The Journal of financ Table Il, Part A, it is interesting to note that there is at least one significant factor beside A, for every period To see whether APt has any explanatory power in cross-section we test the null hypothesis that A,= A2 4=A5=0. This is equivalent to the hypothesis that the expected return of all assets are the same and equal to no The Hotelling it is tricky to apply the test to the APT because, as mentioned is a multivariate test(see Morrison [28])appropriate for this previously, the APT only requires at least one of the factors to be priced. If we then choose only the first few most significant factors to be included in the Hotelling T2, obviously the Type i error is underestimated and there is a bias against the null hypothesis. If we always take all five the test will be weak and the Type II error will be large Despite the relative low power of the test when all five are included, the f statistic is still significant at least at the 0. 1 level for every period (see Table Il, Part A), so the overall significance level would be very high. If we assume independence across the four test periods we can sum up the T(>T=60.96)which asymptotically approaches x with 20 degrees of freedom and with a critical value of 45.3 for the 0.001 level. Therefore with the Fl we can confidently reject the null hypothesis of constant expected return across B. A Co son between the apt and the CaPmio The next question that comes up naturally is: which of the two competing models, CAPM or APT, do the data favor? To answer this, one is tempted to do a regression with both CAPM beta and the FL as independent variables. However th is is not done because:(i)this specification is not justified on theoretical grounds and the two models are nonnested(see also footnote 3), and (ii)the betas and the FL are intended to measure the same thing-risk Thus, to put them together in a regression would mean including the same variable twice on the right-hand side. The high degree of multicollinearity (intertwined with measurement error)tends to produce regression coefficients that make no sense. One possible way to discriminate among nonnested alternative models was suggested in Davidson and Mackinnon [14]. Let FAPT and FCAPm be the expected return generated by the APt and the CAPM, i.e they are obtained from the cross-sectional regression of (3)and(4)(on even days)without the error terms then if we estimate a in ,= rapT +(1-aricy +e (cf [14], Equation(4)), we would expect a to be close to 1 if the apt is the correct model relative to the CAPM. We analyze (5)rather than many of its 8 Gibbons [20] showed that a much more efficient estimate of the risk premium is possible by pooling cross-sectional time series data in a seemingly unrelated regression. The standard his study was roughly one third of the BJS.FM standard error. Unfortunately, there are over a thousand securities in our cross-sectional sample. Thus the SUR, which requires inversion of the sample covariance matrix, is not feasible. Furthermore, the probability limit of the Hotelling T2 statistic is biased downward in the presence of nonsystematic measurement error An approximate F statistic reconstructed from the overall T statistic is 2. 46 with (20. 78)df. am indebted to Stephen Brown for a discussion on this topic