The Empirical Foundations of the Arbitrage Pricing Theory Ii: the Optimal Construction of Basis Portfolios

54 Pages Posted: 11 Nov 2000 Last revised: 21 Sep 2022

See all articles by Bruce N. Lehmann

Bruce N. Lehmann

University of California, San Diego; National Bureau of Economic Research (NBER); Massachusetts Institute of Technology (MIT)

David Modest

Azimuth Alternative Assets Management LLLP

Date Written: October 1985

Abstract

The Arbitrage Pricing Theory (APT) of Ross (1976) presumes that a factor model describes security returns. In this paper, we provide a comprehensive examination of the merits of various strategies for constructing basis portfolios that are, in principle, highly correlated with the common factors affecting security returns. Three main conclusions emerge from our study. First, increasing the number of securities included in the analysis dramatically improves basis portfolio performance. Our results indicate that factor models involving 750 securities provide markedly superior performance to those involving 30 or 250 securities. Second, comparatively efficient estimation procedures such as maximum likelihood and restricted maximum likelihood factor analysis(which imposes the APT mean restriction) significantly outperform the less efficient instrumental variables and principal components procedures that have been proposed in the literature. Third, a variant of the usual Fame-MacBeth portfolio formation procedure, which we call the minimum idiosyncratic risk portfolio formation procedure, outperformed the Fama-MacBeth procedure and proved equal toor better than more expensive quadratic programming procedures.

Suggested Citation

Lehmann, Bruce and Modest, David, The Empirical Foundations of the Arbitrage Pricing Theory Ii: the Optimal Construction of Basis Portfolios (October 1985). NBER Working Paper No. w1726, Available at SSRN: https://ssrn.com/abstract=243214

Bruce Lehmann (Contact Author)

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Massachusetts Institute of Technology (MIT) ( email )

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David Modest

Azimuth Alternative Assets Management LLLP ( email )

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