Portfolio risk evaluation: An approach based on dynamic conditional correlations models and wavelet multiresolution analysis

Khalfaoui, R and Boutahar, M (2012): Portfolio risk evaluation: An approach based on dynamic conditional correlations models and wavelet multiresolution analysis.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Dynamic conditional correlations, Value-at-Risk, wavelet decomposition, Stock prices
• Subjects: D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D53 - Financial Markets; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods; G - Financial Economics > G1 - General Financial Markets > G11 - Portfolio Choice ; Investment Decisions; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C52 - Model Evaluation, Validation, and Selection

References

Aielli, G. P., 2008. Consistent estimation of large scale dynamic conditional correlations. Working paper n.47, University of Messina, Department of Economics, Statistics, Mathematics and Sociology.

Arouri, M. E. H., Lahiani, A., Nguyen, D. K., 2011. Return and volatility transmission between world oil prices and stock markets of the gcc countries. Economic Modelling 28 (4), 1815–1825.

Bauwens, L., Laurent, S., Rombouts, J. V. K., 2006. Multivariate garch models: a survey. Journal of Applied Econometrics 21 (1), 79–109.

Becker, R., Clements, A., 2008. Are combination forecasts of s&p 500 volatility statistically superior? International Journal of Forecasting 24 (1), 122–133.

Bollerslev, T., 1986. Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31 (3), 307–327.

Bollerslev, T., 1990. Modelling the coherence in short-run nominal exchange rates: A multivariate generalized arch model. The Review of Eco-nomics and Statistics 72 (3), 498–505.

Bollerslev, T., Engle, R. F., Wooldridge, J. M., 1988. A capital asset pricing model with time-varying covariances. The Journal of Political Economy 96 (01), 116–131.

Brooks, C., 2002. Introductory Econometrics for Finance. Cambridge University Press, United Kingdom.

Büttner, D., Hayo, B., 2011. Determinants of european stock market integration. Economic Systems 35, 574–585.

Caporin, M., McAleer, M., 2009. Do we really need both bekk and dcc? a tale of two covariance models. Documentos del Instituto Complutense de Análisis Económico 0904, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales.

Caporin, M., McAleer, M., 2010. Do we really need both bekk and dcc? a tale of two multivariate garch models. Working Papers in Economics 10/06, University of Canterbury, Department of Economics and Finance.

Cappiello, L., Engle, R. F., Sheppard, K., 2006. Asymmetric dynamics in the correlations of global equity and bond returns. Journal of Financial Econometrics 04 (04), 537–572.

Chang, C.-L., Khamkaew, T., McAleer, M., Tansuchat, R., 2011. Modelling conditional correlations in the volatility of asian rubber spot and futures returns. Mathematics and Computers in Simulation 81 (7), 1482 – 1490.

Chiang, T. C., Jeon, B. N., Li, H., 2007. Dynamic correlation analysis of financial contagion: Evidence from asian markets. Journal of International Money and Finance 26 (7), 1206–1228.

Christoffersen, P. F., 1998. Evaluating interval forecasts. International Economic Review 39 (4), 841–62.

Dickey, D. A., Fuller, W. A., 1979. Distribution of the estimators for autoregressive time series with unit root. Journal of the American Statistical Association 74, 427–431.

Engle, R. F., 1982. Autoregressive conditional heteroscedasticity with estimates of the variance of united kingdom inflation. Econometrica 50 (4), 987–1007.

Engle, R. F., 2002. Dynamic conditional correlation: A simple class of multivariate generalizd autoregressive conditional heteroskedasticity models. Journal of Business & Economic Statistics 20, 339–350.

Engle, R. F., Kroner, K. F., 1995. Multivariate simultaneous generalized arch. Econometric Theory 11 (01), 122–150.

Engle, R. F., Manganelli, S., 2004. Caviar: Conditional autoregressive value at risk by regression quantiles. Journal of Business & Economic Statistics 22, 367–381.

Gençay, R., Selçuk, F., Whitcher, B., 2002. In: An Introduction to Wavelets and Other Filtering Methods in Finance and Economics. Academic-Press.

Glosten, L. R., Jagannathan, R., Runkle, D. E., 1993. On the relation between the expected value and the volatility of the nominal excess return on stocks. Tech. Rep. 157.

Hansen, P. R., Lunde, A., 2005. A forecast comparison of volatility models: does anything beat a garch(1,1)? Journal of Applied Econometrics 20 (7), 873–889.

Hansen, P. R., Lunde, A., Nason, J. M., 2003. Choosing the best volatility models: the model confidence set approach. Working Paper 2003-28, Federal Reserve Bank of Atlanta.

Ho, K.-Y., Tsui, A. K., Zhang, Z., 2009. Volatility dynamics of the us business cycle: A multivariate asymmetric garch approach. Mathematics and Computers in Simulation 79, 2856–2868.

Kang, S. H., Kang, S.-M., Yoon, S.-M., 2009. Forecasting volatility of crude oil markets. Energy Economics 31 (1), 119–125.

Kenourgios, D., Samitas, A., Paltalidis, N., 2011. Financial crises and stock market contagion in a multivariate time-varying asymmetric framework. Journal of International Financial Markets, Institutions and Money 21 (1), 92–106.

Kim, S., In, F. H., 2003. The relationship between financial variables and real economic activity: Evidence from spectral and wavelet analyses. Studies in Nonlinear Dynamics & Econometrics 7 (4), 4.

Kupiec, P. H., 1995. Techniques for verifying the accuracy of risk measurement models. Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).

Kwiatkowski, D., Phillips, P. C. B., Schmidt, P., Shin, Y., 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 54 (1-3), 159–178.

Lahrech, A., Sylwester, K., 2011. U.s. and latin american stock market linkages. Journal of International Money and Finance 30, 1341–1357.

Laurent, S., Rombouts, J. V. K., Violante, F., 2011. On the forecasting accuracy of multivariate garch models. Journal of Applied Econometrics.

Ling, S., McAleer, M., 2003. Asymptotic theory for a vector arma-garch model. Econometric Theory 19 (02), 280–310.

Lopez, J. A., 1998. Methods for evaluating value-at-risk estimates. Economic Policy Review, 119–124.

Mallat, S. G., 1989. A theory for multiresolution signal decomposition: The wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence 11, 674–693.

Masih, M., Alzahrani, M., Al-Titi, O., 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 19 (1), 10–18.

McAleer, M., Hoti, S., Chan, F., 2009. Structure and asymptotic theory for multivariate asymmetric conditional volatility . Econometric Reviews 28 (5), 422–440.

Nelson, D. B., 1991. Conditional heteroskedasticity in asset returns: A new approach. Econometrica 59 (2), 347–70. Nelson, D. B., Foster, D. P., 1994. Asymptotic filtering theory for univariate arch models. Econometrica 62 (1), 1–41.

Palandri, A., 2009. Sequential conditional correlations: Inference and evaluation. Journal of Econometrics 153 (2), 122–132.

Percival, D. B., Walden, A. T., 2000. Wavelet methods for time series analysis. Cambridge University Press.

Rabemananjara, R., Zakoian, J. M., 1993. Threshold arch models and asymmetries in volatility. Journal of Applied Econometrics 8 (1), 31–49.

Rua, A., 2010. Measuring comovement in the time–frequency space. Journal of Macroeconomics 32 (2), 685–691.

Rua, A., Nunes, L. C., 2009. International comovement of stock market returns: A wavelet analysis. Journal of Empirical Finance 16 (4), 632–639.

Sadorsky, P., 2006. Modeling and forecasting petroleum futures volatility. Energy Economics 28 (4), 467–488. Sharkasi, A., Ruskin, H. J., Crane, M., 2005.

Interrelationships among international stock market indices: Europe, asia and the americas. Interna-tional Journal of Theoretical and Applied Finance 8 (5), 603.

Tse, Y. K., Tsui, A. K. C., 2002. A multivariate generalized autoregressive conditional heteroscedasticity model with time-varying correlations.

Journal of Business & Economic Statistics 20 (3), 351–62. Wei, Y., Wang, Y., Huang, D., 2010. Forecasting crude oil market volatility: Further evidence using garch-class models. Energy Economics 32 (6),1477–1484.

Zakoian, J.-M., 1994. Threshold heteroskedastic models. Journal of Economic Dynamics and Control 18 (5), 931–955