Do Idiosyncratic Risks in Multi-Factor Asset Pricing Models Really Contain a Hidden Non-Diversifiable Factor? A Diagnostic Testing Approach
- 1 School of Business and Management, Azusa Pacific University, Azusa, USA
- 2 College of Business, James Madison University, Harrisonburg, USA
Abstract
This paper employs a new approach to analyze potentially omitted non-diversifiable factors in the idiosyncratic risks from multi-factor asset pricing models. It is shown that if there is an omitted non-diversifiable hidden factor, the idiosyncratic risks will contain persistent cross-sectional memory. An extended Rescaled Variance test generalized from L. Giraitis, P. Kokoszaka, R. Leipus, and G. Teyssiere [1] with finite forecast horizon is provided to investigate the cross-sectional memory of forecast errors in multifactor pricing models. Under the null hypothesis that idiosyncratic risks contain only short memory when there is no hidden non-diversifiable factor, we demonstrate that the extendedT-sample Rescaled Variance test statistic approximates a functional of weighted Brownian Bridge, which is distributed asymptotically as the T-sample Watson’s statistic presented by Maag [2]. Using this approach, our empirical tests that compare forecast errors from the CAPM and Fama-French [3] model with the excess returns of 1391 firms indicate that there is a strong likelihood that the CAPM may require further identification of hidden non-diversifiable factor(s). Yet, there lacks convincing evidence that the Fama-French [3] model has an omitted non-diversifiable factor in idiosyncratic risks.
- L. Giraitis, P. Kokoszaka, R. Leipus and G. Teyssiere, “Rescaled Variance and Related Tests for Long Memory in Volatility and Levels,” Journal of Econometrics, Vol. 112, No. 2, 2003, pp. 265-294. doi:10.1016/S0304-4076(02)00197-5
- U. R. Maag, “A k-Sample Analogue of Watson’s Statistic,” Biometrika, Vol. 53, No. 3-4, 1966, pp. 579-583. doi:10.1093/biomet/53.3-4.579
- E. F. Fama and K. R. French, “Common Risk Factors in the Returns on Stocks and Bonds,” Journal of Financial Economics, Vol. 25, No. 1, 1993, pp. 23-49. doi:10.1016/0304-405X(89)90095-0
- A. Goyal and P. Santa-Clara, “Idiosyncratic Risk Matters,” Journal of Finance, Vol. 58, No. 3, 2003, pp. 975- 1008. doi:10.1111/1540-6261.00555
- D. Mayers, “Nonmarketable Assets, Market Segmentation, and the Level of Asset Prices,” Journal of Financial and Quantitative Analysis, Vol. 11, No. 1, 1976, pp. 1-12. doi:10.2307/2330226
- B. G. Malkiel and Y. Xu, “Idiosyncratic Risk and Security Returns,” Working Paper, University of Texas, Dallas, 2006.
- H. Guo and R. Savickas, “Does Idiosyncratic Risk Matter: Another Look,” Working Paper 2003-025A, Federal Reserve Bank of St. Louis, 2003.
- T. Bali, N. Cakici, X. Yan and Z. Zhang, “Does Idiosyncratic Risk Really Matter?” Journal of Finance, Vol. 60, No. 2, 2005, pp. 905-929. doi:10.1111/j.1540-6261.2005.00750.x
- A. Ang, R. J. Hodrick, Y. Xing and X. Zhang, “The Cross-Section of Volatility and Expected Returns,” Journal of Finance, Vol. 61, No.1 , 2006, pp. 259-298. doi:10.1111/j.1540-6261.2006.00836.x
- F. Fu, “Idiosyncratic Risk and the Cross-Section of Ex- pected Stock Returns,” Journal of Financial Economics, Vol. 91, No. 1, 2009, pp. 24-37. doi:10.1016/j.jfineco.2008.02.003
- H. Guo and R. Savickas, “Average Idiosyncratic Volatility in G7 Countries,” Review of Financial Studies, Vol. 21, No. 3, 2008, pp. 1259-1296. doi:10.1093/rfs/hhn043
- G. Chamberlain and M. Rothschild, “Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets,” Econometrica, Vol. 51, No. 5, 1983, pp. 1281-1304. doi:10.2307/1912275
- F. Lavancier, “Invariance Principles for Non-Isotropic Long Memory Random Fields,” Statistical Inferences on Stochastic Processes, Vol. 10, No. 3, 2007, pp. 255-282. doi:10.1007/s11203-006-9001-9
- H. White, “Asymptotic Theory for Econometricians,” Academic Press, Oxford, 2001, pp. 10-12.