Reference Variables, Factor Structure, and the Approximate Multibeta Representation.

The arbitrage pricing theory implies that if asset returns have a factor structure, then an approximate 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 that 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 arbitrage pricing theory are also discussed. Copyright 1992 by American Finance Association.