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Is the Arbitrage Pricing Theory Dead?

Is the Arbitrage Pricing Theory dead? This paper addresses this question by deriving a multibeta representation theorem, which can price assets using arbitrary reference variables that are not 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. A set of corollaries to the multibeta representation theorem are derived, which are fatal for both the APT as well as the equilibrium APT. Both these theories lead to pricing of arbitrary reference variables, which allows rejection of these theories based on casual empiricism. Since Merton's ICAPM does not suffer from such arbitrary pricing, it represents a viable theoretical framework for the empirical multifactor asset pricing models, such as the 3-factor Fama and French model.