ON TESTING THE ARBITRAGE PRICING THEORY: INTER‐BATTERY FACTOR ANALYSIS

Abstract

This paper tests the Arbitrage Pricing Theory (APT) by estimating the factor loadings that are consistent between two industry groups of securities. One of the pitfalls in the study by Roll and Ross is that the factors estimated in one group may not be the same with the factors estimated in another group. This raises some concerns on the acceptability of their conclusions. For our study, we employ inter-battery factor analysis which enables us to estimate factor loadings by constraining the factors to be the same between two different groups. Our results show that there seem to be five or six inter-group common factors that generate daily returns for two industry groups of securities, and these inter-group common factors do not seem to depend on the size of groups. Also, based on our cross-sectional tests on the risk premia, we conclude that the APT should not be rejected. THE ARBITRAGE PRICING THEORY (APT) introduced by Ross [35, 36] provides another model for explaining the relationship between return and risk. The APT may be conceived as an alternative to the well-known Capital Asset Pricing Model (CAPM) introduced by Sharpe [39], Lintner [27], and Mossin [29] and later modified by Black [1]. Both models assert that every asset must be compensated only according to its systematic risk. One of the major differences is that, in the CAPM, the systematic risk of an asset is defined to be the covariability of the asset with the market portfolio, whereas, in the APT, the systematic risks are defined to be the covariability with not only one factor but also possibly with several economic factors. Another difference is that the CAPM requires the economy to be in equilibrium whereas the APT requires only that the economy has no arbitrage opportunities. Note that the absence-of-arbitrage condition is necessary but not sufficient for the economy to be in equilibrium. Thus, the APT is a more fundamental relationship than the CAPM in the sense that a rejection of the APT implies the rejection of the CAPM but not vice versa. Despite numerous attempts, the CAPM has not been satisfactorily tested and, furthermore, Roll's critique [32, 33] casts serious doubts on the testability of the CAPM itself. Roll argues that the linear relationship between return and risk will hold for any efficient portfolio. Thus, unless the market portfolio is observed, a test of the CAPM using ex post data is ambiguous; it results only in testing the