Single-index and portfolio models for forecasting value-at-risk thresholds
The variance of a portfolio can be forecast using a single index model or the covariance matrix of the portfolio. Using univariate and multivariate conditional volatility models, this paper evaluates the performance of the single index and portfolio models in forecasting value‐at‐risk (VaR) threshol...
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Published in | Journal of forecasting Vol. 27; no. 3; pp. 217 - 235 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Chichester, UK
John Wiley & Sons, Ltd
01.04.2008
Wiley Periodicals Inc |
Subjects | |
Online Access | Get full text |
ISSN | 0277-6693 1099-131X |
DOI | 10.1002/for.1054 |
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Abstract | The variance of a portfolio can be forecast using a single index model or the covariance matrix of the portfolio. Using univariate and multivariate conditional volatility models, this paper evaluates the performance of the single index and portfolio models in forecasting value‐at‐risk (VaR) thresholds of a portfolio. Likelihood ratio tests of unconditional coverage, independence and conditional coverage of the VaR forecasts suggest that the single‐index model leads to excessive and often serially dependent violations, while the portfolio model leads to too few violations. The single‐index model also leads to lower daily Basel Accord capital charges. The univariate models which display correct conditional coverage lead to higher capital charges than models which lead to too many violations. Overall, the Basel Accord penalties appear to be too lenient and favour models which have too many violations. Copyright © 2008 John Wiley & Sons, Ltd. |
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AbstractList | The variance of a portfolio can be forecast using a single index model or the covariance matrix of the portfolio. Using univariate and multivariate conditional volatility models, this paper evaluates the performance of the single index and portfolio models in forecasting value-at-risk (VaR) thresholds of a portfolio. Likelihood ratio tests of unconditional coverage, independence and conditional coverage of the VaR forecasts suggest that the single-index model leads to excessive and often serially dependent violations, while the portfolio models leads to too few violations. The single-index model also leads to lower daily Basel Accord capital charges. The univariate models which display correct conditional coverage lead to higher capital charges than models which lead to too many violations. Overall, the Basel Accord penalties appear to be too lenient and favour models which have too many violations. Copyright John Wiley & Sons. Reproduced with permission. An electronic version of this article is available online at http://www.interscience.wiley.com The variance of a portfolio can be forecast using a single index model or the covariance matrix of the portfolio. Using univariate and multivariate conditional volatility models, this paper evaluates the performance of the single index and portfolio models in forecasting value-at-risk (VaR) thresholds of a portfolio. Likelihood ratio tests of unconditional coverage, independence and conditional coverage of the VaR forecasts suggest that the single-index model leads to excessive and often serially dependent violations, while the portfolio model leads to too few violations. The single-index model also leads to lower daily Basel Accord capital charges. The univariate models which display correct conditional coverage lead to higher capital charges than models which lead to too many violations. Overall, the Basel Accord penalties appear to be too lenient and favour models which have too many violations. [PUBLICATION ABSTRACT] The variance of a portfolio can be forecast using a single index model or the covariance matrix of the portfolio. Using univariate and multivariate conditional volatility models, this paper evaluates the performance of the single index and portfolio models in forecasting value‐at‐risk (VaR) thresholds of a portfolio. Likelihood ratio tests of unconditional coverage, independence and conditional coverage of the VaR forecasts suggest that the single‐index model leads to excessive and often serially dependent violations, while the portfolio model leads to too few violations. The single‐index model also leads to lower daily Basel Accord capital charges. The univariate models which display correct conditional coverage lead to higher capital charges than models which lead to too many violations. Overall, the Basel Accord penalties appear to be too lenient and favour models which have too many violations. Copyright © 2008 John Wiley & Sons, Ltd. |
Author | McAleer, Michael da Veiga, Bernardo |
Author_xml | – sequence: 1 givenname: Michael surname: McAleer fullname: McAleer, Michael email: michael.mcaleer@gmail.com organization: School of Economics and Commerce, University of Western Australia – sequence: 2 givenname: Bernardo surname: da Veiga fullname: da Veiga, Bernardo organization: School of Economics and Commerce, University of Western Australia |
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References | Basel Committee on Banking Supervision. 1988. International Convergence of Capital Measurement and Capital Standards. BIS: Basel, Switzerland. McAleer M, Da Veiga B. 2008. Forecasting value-at-risk with a parsimonious portfolio spillover GARCH (PS-GARCH) model. Journal of Forecasting 27: 1-19. Ding Z, Granger CWJ, Engle RF. 1993. A long memory property of stock market returns and a new model. Journal of Empirical Finance 1: 83-106. Schwert W. 1989. Stock volatility and crash of '87. Review of Financial Studies 3: 77-102. Engle RF, Ito T, Lin W. 1990. Meteor showers or heat waves? Heteroskedastic intra-daily volatility in the foreign exchange market. Econometrica 58: 525-542. Asai M, McAleer M, Yu J. 2006. Multivariate stochastic volatility: a review. Econometric Reviews 25: 145-175. Bollerslev T. 1990. Modelling the coherence in short-run nominal exchange rate: a multivariate generalized ARCH approach. Review of Economics and Statistics 72: 498-505. Kahya E. 1997. 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Econometric Reviews 25: 453-473. Li WK, Ling S, McAleer M. 2002. Recent theoretical results for time series models with GARCH errors. Journal of Economic Surveys 16: 245-269. Reprinted in McAleer M, Oxley L (eds). 2002. Contributions to Financial Econometrics: Theoretical and Practical Issues. Blackwell: Oxford; 9-33. Ling S, McAleer M. 2003. Asymptotic theory for a vector ARMA-GARCH model. Econometric Theory 19: 278-308. Bollerslev T. 1986. Generalised autoregressive conditional heteroscedasticity. Journal of Econometrics 31: 307-327. Scholes M, Williams J. 1977. Estimating betas from nonsynchronous data. Journal of Financial Economics 5: 309-327. Jeantheau T. 1998. Strong consistency of estimators for multivariate ARCH models. Econometric Theory 14: 70-86. Ling S, McAleer M. 2002b. Stationarity and the existence of moments of a family of GARCH processes. Journal of Econometrics 106: 109-117. RiskmetricsTM. 1996. J. P. Morgan Technical Document (4th edn). J. P. Morgan: New York. 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(e_1_2_1_20_1) 2000 e_1_2_1_22_1 Basel Committee on Banking Supervision (e_1_2_1_5_1) 1995 e_1_2_1_27_1 e_1_2_1_28_1 e_1_2_1_25_1 Glosten LR (e_1_2_1_17_1) 1992; 46 e_1_2_1_29_1 Basel Committee on Banking Supervision (e_1_2_1_6_1) 1996 e_1_2_1_7_1 e_1_2_1_31_1 Basel Committee on Banking Supervision (e_1_2_1_4_1) 1988 e_1_2_1_8_1 e_1_2_1_30_1 e_1_2_1_3_1 e_1_2_1_12_1 e_1_2_1_34_1 e_1_2_1_10_1 e_1_2_1_33_1 e_1_2_1_2_1 e_1_2_1_11_1 Elie L (e_1_2_1_13_1) 1995; 320 Kahya E. (e_1_2_1_21_1) 1997; 1 e_1_2_1_14_1 e_1_2_1_37_1 e_1_2_1_15_1 e_1_2_1_36_1 e_1_2_1_9_1 e_1_2_1_18_1 e_1_2_1_19_1 |
References_xml | – reference: RiskmetricsTM. 1996. J. P. Morgan Technical Document (4th edn). J. P. Morgan: New York. – reference: Engle RF, Ito T, Lin W. 1990. Meteor showers or heat waves? Heteroskedastic intra-daily volatility in the foreign exchange market. Econometrica 58: 525-542. – reference: Elie L, Jeantheau T. 1995. Consistency in heteroskedastic models. Comptes Rendus de l'Académie des Sciences, Série I 320: 1255-1258 (in French). – reference: Engle RF. 1982. Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50: 987-1007. – reference: Boussama F. 2000. Asymptotic normality for the quasi-maximum likelihood estimator of a GARCH model. Comptes Rendus de l'Académie des Sciences, Série I 331: 81-84 (in French). – reference: Li WK, Ling S, McAleer M. 2002. Recent theoretical results for time series models with GARCH errors. Journal of Economic Surveys 16: 245-269. Reprinted in McAleer M, Oxley L (eds). 2002. Contributions to Financial Econometrics: Theoretical and Practical Issues. Blackwell: Oxford; 9-33. – reference: Asai M, McAleer M, Yu J. 2006. Multivariate stochastic volatility: a review. Econometric Reviews 25: 145-175. – reference: Bollerslev T. 1986. Generalised autoregressive conditional heteroscedasticity. Journal of Econometrics 31: 307-327. – reference: Basel Committee on Banking Supervision. 1988. International Convergence of Capital Measurement and Capital Standards. BIS: Basel, Switzerland. – reference: McAleer M. 2005. Automated inference and learning in modeling financial volatility. Econometric Theory 21: 232-261. – reference: Taylor S. 1986. Modelling Financial Time Series. Wiley: New York. – reference: Scholes M, Williams J. 1977. Estimating betas from nonsynchronous data. Journal of Financial Economics 5: 309-327. – reference: Ling S, McAleer M. 2002a. Necessary and sufficient moment conditions for the GARCH(r,s) and asymmetric power GARCH(r,s) models. Econometric Theory 18: 722-729. – reference: Oxley L, McAleer M. 1993. Econometric issues in macroeconomic models with generated regressors. Journal of Economic Surveys 7: 1-40. – reference: Jorion P. 2000. Value at Risk: The New Benchmark for Managing Financial Risk. McGraw-Hill: New York. – reference: Jeantheau T. 1998. Strong consistency of estimators for multivariate ARCH models. Econometric Theory 14: 70-86. – reference: Ling S, McAleer M. 2003. Asymptotic theory for a vector ARMA-GARCH model. Econometric Theory 19: 278-308. – reference: Asai M, McAleer M. 2006. Asymmetric multivariate stochastic volatility. Econometric Reviews 25: 453-473. – reference: Basel Committee on Banking Supervision. 1995. An Internal Model-Based Approach to Market Risk Capital Requirements. BIS: Basel, Switzerland. – reference: Lopez JA. 1998. Methods for evaluating value-at-risk estimates. Federal Reserve Bank of New York Economic Policy Review 119-124. – reference: Kahya E. 1997. Correlation of returns in non-contemporaneous markets. Multinational Finance Journal 1: 123-135. – reference: Ding Z, Granger CWJ, Engle RF. 1993. A long memory property of stock market returns and a new model. Journal of Empirical Finance 1: 83-106. – reference: McAleer M, Chan F, Marinova D. 2007. An econometric analysis of asymmetric volatility: theory and application to patents. Invited paper presented to the Australasian Meeting of the Econometric Society, Brisbane, July 2002. Journal of Econometrics 139: 259-284. – reference: Bollerslev T. 1990. Modelling the coherence in short-run nominal exchange rate: a multivariate generalized ARCH approach. Review of Economics and Statistics 72: 498-505. – reference: Christoffersen PF. 1998. Evaluating interval forecasts. International Economic Review 39: 841-862. – reference: Franses PH, van Dijk D. 1999. Nonlinear Time Series Models in Empirical Finance. Cambridge University Press: Cambridge, UK. – reference: Nelson D. 1991. 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SubjectTerms | Basel Accord penalties conditional correlations Financial engineering Forecasting Forecasting techniques Mathematical finance multivariate conditional volatility Penalties Portfolio performance Portfolio selection portfolio spillover Risk exposure Risk management single index Spillovers Studies Thresholds value-at-risk thresholds Violations Volatility |
Title | Single-index and portfolio models for forecasting value-at-risk thresholds |
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