Some Results in the Theory of Arbitrage Pricing



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    • School of Organization and Management, Yale University. This research was conducted primarily during the academic year 1981–82 when the author was a Batterymarch Fellow. Additional support was provided by the Sloan Foundation. I am grateful to Doug Diamond, Phil Dybvig, Gur Huberman, Bruce Lehmann, Steve Ross, and an anonymous referee who have provided comments and helpful suggestions on these topics.


This paper derives a stronger version of Huberman's recent “preference free” pricing theorem. This pricing result relates the expected return on an asset to its factor responses and the covariance structure of the residuals from a linear factor model. It must characterize any infinite asset economy in which no arbitrage opportunities are present whether or not the factor model has uncorrelated residuals. This result provides the intuition for the role of residual risk in the pricing model and eliminates some classes of arbitrage opportunities still present under Huberman's bound. Some applications to empirical tests and performance measurement are also discussed.