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Is the APT Even Testable? Similar to Roll's critique of the CAPM, Shanken challenged whether it is possible for the APT to be empirically verified at all.15 Rather than question specific tests or methods, Shanken questioned whether the APT is more susceptible to testing than the CAPM based on the usual empirical test that determines whether asset returns conform to a K factor model. One problem is that if stock returns are not explained by such a model, it is not considered a rejection of the model; however, if the factors do explain returns, it is considered support. Also, it is contended that APT has no advantage because the factors need not be observable, which means that equivalent sets of securities may conform to different factor structures. Therefore, the empirical formulation of the APT may yield different implications regarding the expected returns for a given set of securities. Unfortunately, this implies that the theory cannot explain differential returns between securities because it cannot identify the relevant factor structure that explains the differential returns. This need to identify the relevant factor structure that affects asset returns is similar to the CAPM benchmark problem. In summary, each of the models has a problem with testing. Specifically, before you can test the CAPM, you must identify and use the true market portfolio; whereas, before you can test the APT, you must identify the relevant factor structure that affects security returns.

Dybvig and Ross replied by suggesting that the APT is testable as an equality rather than the "empirical APT" proposed by Shanken.16 Shanken responded that what has developed is a set of equilibrium APT pricing models that are testable but that arbitrage-based models are not testable as originally specified.17

Alternative Techniques for Testing the APT In addition to the test procedures just described, several other articles have proposed alternative statistical techniques for testing the APT model. Jobson proposes that the APT be tested using a multivariate linear regression model.18 Brown and Weinstein propose an approach to estimating and testing asset pricing models using a bilinear paradigm.19 Geweke and Zhou produce an exact Bayesian framework for testing the APT and conclude that there is little reduction in pricing error from including additional factors beyond the first one.20 A number of subsequent papers have proposed new methodologies for testing the APT.21

15Jay Shanken, "The Arbitrage Pricing Theory: Is It Testable?" Journal of Finance 37, no. 5 (December 1982: 1129-1140.

16Philip H. Dybvig and Stephen A. Ross, "Yes, The APT Is Testable," Journal of Finance 40, no. 4 (September 1985): 1173-1188.

17Jay Shanken, "Multi-Beta CAPM or Equilibrium APT?: A Reply," Journal of Finance 40, no. 4 (September 1985): 1189-1196.

18J. D. Jobson, "A Multivariate Linear Regression Test for the Arbitrage Pricing Theory," Journal of Finance 37, no. 4 (September 1982): 1037-1042.

19Stephen J. Brown and Mark I. Weinstein, "A New Approach to Testing Asset Pricing Models: The Bilinear Paradigm," Journal of Finance 38, no. 3 (June 1983): 711-743.

20John Geweke and Guofu Zhou, "Measuring the Price of the Arbitrage Pricing Theory," Review of Financial Studies 9, no. 2 (Summer 1996): 557-587.

21Among the papers are Chinhyang Cho, "On Testing the Arbitrage Pricing Theory: Inter-Battery Factor Analysis," Journal of Finance 39, no. 5 (December 1984): 1485-1502; Robert McCulloch and Peter Rossi, "Posterior, Predictive, and Utility-Based Approaches to Testing the Arbitrage Pricing Theory," Journal of Financial Economics 28, no. 1 and 2 (November-December 1990): 7-38; and Ravi Shakla and Charles Trzcinka, "Sequential Tests of the Arbitrage Pricing Theory: A Comparison of Principle Components and Maximum Likelihood Factors," Journal of Finance 45, no. 5 (December 1990): 1542-1564.

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