Asset Pricing Tests, Endogeneity issues and Fama-French factors

Allen, David (2022): Asset Pricing Tests, Endogeneity issues and Fama-French factors.

Abstract

This paper features a statistical analysis of the independence of the core Fama/French factors; SMB and HML, using daily data, of the factor return series, for the USA, Developed Markets and Japan, using a sample taken from the data-sets that are available on French's website. The various series and their inter-relationships are analysed using rolling OLS regressions, so as to explore their independence and issues related to their endogeneity. The OLS analysis incorporates Ramsey's RESET tests of functional form misspecifcation. The empirical results suggest that these factors, when combined in OLS regression analysis, as suggested by Fama and French (2018), and generally in the empirical asset pricing literature featuring time-series tests, are frequently not independent, and thus likely to suffer from endogeneity. The rolling regression analysis suggests significant and time-varying relationships between the core factors and rejects their independence for long periods of time within the samples. A significant non-linear relationship exists between some of the series, as indicated by the employment of squared terms, which are frequently significant. The empirical results suggest that using these factors in linear regression analysis, such as suggested by Fama and French (2018), as a method of screening factor relevance, is likely to be problematic, in that the estimated standard errors are likely to be sensitive to the non-independence of factors. This is also likely to be a potential problem for asset pricing tests that use the popular time-series approach, as first suggested by Fama and Macbeth (1973).

• Item Type: MPRA Paper
• Language: English
• Keywords: Fama-French Factors, Correct specification, Ramsey's RESET, Endogeneity, Strong Endogeneity, Consistent standard errors
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C12 - Hypothesis Testing: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General; G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates

References

1] Anatolyev, S., and A. Mikusheva, (2022) Factor models with many assets: strong factors, weak factors, and the two-pass procedure, Journal of Econometrics, 229(1), 103-126. [2] Andrews, I., and A. Mikusheva, (2016) A geometric approach to non-linear econometric models, Econometrica, 84(3): 1249-1264. [3] Allen, D. E. and M. McAleer (2018) 'Choosing Factors' by Fama and French (2018): A Comment, Available at SSRN: https://ssrn.com/abstract=3272608 or http://dx.doi.org/10.2139/ssrn.3272608. [4] Barillas, F., and J. Shanken, (2018) Comparing asset pricing models, Journal of Finance, 73(2), 715-754. [5] Cochrane, J.H. (2011) Presidential Address: Discount rates, Journal of Finance, 66(4), 1047-1108. [6] Durbin, J. (1954) Errors in variables, Review of the International Statistical Institute, 22(1/3), 23�32. [7] Engle, R.F., D.F. Hendry, and J-F. Richard, (1983) Exogeneity, Econometrica, 51(2): 277-304. [8] Fama, E.F., and K.R. French (1993) Common risk factors in the returns on stocks and bonds, Journal of Financial Economics, 33, 3-56. [9] Fama, E.F., and K.R. French (2018) Choosing factors, Journal of Financial Economics, 128(2), 234-252. [10] Fama, E. F. (1976) Foundations of �nance, Basic Books: New York. [11] Fama, E.F., and K.R French (2020) Comparing Cross-Section and TimeSeries Factor Models, The Review of Financial Studies, 33: 1891�1926. [12] Fama, E.F., and K.R French (1993) Common risk factors in the returns on stocks and bonds, Journal of Financial Economics, 33:3�56. [13] Fama, E.F., and K.R French (2015) A �ve-factor asset pricing model, Journal of Financial Economics, 116:1�22. [14] Fama, E. F., and J. D. MacBeth (1973) Risk return, and equilibrium: empirical tests, Journal of Political Economy, 81:607�36. [15] Gibbons, M.R., S.A. Ross, and J. Shanken (1989) A test of the efficiency of a given portfolio, Econometrica, 57(5), 1121-1152. [16] Granger, C.W. J. (1969) Investigating causal relations by econometric models and Cross-Spectral methods, Econometrica, 37: 424-438 [17] Harvey, C.R., Y. Liu, and H. Zhu, (2015) . . . and the cross-section of expected returns, Review of Financial Studies, 29, 5-68. [18] Hausman, J.A. (1978) Specification tests in econometrics, Econometrica, 46(6), 1251�1271. [19] Kan, R., and C. Zhang, (1999) Two-Pass Tests of Asset Pricing Models with Useless Factors, Journal of Finance, 54(1): 203-235. [20] Kleibergen, F. (2009) Tests of Risk Premia in Linear Factor Models, Journal of Econometrics, 149(2), 149-173. [21] Kleibergen, F. and Z. Zhan, (2015) Unexplained Factors and Their Effects on Second Pass R-squared's, Journal of Econometrics, 189, 101-116. [22] Mikusheva, A., and L. Sun (2022) Inference with many weak instruments, Review of Economic Studies (forthcoming), https://academic.oup.com/restud/advance-articleabstract/doi/10.1093/restud/rdab097/6482756?redirectedFrom=fulltext. [23] Nakamura, A. and M. Nakamura (1981) On the relationships among several specification error tests presented by Durbin, Wu, and Hausman, Econometrica, 49(6), 1583-1588. [24] Onatski, A. (2015) Asymptotic analysis of the squared estimation error in misspecified factor models, Journal of Econometrics, 186:386-406. [25] Petersen, M. (2009) Estimating standard errors in finance panel data sets: comparing approaches, Review of Financial Studies, 22(1), 435-480. [26] Ramsey, J. B. (1969) Tests for specification errors in classical linear least squares regression analysis, Journal of the Royal Statistical Society, Series B. 31 (2): 350�371. [27] Raponi, V, Robotti, C., and P. Zafaroni (2020) Testing BetaPricing Models Using Large Cross-Sections, Review of Financial Studies, 33(6):2796�2842. [28] Wu, D-M. (1973) Alternative tests of independence between stochastic regressors and disturbances, Econometrica, 41(4), 733-750.