Arbitrage Pricing, Factor Structure, Eigenvectors and all That—An Exposition

This paper re-presents the essentials of Ross' (1976) derivation of his Arbitrage Pricing Theory (APT) and explains the empirical implications of recent extensions to the APT due to Chamberlain & Rothschild (1983). The natural statistical methodology for empirically testing Ross' for Mulation is to factor-analyze a certain variance-covariance matrix. This factor analysis bears a close relationship to the natural empirical counterpart of Chamberlain & Rothschild's generalisations of the APT: computation of the eigenvalues and eigenvectors. An important implication is that this new method for testing the APT is simpler than factor analysis but perfor Ms as well, is much less of a computational burden, and includes a new way to count the factors.