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 inJournal of forecasting Vol. 27; no. 3; pp. 217 - 235
Main Authors McAleer, Michael, da Veiga, Bernardo
Format Journal Article
LanguageEnglish
Published Chichester, UK John Wiley & Sons, Ltd 01.04.2008
Wiley Periodicals Inc
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ISSN0277-6693
1099-131X
DOI10.1002/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.
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
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  fullname: da Veiga, Bernardo
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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.
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Snippet 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...
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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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Volume 27
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