The Capital-Asset-Pricing Model and Arbitrage Pricing Theory: a Unification
P roc. Natl. Acad. Sci. USA
Vol. 94, pp. 4229–4232, April 1997
Economic Sciences
The capital-asset-pricing model and arbitrage pricing theory: A unification
M. A LI K HAN*
AND
YENENG SUN†‡
*Department of Economics, Johns Hopkins University, Baltimore, MD 21218; †Department of Mathematics, National University of Singapore, Singapore 119260; and ‡Cowles Foundation, Yale University, New Haven, CT 06520
Communicated by Paul A. Samuelson, Massachusetts Institute of Technology, Cambridge, MA, October 3, 1996 (received for review August 14, 1996)
The publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked ‘‘advertisement’’ in accordance with 18 U.S.C. §1734 solely to indicate this fact.
expected return of an asset is related to its exposure to each of these factors, and now summarized by a vector of factor loadings. The reward to the residual component in the return to a particular asset, unsystematic or idiosyncratic risk, can be made arbitrarily small simply by considering portfolios with an arbitrarily large number of assets.
The basic point, however, is that the two theories capture two different sets of risks and address different aspects of the premium-awarding scheme for taking such risks. The CAPM, by its emphasis on efficient diversification in the context of a finite number of assets, neglects unsystematic risks in the sense of the APT; whereas the APT, with its explicit focus on markets with a ‘‘large’’ number of assets, and by its emphasis on naive diversification and on the law of large numbers, neglects essential risks. The two theories seem to be inherently disjoint. It is surprising, however, that a model which unifies their basic ingredients can nevertheless be found; and moreover, that it is one in which the absence of arbitrage opportunities is not only sufficient, but in contrast to the literature, also necessary for the validity of the APT
Vol. 94, pp. 4229–4232, April 1997
Economic Sciences
The capital-asset-pricing model and arbitrage pricing theory: A unification
M. A LI K HAN*
AND
YENENG SUN†‡
*Department of Economics, Johns Hopkins University, Baltimore, MD 21218; †Department of Mathematics, National University of Singapore, Singapore 119260; and ‡Cowles Foundation, Yale University, New Haven, CT 06520
Communicated by Paul A. Samuelson, Massachusetts Institute of Technology, Cambridge, MA, October 3, 1996 (received for review August 14, 1996)
The publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked ‘‘advertisement’’ in accordance with 18 U.S.C. §1734 solely to indicate this fact.
expected return of an asset is related to its exposure to each of these factors, and now summarized by a vector of factor loadings. The reward to the residual component in the return to a particular asset, unsystematic or idiosyncratic risk, can be made arbitrarily small simply by considering portfolios with an arbitrarily large number of assets.
The basic point, however, is that the two theories capture two different sets of risks and address different aspects of the premium-awarding scheme for taking such risks. The CAPM, by its emphasis on efficient diversification in the context of a finite number of assets, neglects unsystematic risks in the sense of the APT; whereas the APT, with its explicit focus on markets with a ‘‘large’’ number of assets, and by its emphasis on naive diversification and on the law of large numbers, neglects essential risks. The two theories seem to be inherently disjoint. It is surprising, however, that a model which unifies their basic ingredients can nevertheless be found; and moreover, that it is one in which the absence of arbitrage opportunities is not only sufficient, but in contrast to the literature, also necessary for the validity of the APT