6.6 Simulation

The aim of the simulation study is to examine the effect of using different sorting criteria. Two grouping criteria, size of stock and estimated beta, are considered. This simulation study is similar to the Lo and MacKinlay (1990) paper in that the criteria of sorting are generated in-sample, as opposed to the empirical work in this chapter which uses criteria obtained prior to the sampling period. The reason for using in-sample criteria is that we can avoid imposing too many assumptions on the time-series structure of ?. The crucial point which distinguishes this study from Lo and MacKinlay s paper is that we study the effect of sorting on both regression-based and stochastic discount factor-based frameworks. Lo and MacKinlay s paper studied the test s size distortion on the linear factor model in regression framework. More specifically, their study shows the size distortion of the asymptotic ? ² test and the GRS test. The asymptotic ? ² test they examined is not very practical: it assumes that the variance of ? is the same and uncorrelated across stocks. In addition, their study used only the asymptotic ? ² test to analyse the test size distortion in beta-sorted portfolios. Lastly, their work did not include any analysis of the stochastic discount factor-based asset pricing test.

The asset pricing tests examined in this study include both regression-based tests and stochastic discount factor-based tests. For...