The residual market factor, the APT, and mean-variance efficiency
The rapidly increasing volume of both published and unpublished work on the arbitrage pricing theory (APT) of Ross (1976) has given rise to a number of misunderstandings at the interface of theoretical and econometric work. In this article we extend the theoretical structure of our previous work (McElroy and Burmeister, 1985, 1988; Burmeister and McElroy, 1987, 1988) to provide a broad yet rigorous framework both for econometric estimation and for better economic interpretation of new empirical results. We begin with the case where all K factors are observed, and then present the second case of K-1≡J observed APT factors and one unobserved factor, the residual market factor introduced in McElroy and Burmeister (1985). The economic interpretations for equivalent specifications of this model are discussed, and we enumerate several immediate payoffs to these specifications. The main new results are concerned with the sometimes intricate relationships among APT models with K factors and APT models with K factors that are constrained to satisfy mean-variance efficiency restrictions. These results are not only of theoretical interest, but more importantly they provide the basis for econometric estimation and testing of nested hypotheses. These econometric issues are discussed in detail. © 1991 Kluwer Academic Publishers.
Burmeister, E; McElroy, MB
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