Reference variables, factor structure, and the approximate multibeta representation

Article Abstract:

The Arbitrage Pricing Theory (APT) implies that if asset returns have a factor structure, then an appropriate multibeta representation holds with respect to the factors as reference variables. This paper assumes that asset returns satisfy a factor structure and derives a condition under which the approximate multibeta representation holds with respect to a set of reference variables which may not be the factors. This condition is that the regression matrix of the reference variables on the factors is nonsingular. Implications for the testability of the APT are also discussed. (Reprinted by permission of the publisher.)

Prices and rates, Pricing, Assets (Accounting)

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The current state of the arbitrage pricing theory

Article Abstract:

This paper provides a simple proof of a recent theorem presented by Reisman (1992), concerning the use of proxies for the factors in the return-generating process of the arbitrage pricing theory (APT). In the single- factor case, the theorem asserts that any variable correlated with the factor can serve as the benchmark in an approximate APT expected return relation. The significance of this result is considered and a new direction for empirical work on "arbitrage pricing" is outlined. (Reprinted by permission of the publisher.)

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