Home Modelling nonlinearities in equity returns: the mean impact curve analysis
Article
Licensed
Unlicensed Requires Authentication

Modelling nonlinearities in equity returns: the mean impact curve analysis

  • Vance L. Martin EMAIL logo , Saikat Sarkar and Antti Jaakko Kanto
Published/Copyright: August 21, 2013
Become an author with De Gruyter Brill
Submit Manuscript Author Information
Studies in Nonlinear Dynamics and Econometrics
From the journal Studies in Nonlinear Dynamics and Econometrics Volume 18 Issue 1

Abstract

A time-varying model of equity returns consisting of a volatility factor with time-varying loading, is specified to investigate the dynamical effects of shocks on expected returns. The proposed specification yields a nonlinear relationship between the conditional mean and the news, referred to as the mean impact curve (MIC). Applying this framework to the AORD, Hang Seng and Straits Times equity indexes yields estimated MICs with qualitatively similar nonlinear characteristics for each equity market. An important implication of the empirical results is that the relationship between the conditional mean and the news is found to be dependent upon the size of the shock, a result which is consistent with equity markets displaying mean aversion over short horizons and mean reversion over long horizons.

Keywords: asymmetry; news impact curve; nonlinear mean reversion and aversion
Corresponding author: Vance L. Martin, University of Melbourne, Melbourne, Australia, e-mail:
  1. 1

    An alternative approach is to scale the daily residual standard deviation in Table 10 by the pertinent time period. In the case of Australia for example, the one year standard deviation is which is close to the value of 12.194 reported in Table 10 assuming conditional normality.

  2. 2

    Another potential strategy to identify the relationship between the nonlinearities of the MIC and the observed change in the autocorrelation properties of returns over alternative time horizons is to estimate the MIC model for longer time horizons than a day. However, this approach is problematic as estimation of GARCH models using lower frequency data are less precise as the observed volatility clustering in higher frequency data is less prominant for lower frequency data with the strength of the signal diminishing the lower the frequency.

  3. 3

    Another approach to understanding the nonlinearity properties of the model and its implications for the mean aversion/reversion effects on returns over alternative time horizons was explored in an earlier version of the paper using the generalized impulse response methods of Koop, Pesaran and Potter (1996) and Potter (2000). These results showed that changes in the sign of a shock had a significant impact on the shape of the impulse response function suggesting strong evidence of nonlinearities in the structure of the estimated model.

References

Ashton, D., and M. Tippett. 2006. “Mean Reversion and the Distribution of United Kingdom Stock Index Returns.” Journal of Business and Accounting 33: 1586–1609.10.1111/j.1468-5957.2006.00637.xSearch in Google Scholar

Bali, T., K. Demirtas, and H. Levy. 2008. “Nonlinear Mean Reversion in Stock Prices.” Journal of Banking and Finance 32: 767–782.10.1016/j.jbankfin.2007.05.013Search in Google Scholar

Balvers, R. J., and Y. Wu. 2006. “Momentum and Mean Reversion Across National Equity Markets.” Journal of Empirical Finance 13: 24–48.10.1016/j.jempfin.2005.05.001Search in Google Scholar

Balvers, R. J., Y. Wu, and E. Gilliland. 2000. “Mean Reversion Across National Stock Markets and Parametric Contrarian Investment Strategies.” Journal of Finance 55: 745–772.10.1111/0022-1082.00225Search in Google Scholar

Bansal, R. and S. Viswanathan. 1993. “No-Arbitrage and Arbitrage Pricing: A New Approach.” Journal of Finance 48: 1231–1262.10.1111/j.1540-6261.1993.tb04753.xSearch in Google Scholar

Blake, A. P., and G. Kapetanios. 2003. “Pure Significance Tests of the Unit Root Hypothesis Against Nonlinear Alternatives.” Journal of Time Series Analysis 24: 253–267.10.1111/1467-9892.00306Search in Google Scholar

Blake, A. P., and G. Kapetanios. 2007. “Testing for ARCH in the Presence of Nonlinearity of Unknown Form in the Conditional Mean.” Journal of Econometrics 137: 472–488.10.1016/j.jeconom.2005.08.007Search in Google Scholar

Bollen, N. P. B., and R. E. Whaley. 2009. “Hedge Fund Risk Dynamics: Implications for Performance Appraisal.” Journal of Finance 64: 985–1035.10.1111/j.1540-6261.2009.01455.xSearch in Google Scholar

Bollerslev, T. 1987. “A Conditional Heteroskedastic Model for Speculative Prices and Rates of Return.” The Review of Economics and Statistics 69: 542–547.10.2307/1925546Search in Google Scholar

Bollerslev, T., N. Sizova, and G. Tauchen. 2012. “Volatility in Equilibrium: Asymmetries and Dynamic Dependencies.” Review of Finance 16: 31–80.10.1093/rof/rfr005Search in Google Scholar

Brock, W., D. Dechert, J. Scheinkman, and B. LeBaron. 1996. “A Test for Independence Based on the Correlation Dimension.” Econometric Reviews 15: 197–235.10.1080/07474939608800353Search in Google Scholar

Campbell, J. Y., and L. Hentschell. 1992. “No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns.” Journal of Financial Economics 31: 281–318.10.1016/0304-405X(92)90037-XSearch in Google Scholar

Cao, C., Y. Chen, and B. Liang. 2009. “Can Hedge Funds Time Market Liquidity?” Unpublised working paper, University of Massachusetts at Amherst.10.2139/ssrn.1658972Search in Google Scholar

Choe, K., K. Nam, and F. Vahid. 2007. “Necessity of Negative Serial Correlation for Mean-Reversion of Stock Prices.” The Quarterly Review of Economics and Finance 47: 576–583.10.1016/j.qref.2005.04.005Search in Google Scholar

Dittmar, R. F. 2002. “Nonlinear Pricing Kernels, Kurtosis Preference, and Evidence from the Cross Section of Equity Returns.” Journal of Finance 57: 369–403.10.1111/1540-6261.00425Search in Google Scholar

Engle, R. F., and V. K. Ng. 1993. “Measuring and Testing the Impact of News on Volatility.” Journal of Finance 48: 1749–1778.10.1111/j.1540-6261.1993.tb05127.xSearch in Google Scholar

Engle, R. F., D. Lilien, and R. Robins. 1987. “Estimating Time Varying Risk Premia in the Term Structure: The ARCH-M model.” Econometrica 55: 391–407.10.2307/1913242Search in Google Scholar

Fama, E. F., and K. R. French. 1988. “Permanent and Temporary Components of Stock Prices.” Journal of Political Economy 96: 246–273.10.1086/261535Search in Google Scholar

Ferson, W. E., and R. W. Schadt. 1996. “Measuring Fund Strategy and Performance in Changing Economic Conditions.” Journal of Finance 51: 425–461.10.1111/j.1540-6261.1996.tb02690.xSearch in Google Scholar

Fry, R., V. L. Martin, and C. Tang. 2010. “A New Class of Tests of Contagion with Applications.” Journal of Business and Economic Statistics 28: 423–437.10.1198/jbes.2010.06060Search in Google Scholar

Ghysels, E., P. Santa-Clara, and R. Valkanov. 2005. “There is a Risk-Return Tradeoff After All.” Journal of Financial Economics 76: 509–548.10.1016/j.jfineco.2004.03.008Search in Google Scholar

Glosten, L. R., R. Jagannathan, and D. E. Runkle. 1993. “On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks.” Journal of Finance 48: 1779–1801.10.1111/j.1540-6261.1993.tb05128.xSearch in Google Scholar

Granger, C. W. J. 2008. “Non-Linear Models: Where Do We Go Next - Time Varying Parameter Models?” Studies in Nonlinear Dynamics & Econometrics 12: 1–9.10.2202/1558-3708.1639Search in Google Scholar

Harvey, C. R., and A. Siddique. 2000. “Conditional Skewness in Asset Pricing Tests.” The Journal of Finance 55: 1263–1295.10.1111/0022-1082.00247Search in Google Scholar

Harvey, D. I., and S. J. Leybourne. 2007. “Testing for Time Series Linearity.” Econometrics Journal 10: 149–165.10.1111/j.1368-423X.2007.00203.xSearch in Google Scholar

Kim, M. J., C. R. Nelson, and R. Startz. 1991. “Mean Reversion in Stock Prices? A Reappraisal of the Empirical Evidence.” Review of Economic Studies 58: 515–528.10.2307/2298009Search in Google Scholar

Koop, G., M. H. Pesaran, and S. M. Potter. 1996. “Impulse Response Analysis in Nonlinear Multivariate Models.” Journal of Econometrics 74: 119–147.10.1016/0304-4076(95)01753-4Search in Google Scholar

Koopman, S. J., and E. Hol Uspensky. 2002. “The Stochastic Volatility in Mean Model: Empirical Evidence from International Stock Markets.” Journal of Applied Econometrics 17: 667–689.10.1002/jae.652Search in Google Scholar

Lettau, M., and S. Ludvigson. 2001. “Resurrecting the (C)CAPM: A Cross-Sectional Test when Risk Premia are Time-Varying.” Journal of Political Economy 109: 1238–1287.10.1086/323282Search in Google Scholar

Levent, A., A. Altay-Salih, and M. Caner. 2003. “Time-Varying Betas Help in Asset Pricing: The Threshold CAPM.” Studies in Nonlinear Dynamics & Econometrics 6: 1–7.Search in Google Scholar

Luukkonen, R., P. Saikkonen, and T. Teräsvirta. 1988. “Testing Linearity Against Smooth Transition Autoregressive Models.” Biometrika 75: 491–499.10.1093/biomet/75.3.491Search in Google Scholar

Ma, J., C. R. Nelson, and R. Startz. 2007. “Spurious Inference in the GARCH(1,1) Model when It is Weakly Identified.” Studies in Nonlinear Dynamics & Econometrics 11: Article 1.Search in Google Scholar

Mamaysky, H., M. Spiegel, and H. Zhang. 2008. “Estimating the Dynamics of Mutual Fund Alphas and Betas.” Review of Financial Studies 21: 233–264.10.1093/rfs/hhm049Search in Google Scholar

Merton, R. C. 1973. “An Intertemporal Capital Asset Pricing Model.” Econometrica 41: 867–887.10.2307/1913811Search in Google Scholar

Nam, K., C. S. Pyun, and A. C. Arize. 2002. “Asymmetric Mean-Reversion and Contrarian Profits: ANST-GARCH Approach.” Journal of Empirical Finance 9: 563–588.10.1016/S0927-5398(02)00011-7Search in Google Scholar

Nelson, D. B. 1991. “Conditional Heteroskedasticity in Asset Returns: A New Approach.” Econometrica 59: 347–370.10.2307/2938260Search in Google Scholar

Nelson, C. R., and R. Startz. 2007. “The Zero-Information-Limit Condition and Spurious Inference in Weakly Identified Models.” Journal of Econometrics 138: 47–62.10.1016/j.jeconom.2006.05.014Search in Google Scholar

Patton, A. J., and T. Ramadorai. 2013. “On the High-Frequency Dynamics of Hedge Fund Risk Exposures.” Journal of Finance 68: 597–635.10.1111/jofi.12008Search in Google Scholar

Potter, S. M. 2000. “Nonlinear Impulse Response Functions.” Journal of Economic Dynamics and Control 24: 1425–1446.10.1016/S0165-1889(99)00013-5Search in Google Scholar

Teräsvirta, T., D. Tjøstheim, and C. W. J. Granger. 2010. Modelling Nonlinear Economic Time Series. New York: Oxford University Press.10.1093/acprof:oso/9780199587148.001.0001Search in Google Scholar

Published Online: 2013-08-21
Published in Print: 2014-02-01

©2014 by Walter de Gruyter Berlin Boston

Articles in the same Issue

  1. Masthead
  2. Masthead
  4. A tractable model for indices approximating the growth optimal portfolio
  5. Breaks, trends and unit roots in commodity prices: a robust investigation
  6. Time variation in an optimal asymmetric preference monetary policy model
  7. Modelling nonlinearities in equity returns: the mean impact curve analysis
  8. Persistence in real exchange rate convergence
  9. Herd behavior, bubbles and social interactions in financial markets
https://doi.org/10.1515/snde-2012-0030
Keywords for this article
asymmetry; news impact curve; nonlinear mean reversion and aversion

Articles in the same Issue

  1. Masthead
  2. Masthead
  4. A tractable model for indices approximating the growth optimal portfolio
  5. Breaks, trends and unit roots in commodity prices: a robust investigation
  6. Time variation in an optimal asymmetric preference monetary policy model
  7. Modelling nonlinearities in equity returns: the mean impact curve analysis
  8. Persistence in real exchange rate convergence
  9. Herd behavior, bubbles and social interactions in financial markets
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 21.11.2025 from https://www.degruyterbrill.com/document/doi/10.1515/snde-2012-0030/html
Scroll to top button