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Portfolio Risk Evaluation An Approach Based on Dynamic Conditional Correlations Models and Wavelet Multi-Resolution Analysis

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  • Rabeh Khalfaoui

    (Aix-Marseille Université, Greqam)

  • Mohammed Boutahar

    (Aix-Marseille Université, IML)

Abstract

We analyzed the volatility dynamics of three developed markets (U.K., U.S. and Japan), during the period 2003-2011, by comparing the performance of several multivariate volatility models, namely Constant Conditional Correlation (CCC), Dynamic Conditional Correlation (DCC) and consistent DCC (cDCC) models. To evaluate the performance of models we used four statistical loss functions on the daily Value-at-Risk (VaR) estimates of a diversified portfolio in three stock indices: FTSE 100, S&P 500 and Nikkei 225. We based on one-day ahead conditional variance forecasts. To assess the performance of the abovementioned models and to measure risks over different time-scales, we proposed a wavelet-based approach which decomposes a given time series on different time horizons. Wavelet multiresolution analysis and multivariate conditional volatility models are combined for volatility forecasting to measure the comovement between stock market returns and to estimate daily VaR in the time-frequency space. Empirical results shows that the asymmetric cDCC model of Aielli (2008) is the most preferable according to statistical loss functions under raw data. The results also suggest that wavelet-based models increase predictive performance of financial forecasting in low scales according to number of violations and failure probabilities for VaR models

Suggested Citation

  • Rabeh Khalfaoui & Mohammed Boutahar, 2012. "Portfolio Risk Evaluation An Approach Based on Dynamic Conditional Correlations Models and Wavelet Multi-Resolution Analysis," AMSE Working Papers 1208, Aix-Marseille School of Economics, France.
  • Handle: RePEc:aim:wpaimx:1208
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    1. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-131, February.
    2. Büttner, David & Hayo, Bernd, 2011. "Determinants of European stock market integration," Economic Systems, Elsevier, vol. 35(4), pages 574-585.
    3. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(2), pages 280-310, April.
    4. Peter Reinhard Hansen & Asger Lunde & James M. Nason, 2003. "Choosing the Best Volatility Models: The Model Confidence Set Approach," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 65(s1), pages 839-861, December.
    5. Sébastien Laurent & Jeroen V. K. Rombouts & Francesco Violante, 2012. "On the forecasting accuracy of multivariate GARCH models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 934-955, September.
    6. Kin-Yip Ho & Albert K. Tsui & Zhaoyong Zhang, 2009. "Volatility Dynamics of the UK Business Cycle: a Multivariate Asymmetric Garch Approach," Economie Internationale, CEPII research center, issue 117, pages 31-46.
    7. Asger Lunde & Peter R. Hansen, 2005. "A forecast comparison of volatility models: does anything beat a GARCH(1,1)?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 873-889.
    8. Sadorsky, Perry, 2006. "Modeling and forecasting petroleum futures volatility," Energy Economics, Elsevier, vol. 28(4), pages 467-488, July.
    9. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
    10. Chang, Chia-Lin & Khamkaew, Thanchanok & McAleer, Michael & Tansuchat, Roengchai, 2011. "Modelling conditional correlations in the volatility of Asian rubber spot and futures returns," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(7), pages 1482-1490.
    11. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    12. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    13. Kim Sangbae & In Francis Haeuck, 2003. "The Relationship Between Financial Variables and Real Economic Activity: Evidence From Spectral and Wavelet Analyses," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 7(4), pages 1-18, December.
    14. Massimiliano Caporin & Michael McAleer, 2012. "Do We Really Need Both Bekk And Dcc? A Tale Of Two Multivariate Garch Models," Journal of Economic Surveys, Wiley Blackwell, vol. 26(4), pages 736-751, September.
    15. Nelson, Daniel B & Foster, Dean P, 1994. "Asymptotic Filtering Theory for Univariate ARCH Models," Econometrica, Econometric Society, vol. 62(1), pages 1-41, January.
    16. Arouri, Mohamed El Hedi & Lahiani, Amine & Nguyen, Duc Khuong, 2011. "Return and volatility transmission between world oil prices and stock markets of the GCC countries," Economic Modelling, Elsevier, vol. 28(4), pages 1815-1825, July.
    17. Massimiliano Caporin & Michael McAleer, 2009. "Do We Really Need Both BEKK and DCC? A Tale of Two Covariance Models," CARF F-Series CARF-F-156, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    18. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    19. Wei, Yu & Wang, Yudong & Huang, Dengshi, 2010. "Forecasting crude oil market volatility: Further evidence using GARCH-class models," Energy Economics, Elsevier, vol. 32(6), pages 1477-1484, November.
    20. Michael McAleer & Suhejla Hoti & Felix Chan, 2009. "Structure and Asymptotic Theory for Multivariate Asymmetric Conditional Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 28(5), pages 422-440.
    21. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
    22. Rua, António & Nunes, Luís C., 2009. "International comovement of stock market returns: A wavelet analysis," Journal of Empirical Finance, Elsevier, vol. 16(4), pages 632-639, September.
    23. Becker, Ralf & Clements, Adam E., 2008. "Are combination forecasts of S&P 500 volatility statistically superior?," International Journal of Forecasting, Elsevier, vol. 24(1), pages 122-133.
    24. Kenourgios, Dimitris & Samitas, Aristeidis & Paltalidis, Nikos, 2011. "Financial crises and stock market contagion in a multivariate time-varying asymmetric framework," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 21(1), pages 92-106, February.
    25. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    26. Masih, Mansur & Alzahrani, Mohammed & Al-Titi, Omar, 2010. "Systematic risk and time scales: New evidence from an application of wavelet approach to the emerging Gulf stock markets," International Review of Financial Analysis, Elsevier, vol. 19(1), pages 10-18, January.
    27. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    28. Palandri, Alessandro, 2009. "Sequential conditional correlations: Inference and evaluation," Journal of Econometrics, Elsevier, vol. 153(2), pages 122-132, December.
    29. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    30. Lorenzo Cappiello & Robert F. Engle & Kevin Sheppard, 2006. "Asymmetric Dynamics in the Correlations of Global Equity and Bond Returns," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(4), pages 537-572.
    31. Adel Sharkasi & Heather J. Ruskin & Martin Crane, 2005. "Interrelationships Among International Stock Market Indices: Europe, Asia And The Americas," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(05), pages 603-622.
    32. Zakoian, Jean-Michel, 1994. "Threshold heteroskedastic models," Journal of Economic Dynamics and Control, Elsevier, vol. 18(5), pages 931-955, September.
    33. Chiang, Thomas C. & Jeon, Bang Nam & Li, Huimin, 2007. "Dynamic correlation analysis of financial contagion: Evidence from Asian markets," Journal of International Money and Finance, Elsevier, vol. 26(7), pages 1206-1228, November.
    34. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    35. Lahrech, Abdelmounaim & Sylwester, Kevin, 2011. "U.S. and Latin American stock market linkages," Journal of International Money and Finance, Elsevier, vol. 30(7), pages 1341-1357.
    36. Tse, Y K & Tsui, Albert K C, 2002. "A Multivariate Generalized Autoregressive Conditional Heteroscedasticity Model with Time-Varying Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 351-362, July.
    37. Rabemananjara, R & Zakoian, J M, 1993. "Threshold Arch Models and Asymmetries in Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(1), pages 31-49, Jan.-Marc.
    38. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    39. Rua, António, 2010. "Measuring comovement in the time-frequency space," Journal of Macroeconomics, Elsevier, vol. 32(2), pages 685-691, June.
    40. Kang, Sang Hoon & Kang, Sang-Mok & Yoon, Seong-Min, 2009. "Forecasting volatility of crude oil markets," Energy Economics, Elsevier, vol. 31(1), pages 119-125, January.
    41. 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.
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    3. Teply, Petr & Kvapilikova, Ivana, 2017. "Measuring systemic risk of the US banking sector in time-frequency domain," The North American Journal of Economics and Finance, Elsevier, vol. 42(C), pages 461-472.
    4. Maghyereh, Aktham I. & Awartani, Basel & Abdoh, Hussein, 2019. "The co-movement between oil and clean energy stocks: A wavelet-based analysis of horizon associations," Energy, Elsevier, vol. 169(C), pages 895-913.
    5. Meng, Xiangcai & Huang, Chia-Hsing, 2019. "The time-frequency co-movement of Asian effective exchange rates: A wavelet approach with daily data," The North American Journal of Economics and Finance, Elsevier, vol. 48(C), pages 131-148.
    6. Maghyereh, Aktham & Awartani, Basel & Abdoh, Hussein, 2020. "The effects of investor emotions sentiments on crude oil returns: A time and frequency dynamics analysis," International Economics, Elsevier, vol. 162(C), pages 110-124.

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    More about this item

    Keywords

    Dynamic conditional correlations; Value-at-Risk; wavelet decomposition; Stock prices.;
    All these keywords.

    JEL classification:

    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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