Risk-return relationship in equity markets: using a robust GMM estimator for GARCH-M models
While most asset pricing models postulate a positive relationship between excess returns and risk, there is no consensus on the nature of the relationship due to conflicting empirical evidence. The relationship is particularly ambiguous within a GARCH-M framework. This paper demonstrates that such a conflict can be attributed primarily to the downward bias of standard estimators that neglect additive outliers (AO) commonly observed in financial returns, and proposes a feasible estimation method (RGMME) for the GARCH-M model based upon a robust variant of the GMM. Monte Carlo experiments demonstrate that AOs cause more serious bias in the ML and GMM estimates of the relationship coefficient than previously expected. Therefore, in the presence of AOs, the RGMME appears superior to other standard estimators in terms of the root mean square error criterion. There is strong evidence favouring the RGMME over standard estimators based on its empirical application. In particular, it is substantially evident from the results of the RGMME that there is support for a positive relationship between excess returns and conditional volatility for all three major equity markets.
Volume (Year): 9 (2009)
Issue (Month): 1 ()
|Contact details of provider:|| Web page: http://www.tandfonline.com/RQUF20|
|Order Information:||Web: http://www.tandfonline.com/pricing/journal/RQUF20|
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- M. Angeles Carnero & Daniel Peña & Esther Ruiz, 2004.
"Spurious And Hidden Volatility,"
Working Papers. Serie AD
2004-45, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
- Ruiz, Esther & Peña, Daniel & Carnero, María Ángeles, 2004. "Spurious and hidden volatility," DES - Working Papers. Statistics and Econometrics. WS ws042007, Universidad Carlos III de Madrid. Departamento de Estadística.
- Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
- Harvey, Campbell R., 2001. "The specification of conditional expectations," Journal of Empirical Finance, Elsevier, vol. 8(5), pages 573-637, December.
- Campbell, John Y. & Hentschel, Ludger, 1992. "No news is good news *1: An asymmetric model of changing volatility in stock returns," Journal of Financial Economics, Elsevier, vol. 31(3), pages 281-318, June.
- John Y. Campbell & Ludger Hentschel, 1991. "No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns," NBER Working Papers 3742, National Bureau of Economic Research, Inc.
- Hentschel, Ludger & Campbell, John, 1992. "No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns," Scholarly Articles 3220232, Harvard University Department of Economics.
- Koenker, Roger & Machado, Jose A. F., 1999. "GMM inference when the number of moment conditions is large," Journal of Econometrics, Elsevier, vol. 93(2), pages 327-344, December.
- Ronchetti, Elvezio & Trojani, Fabio, 2001. "Robust inference with GMM estimators," Journal of Econometrics, Elsevier, vol. 101(1), pages 37-69, March.
- Altonji, Joseph G & Segal, Lewis M, 1996. "Small-Sample Bias in GMM Estimation of Covariance Structures," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 353-366, July.
- Joseph G. Altonji & Lewis M. Segal, 1994. "Small sample bias in GMM estimation of covariance structures," Working Paper Series, Macroeconomic Issues 94-8, Federal Reserve Bank of Chicago.
- Joseph G. Altonji & Lewis M. Segal, 1994. "Small Sample Bias in GMM Estimation of Covariance Structures," NBER Technical Working Papers 0156, National Bureau of Economic Research, Inc.
- Koenker, Roger & Machado, José A.F. & Skeels, Christopher L. & Welsh, Alan H., 1994. "Momentary Lapses: Moment Expansions and the Robustness of Minimum Distance Estimation," Econometric Theory, Cambridge University Press, vol. 10(01), pages 172-197, March.
- Baillie, Richard T. & DeGennaro, Ramon P., 1990. "Stock Returns and Volatility," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(02), pages 203-214, June.
- Baillie, R.T. & Degennaro, R.P., 1988. "Stock Returns And Volatility," Papers 8803, Michigan State - Econometrics and Economic Theory.
- John Y. Campbell & John Cochrane, 1999. "Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior," Journal of Political Economy, University of Chicago Press, vol. 107(2), pages 205-251, April.
- Xing, Xuejing & Howe, John S., 2003. "The empirical relationship between risk and return: evidence from the UK stock market," International Review of Financial Analysis, Elsevier, vol. 12(3), pages 329-346.
- Jorion, Philippe, 1995. " Predicting Volatility in the Foreign Exchange Market," Journal of Finance, American Finance Association, vol. 50(2), pages 507-528, June.
- French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
- Ernst R. Berndt & Bronwyn H. Hall & Robert E. Hall & Jerry A. Hausman, 1974. "Estimation and Inference in Nonlinear Structural Models," NBER Chapters,in: Annals of Economic and Social Measurement, Volume 3, number 4, pages 653-665 National Bureau of Economic Research, Inc.
- Jurgen A. Doornik & Marius Ooms, 2005. "Outlier Detection in GARCH Models," Tinbergen Institute Discussion Papers 05-092/4, Tinbergen Institute.
- Jurgen A. Doornik & Marius Ooms, 2005. "Outlier Detection in GARCH Models," Economics Papers 2005-W24, Economics Group, Nuffield College, University of Oxford.
- Rich, Robert W. & Raymond, Jennie & Butler, J. S., 1991. "Generalized instrumental variables estimation of autoregressive conditional heteroskedastic models," Economics Letters, Elsevier, vol. 35(2), pages 179-185, February.
- Franses, Philip Hans & Ghijsels, Hendrik, 1999. "Additive outliers, GARCH and forecasting volatility," International Journal of Forecasting, Elsevier, vol. 15(1), pages 1-9, February.
- Bansal, Ravi & Lundblad, Christian, 2002. "Market efficiency, asset returns, and the size of the risk premium in global equity markets," Journal of Econometrics, Elsevier, vol. 109(2), pages 195-237, August.
- Park, Beum-Jo, 2002. "An Outlier Robust GARCH Model and Forecasting Volatility of Exchange Rate Returns," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 21(5), pages 381-393, August.
- Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
- Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, vol. 55(2), pages 391-407, March.
- Jarque, Carlos M. & Bera, Anil K., 1980. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals," Economics Letters, Elsevier, vol. 6(3), pages 255-259.
- Ruiz, Esther & Peña, Daniel & Carnero, María Ángeles, 2001. "Outliers and conditional autoregressive heteroscedasticity in time series," DES - Working Papers. Statistics and Econometrics. WS ws010704, Universidad Carlos III de Madrid. Departamento de Estadística.
- Peter Hall & Qiwei Yao, 2003. "Inference in Arch and Garch Models with Heavy--Tailed Errors," Econometrica, Econometric Society, vol. 71(1), pages 285-317, January.
- Nam, Kiseok & Pyun, Chong Soo & Avard, Stephen L., 2001. "Asymmetric reverting behavior of short-horizon stock returns: An evidence of stock market overreaction," Journal of Banking & Finance, Elsevier, vol. 25(4), pages 807-824, April.
- Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:taf:quantf:v:9:y:2009:i:1:p:93-104. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Michael McNulty)
If references are entirely missing, you can add them using this form.