The Analysis of the Cross-Section of Security Returns

This chapter reviews various econometric methods that are available for empirical evaluation of linear beta pricing models by using time-series observations on returns and characteristics on a large collection of financial assets. The econometric methods can be grouped into three classes, which include the two-stage cross-sectional regression (CSR) method, the ML method, and the generalized method of moments (GMM). In general, the number of assets is large relative to the length of the time-series of return observations. The classical approach to reducing the dimensionality, without losing too much information, is to use the portfolio grouping procedure. As portfolio betas are estimated more precisely than individual security betas, the portfolio grouping procedure attenuates the EIV problem faced by the econometrician while using the classical two-stage cross-sectional regression method. The portfolio formation method can highlight or mask characteristics in the data that have valuable information about the validity or otherwise of the asset pricing model being examined. In the context of the CSR method, the two-pass procedure of Fama and MacBeth are reviewed and the use of security characteristics to test a factor model are described.