NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

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

Bruce N. Lehmann, David M. Modest

NBER Working Paper No. 1726
Issued in October 1985
NBER Program(s):   ME

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.

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Document Object Identifier (DOI): 10.3386/w1726

Published: "The Empirical Foundations of the Arbitrage Pricing Theory." From Journal of Financial Economics, Vol. 21, No. 2, pp. 213-254, (September 1988).(NOTE: R1221 is based on BOTH W1725 and W1726.)

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