Empirical Tests of Arbitrage Pricing 397 Table i Data Description Center for Research in Security Prices University of Chicago 1963-78 inclusive. The entire period is divi subperiods: I. 1963-66, IL. 1967-70, III IV.1975-78. election criterion All the securities that do not have missing data during Basic data unit Return adjusted for all capital changes and including Number of selected Subperiod Total sample II 1522 Their average daily return in absolute value is less than 0.01 to eliminate outliers Only Burma Mining Inc was excluded with this criterion during the first subperiod placed by the processing capacity of the IBM 3033 used (in 1980)for the computation of the factor loadi (ii)The first ten factor loadings for each stock are obtained with the computer software package EFAP II (iii)Five portfolios are formed using linear programming so that the resultant portfolios will balance estimation errors with other desirable properties The time series of the five portfolios will contain linear combinations of the 1,..., Sk(i.e, the factor scores) (iv) The first five factor loadings are produced for every stock in the sample by solving a matrix equation(Equation(Al)in the Appendix) One of the difficulties in empirically testing the apt is that it does not tell us what the number of common factors should be. Since ex post data are being used to test for an ex ante relation the number of factors to be included must be independently determined and prespecified in order to avoid potential data mining and to give the alternative hypothesis a fair chance ex post. Five were selected based on previous empirical studies(see Roll and Ross [34] and Rein ganum [30). A study by Brown and Weinstein [5] also confirms that the number of pervasive factors is probably no greater than five II. Cross-Sectional results A. The APT and the CAPM To see how well the data support the models, we examine the result of cross- sectional regression of assets'returns on the hypothesized parameters in each of the subperiods. The independent variables will be the FL for the aPt and the 5 This is the gUB programming within the elastic programming in the XS mathematical program- ming system developed by Glenn Graves, UCLA " Based on the analysis and the plot of eigenvalues, for each period five factors also look sufficient