Linear Transformation of Asset Returns and the APT

The capital market is abound of mergers, spin-offs, sell-offs, and construction of mutual funds. All these activities impose linear or nonlinear transformations on the return generating process. The validity of the APT under linear transformations of asset returns has been discussed but not fully explored in the literature. The purpose of this paper is to examine the robustness of the APT with respect to arbitrary linear transformations. We show that the APT holds under any linear transformation as long as the product of the transformation matrix and its transpose is uniformly bounded.