Wayne Ferson for letting me use his data. The paper has benefited greatly from valuable suggestions by René Stulz, the editor, and an anonymous referee. Helpful comments from Gregory Chow, Silverio Foresi, Larry Lang, Bruce Lehmann, Crocker Liu, Albert Margolis, Burton Malkiel, Whitney Newey, Richard Quandt, Bob Stambaugh, and seminar participants at Princeton University and at the NBER summer workshop are gratefully acknowledged. The paper was originally entitled “Extracted factors and time-varying conditional risk premiums: A new approach to the APT.” This research is partly supported by the John M. Olin Foundation for Study of Economic Organization and Public Policy.


This paper developes a semiautoregression (SAR) approach to estimate factors of the arbitrage pricing theory (APT) that has the advantage of providing a simple asymptotic variance-covariance matrix for the factor estimates, which makes it easy to adjust for measurement errors. Using the extracted factors, I confirm the finding that the APT describes asset returns slightly better than the CAPM, although there is still some mispricing in the APT model. I find that not only are the factors “priced” by the market, but the factor premiums move over time in relation to business cycle variables.