Modelos Multivariados na Previsão do Valor em Risco de Carteiras de Investimento: da crise das empresas tecnológicas à crise financeira global

Gabriel, Vítor Manuel de Sousa

doi:10.7819/rbgn.v16i51.1802

RESUMO

Neste estudo é analisado o risco de mercado de uma carteira de investimento internacional por meio de uma nova proposta metodológica, baseada no Value-at-Risk, recorrendo à matriz de covariâncias de modelos multivariados do tipo GARCH e à teoria dos valores extremos, para perceber se uma estratégia de diversificação internacional minimiza o risco de mercado, assim como para verificar se a metodologia VaR capta adequadamente esse mesmo risco, aplicando testes de validação de performance. Para o efeito, foram selecionados 12 índices bolsistas internacionais, representativos de cerca de 62% da capitalização bolsista mundial, e escolhido o período compreendido entre a crise Dot-Com e a atual crise financeira global. Os resultados obtidos mostram que a proposta metodológica é uma boa alternativa na acomodação da elevada turbulência dos mercados, podendo ser considerada como uma ferramenta válida na gestão do risco de carteiras de investimento.

Palavras-chave:
Mercados bolsistas; Value-at-Risk; Modelos multivariados GARCH; Teoria dos valores extremos; Backtesting

RESUMEN

Este estudio analiza el riesgo de mercado de una cartera de inversiones internacionales a través de una nueva propuesta metodológica en torno al valor en riesgo, usando la matriz de covarianza de modelos multivariados GARCH y la teoría de valores extremos, para ver si una estrategia de diversificación internacional minimiza el riesgo de mercado, así como para observar si la metodología VaR capta adecuadamente el riesgo de mercado, aplicando pruebas de validación. Con este fin, se consideraron doce índices bursátiles internacionales que representan aproximadamente el 62% de la capitalización bursátil mundial, eligiéndose el período entre las crisis Dot.com y financiera mundial. Los resultados muestran que la metodología propuesta puede ser utilizada para acomodar la alta turbulencia de los mercados, y que puede ser considerada como una herramienta válida en la gestión del riesgo de las carteras de inversión.

Palabras clave:
Mercados de valores; Valor en riesgo; Modelos multivariados GARCH; Teoría de los valores extremos; Backtesting

ABSTRACT

This study analyzed market risk of an international investment portfolio by means of a new methodological proposal based on Value-at-Risk, using the covariance matrix of multivariate GARCH-type models and the extreme value theory to realize if an international diversification strategy minimizes market risk, and to determine if the VaR methodology adequately captures market risk, by applying Backtesting tests. To this end, we considered twelve international stock indexes, accounting for about 62% of the world stock market capitalization, and chose the period from the Dot-Com crisis to the current global financial crisis. Results show that the proposed methodology is a good alternative to accommodate the high market turbulence and can be considered as an adequate portfolio risk management instrument.

Keywords:
Stock markets; Value at Risk; Multivariate GARCH models; Extreme value theory; Backtesting

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REFERÊNCIAS

ANDREEV, V. O. et al. An application of EVT, GPD and POT methods in the russian stock market (RTS index). Nov. 2009. Working Papers Series. Disponível em: <Disponível em: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1507678 >. Acesso em: 12 mar. 2013.
» http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1507678
ANGELIDIS, T.; BENOS, A.; DEGIANNAKIS, S. The use of GARCH models in VaR estimation. Statistical Methodology, [S. l.], v.1, n. 1-2, p. 105-128, Dec. 2004.
ASSAF, A. Extreme observations and risk assessment in the equity markets of MENA region: tail measures and Value-at-Risk. International Review of Financial Analysis, Amsterdam, v. 18, n. 3. p. 109-116, June 2009.
BEST, P. Implementing Value-at-Risk. Chichester: John Wiley & Sons, 1998.
BOLLERSLEV, T. Modeling the coherence in the short-run nominal exchange rates: a multivariate generalized ARCH model. Review of Economics and Statistics, Cambridge, v. 72, n. 3, p. 498-505, Aug. 1990.
BOLLERSLEV, T.; ENGLE, R. F.; WOOLDRIDGE, J. M. A capital asset pricing model with time-varying covariances. Journal of Political Economy, Chicago, v. 96, n. 1, p. 116-131, Feb. 1988.
CAMPBELL, S. D. A review of backtesting and backtesting procedures. 2005. Finance and Economics Discussion Series, Federal Reserve Board, Washington, D.C. Disponível em: <Disponível em: http://www.federalreserve.gov/pubs/feds/2005/200521/200521pap.pdf >. Acesso em: 12 mar. 2013.
» http://www.federalreserve.gov/pubs/feds/2005/200521/200521pap.pdf
CAPORIN, M.; MCALEER, M. Robust ranking of multivariate GARCH models by problem dimension. June, 2012. Kyoto University/KIER Working Papers 815.
CHRISTOFFERSEN, P. Elements of financial risk management. Amsterdam: Academic Press, 2003.
DANIELSSON, J.; DE VRIES, C. G. Value-at-Risk and extreme returns. 1997. Discussion Paper 273 LSE Financial Markets Group, London School of Economics.
EMBRECHTS, P.; KLUPPERLBERG, C.; MIKOSCH, T. Modelling extreme events for insurance and finance. Berlin, Germany: Springer, 1997.
ENGLE, R. F. Autoregressive conditional hetereoskedasticity with estimates of the variance of United Kingdom inflation. Econometrica, Oxford, v. 50, n. 4 p. 987-1007, July 1982.
ENGLE, R. F.; KRONER, K. F. Multivariate simultaneous generalised GARCH. Econometric Theory, Cambridge, v. 11, n. 1, p. 122-150, Mar. 1995.
ESCH, L.; KIEFFER, R.; LOPEZ, T. Asset and risk management: risk oriented finance. England: Wiley Finance, 2005.
FERREIRA, M. A.; LOPEZ, J. A. Evaluating interest rate covariance models within a Value-at-Risk framework. Journal of Financial Econometrics, Oxford, v. 3, n. 1, p. 126-168, Winter 2005.
GIOT, P.; LAURENT, S. Value-at-risk for long and short trading positions. Journal of Applied Econometrics, Chichester, v. 18, n. 6, p. 641-664, Nov./Dec. 2003.
HARRIS, R.; SOLLIS, R. Modelling and forecasting financial time series. New York: Wiley, 2003.
JORION, P. Value at risk: the new benchmark for managing financial risk. 3rd ed. United States: McGraw-Hill, 2007.
KUPIEC, P. H. Techniques for verifying the accuracy of risk management models. Journal of Derivatives, [S. l.], v. 3, n. 2, p. 73-84, Winter 1995.
LOPEZ, J. A.; WALTER, C. A. Evaluating covariance matrix forecasts in a value-at-risk framework. Journal of Risk, London, v.3, p. 69-98, Apr. 2001.
MANGANELLI, S.; ENGLE, R. F. Value at risk models in finance. Aug. 2001. European Central Bank, Working Paper Nº 75, p.1-40.
MARKOWITZ, H. Portfolio selection. Journal of Finance, Malden, v.7, n.1, p. 77-91, Mar. 1952.
MARIMOUTOU, V.; RAGGAD, B.; TRABELSI, A. Extreme value theory and Value at Risk: application to oil market. Energy Economics, Amsterdam, n. 31, p. 519-530, Feb. 2009.
MCNEIL, A. J. Calculating quantile risk measures for financial return series using extreme value theory. 1998. Department Mathematik, ETH Institutional Repository, Zentrum, Zurich.
MCNEIL, A. J. Extreme value theory for risk managers. Internal modelling and CAD II. London: Risk Books, 1999.
MCNEIL, A. J.; FREY, R. Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach. Journal of Empirical Finance, Amsterdam, v.7, n. 3-4, p. 271-300, Nov. 2000.
MORIMOTO, T.; KAWASAKI, Y. Empirical comparison of multivariate GARCH models for estimation of intraday Value at Risk. 2008. Disponível em: <Disponível em: http://dx.doi.org/ 10.2139/ssrn>. Acesso em: 02 maio 2013.
» http://dx.doi.org/ 10.2139/ssrn>.
NIGUEZ, T. M. Volatility and VaR forecasting in the Madrid Stock Exchange. Spanish Economic Review, Heidelberg, v. 10, p. 169-196, 2008.
REISS, R. D.; THOMAS, M. Statistical analysis of extreme values: with applications to insurance, finance, hydrology and other fields. Basel, Switzerland: Birkhauser-Verlag, 1997.
SCHERRER, W.; RIBARITS, E. On the parameterization of multivariate GARCH models. Econometric Theory, Cambridge, v. 23, n. 3, p.464-484, Jun. 2007.
SO, M. K. P.; YU, P. L. H. Empirical analysis of GARCH models in value at risk estimation. International Financial Markets, Institutions and Money, Binghamton; Amsterdam, v. 16, n. 2, p. 180-197, Apr. 2006.
TSAY, R. S. Analysis of financial time series. New Jersey: John Wiley & Sons, 2005.
WORLD BANK GROUP. c2014. Disponível em: <Disponível em: http://data.worldbank.org/indicator/CM.MKT.LCAP.CD >. Acesso em: 02 maio 2013.
» http://data.worldbank.org/indicator/CM.MKT.LCAP.CD
WU, P. T.; SHIEH, S. J. Value-at-Risk analysis for long-term interest rate futures: Fat-tail and long memory in return innovations. Journal of Empirical Finance, Amsterdam, v. 14, n. 2, p. 248-259, Mar. 2007.

2
Processo de avaliação: Double Blind Review

Datas de Publicação

Publicação nesta coleção
Apr-Jun 2014

Histórico

Recebido
19 Nov 2013
Aceito
22 Maio 2014

Este é um artigo publicado em acesso aberto sob uma licença Creative Commons

[1] ANDREEV, V. O. et al. An application of EVT, GPD and POT methods in the russian stock market (RTS index). Nov. 2009. Working Papers Series. Disponível em: <Disponível em: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1507678 >. Acesso em: 12 mar. 2013.
» http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1507678

[2] ANGELIDIS, T.; BENOS, A.; DEGIANNAKIS, S. The use of GARCH models in VaR estimation. Statistical Methodology, [S. l.], v.1, n. 1-2, p. 105-128, Dec. 2004.

[3] ASSAF, A. Extreme observations and risk assessment in the equity markets of MENA region: tail measures and Value-at-Risk. International Review of Financial Analysis, Amsterdam, v. 18, n. 3. p. 109-116, June 2009.

[4] BEST, P. Implementing Value-at-Risk. Chichester: John Wiley & Sons, 1998.

[5] BOLLERSLEV, T. Modeling the coherence in the short-run nominal exchange rates: a multivariate generalized ARCH model. Review of Economics and Statistics, Cambridge, v. 72, n. 3, p. 498-505, Aug. 1990.

[6] BOLLERSLEV, T.; ENGLE, R. F.; WOOLDRIDGE, J. M. A capital asset pricing model with time-varying covariances. Journal of Political Economy, Chicago, v. 96, n. 1, p. 116-131, Feb. 1988.

[7] CAMPBELL, S. D. A review of backtesting and backtesting procedures. 2005. Finance and Economics Discussion Series, Federal Reserve Board, Washington, D.C. Disponível em: <Disponível em: http://www.federalreserve.gov/pubs/feds/2005/200521/200521pap.pdf >. Acesso em: 12 mar. 2013.
» http://www.federalreserve.gov/pubs/feds/2005/200521/200521pap.pdf

[8] CAPORIN, M.; MCALEER, M. Robust ranking of multivariate GARCH models by problem dimension. June, 2012. Kyoto University/KIER Working Papers 815.

[9] CHRISTOFFERSEN, P. Elements of financial risk management. Amsterdam: Academic Press, 2003.

[10] DANIELSSON, J.; DE VRIES, C. G. Value-at-Risk and extreme returns. 1997. Discussion Paper 273 LSE Financial Markets Group, London School of Economics.

[11] EMBRECHTS, P.; KLUPPERLBERG, C.; MIKOSCH, T. Modelling extreme events for insurance and finance. Berlin, Germany: Springer, 1997.

[12] ENGLE, R. F. Autoregressive conditional hetereoskedasticity with estimates of the variance of United Kingdom inflation. Econometrica, Oxford, v. 50, n. 4 p. 987-1007, July 1982.

[13] ENGLE, R. F.; KRONER, K. F. Multivariate simultaneous generalised GARCH. Econometric Theory, Cambridge, v. 11, n. 1, p. 122-150, Mar. 1995.

[14] ESCH, L.; KIEFFER, R.; LOPEZ, T. Asset and risk management: risk oriented finance. England: Wiley Finance, 2005.

[15] FERREIRA, M. A.; LOPEZ, J. A. Evaluating interest rate covariance models within a Value-at-Risk framework. Journal of Financial Econometrics, Oxford, v. 3, n. 1, p. 126-168, Winter 2005.

[16] GIOT, P.; LAURENT, S. Value-at-risk for long and short trading positions. Journal of Applied Econometrics, Chichester, v. 18, n. 6, p. 641-664, Nov./Dec. 2003.

[17] HARRIS, R.; SOLLIS, R. Modelling and forecasting financial time series. New York: Wiley, 2003.

[18] JORION, P. Value at risk: the new benchmark for managing financial risk. 3rd ed. United States: McGraw-Hill, 2007.

[19] KUPIEC, P. H. Techniques for verifying the accuracy of risk management models. Journal of Derivatives, [S. l.], v. 3, n. 2, p. 73-84, Winter 1995.

[20] LOPEZ, J. A.; WALTER, C. A. Evaluating covariance matrix forecasts in a value-at-risk framework. Journal of Risk, London, v.3, p. 69-98, Apr. 2001.

[21] MANGANELLI, S.; ENGLE, R. F. Value at risk models in finance. Aug. 2001. European Central Bank, Working Paper Nº 75, p.1-40.

[22] MARKOWITZ, H. Portfolio selection. Journal of Finance, Malden, v.7, n.1, p. 77-91, Mar. 1952.

[23] MARIMOUTOU, V.; RAGGAD, B.; TRABELSI, A. Extreme value theory and Value at Risk: application to oil market. Energy Economics, Amsterdam, n. 31, p. 519-530, Feb. 2009.

[24] MCNEIL, A. J. Calculating quantile risk measures for financial return series using extreme value theory. 1998. Department Mathematik, ETH Institutional Repository, Zentrum, Zurich.

[25] MCNEIL, A. J. Extreme value theory for risk managers. Internal modelling and CAD II. London: Risk Books, 1999.

[26] MCNEIL, A. J.; FREY, R. Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach. Journal of Empirical Finance, Amsterdam, v.7, n. 3-4, p. 271-300, Nov. 2000.

[27] MORIMOTO, T.; KAWASAKI, Y. Empirical comparison of multivariate GARCH models for estimation of intraday Value at Risk. 2008. Disponível em: <Disponível em: http://dx.doi.org/ 10.2139/ssrn>. Acesso em: 02 maio 2013.
» http://dx.doi.org/ 10.2139/ssrn>.

[28] NIGUEZ, T. M. Volatility and VaR forecasting in the Madrid Stock Exchange. Spanish Economic Review, Heidelberg, v. 10, p. 169-196, 2008.

[29] REISS, R. D.; THOMAS, M. Statistical analysis of extreme values: with applications to insurance, finance, hydrology and other fields. Basel, Switzerland: Birkhauser-Verlag, 1997.

[30] SCHERRER, W.; RIBARITS, E. On the parameterization of multivariate GARCH models. Econometric Theory, Cambridge, v. 23, n. 3, p.464-484, Jun. 2007.

[31] SO, M. K. P.; YU, P. L. H. Empirical analysis of GARCH models in value at risk estimation. International Financial Markets, Institutions and Money, Binghamton; Amsterdam, v. 16, n. 2, p. 180-197, Apr. 2006.

[32] TSAY, R. S. Analysis of financial time series. New Jersey: John Wiley & Sons, 2005.

[33] WORLD BANK GROUP. c2014. Disponível em: <Disponível em: http://data.worldbank.org/indicator/CM.MKT.LCAP.CD >. Acesso em: 02 maio 2013.
» http://data.worldbank.org/indicator/CM.MKT.LCAP.CD

[34] WU, P. T.; SHIEH, S. J. Value-at-Risk analysis for long-term interest rate futures: Fat-tail and long memory in return innovations. Journal of Empirical Finance, Amsterdam, v. 14, n. 2, p. 248-259, Mar. 2007.

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