The Number of Factors in Security Returns



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    • Yamaichi Faculty Fellow, Leonard N. Stern School of Business, New York University. I wish to acknowledge helpful comments of Michael Brennan, Gary Chamberlain, Dolores Conway, Phil Dybvig, Ned Elton, David Fowler, Jon Ingersoll, Shmuel Kandel, Steve Ross, Mike Rothschild, Ravi Shukla, Charles Trzcinka, and especially Jay Shanken, David Mayers (the co-editor), and the referee, as well as the participants of the Empirical Research in the Arbitrage Pricing Theory conference held at the University of Southern California, November 1985. I do not implicate any of these people in the errors that remain.


Both factor analysis of security returns and the analysis of eigenvalues seem to indicate that a market factor explains the major part of security returns. We find that such evidence is consistent with an economy where there are in fact k “equally important” priced factors; eigenvalue analysis in the context of such an economy will lead an investigator to the false inference that the one important “factor” is the return on an equally weighted market index.