Investigating linear multi-factor models in asset pricing: considerable supplemental evidence^*

* Accepted by Yue Ma upon recommendation by Junbo Wang.

Abstract

The literature has offered an interesting debate about whether the performance of Fama-French’s three-factor benchmark model is inadequate because it fails to pass some model specification tests and its R2 is not convincingly high in cross-sectional estimations. Previous studies have been quite limited, since they only focused on the time-series procedure with many models. We extend their work by providing a more robust investigation of the performance of several well-regarded pricing models in pooled portfolios and other portfolios sorted by new and important anomalies, using cross-sectional GMM tests for robustness. Finally, we find that, in addition to Fama and French’s five-factor model proposed in 1993, Fama-French’s three-factor model augmented by other factors usually outperforms Fama-French’s three-factor model across a significant proportion of different portfolios. In particular, Frazzini, Kabiller, and Pedersen’s model shows the best overall performance and consistency across different portfolios.

Keywords:

• Expanding portfolios
• different portfolios
• asset pricing models
• consistency

Notes

* Accepted by Yue Ma upon recommendation by Junbo Wang.

1. If the augmented correct pricing factors are all significant, one can expect that a model with more factors generally achieves better overall goodness of fit than a model with fewer factors.

2. Cochrane (2005) explicitly stated that the GMM, time-series, and cross-sectional procedures and distribution theory are similar but not identical. Time-series procedures are also the first stage of a two-pass cross-sectional regression. Since the two methodologies are not directly comparable, most current studies use both methods to circumvent any estimation problems associated with a specific methodology.

3. Fama and French (2008) find that the anomalous returns associated with net stock issues, accruals, and momentum are pervasive in all size groups in cross-sectional regressions.

4. The model incorporates Pástor and Stambaugh’s (2003) liquidity-related risk factor (liq). The setup of this model follows Lam and Tam (2011) and Keene and Peterson (2007).

5. The estimations of risk premiums in our Supplementary material are available upon request.

6. Fama and MacBeth’s (1973) two-pass OLS regression often achieves results similar to or consistent with the first-stage GMM approach, as shown in previous studies (see Maio 2013; Petkova 2006).

7. http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html.

8. Following Aretz, Bartram, and Pope (2010), we use the dividend yield to estimates Petkova’s (2006) ICAPM model.

9. http://www.econ.yale.edu/~shiller/data.htm.

10. We use the non-traded liquidity factor (Pástor and Stambaugh 2003; Equation 8).

11. The quality stock indicates that high-quality firms command the highest prices. These firms can finance their operations and invest. A quality-minus-junk (qmj) factor that goes long high-quality stocks and shorts low-quality stocks earns significant risk-adjusted returns.

12. http://www.econ.yale.edu/~af227/data_library

13. We judge the superior performance of Petkova’s model via four ‘key’ rules, except the J-difference test.

14. For example, Balvers and Huang (2007), Michel (2009) and other studies all use the same setup. The poor testing results may be attributable to the fact that industry portfolios are typically difficult to predict, as the return variation of industry portfolios is too volatile for an asset-pricing model to capture. Specifically, more than half of the combinations of 55 portfolios are industrial portfolios.

15. Please see this value in the Supplementary material , which is available upon request.