A Multibeta Representation Theorem for Linear Asset Pricing Theories

This paper derives a multibeta representation theorem for pricing assets using arbitrary reference variables that are not necessarily the true factors. Under this theorem, the upper bound on pricing deviations depends upon the correlations not only between the reference variables and the factors but also between the reference variables and the residual risks. A new concept of a well-diversified variable is introduced, which though free of residual risk, may be less than perfectly correlated with the true factors. Well diversified variables correlated with the factors play a key role in the pricing of assets, since these variables can replace the factors without any loss in pricing accuracy under all linear asset pricing theories