An application of Regular Vine copula in portfolio risk forecasting: evidence from Istanbul stock exchange

Cemile Özgür; Vedat Sarıkovanlık; Cemile Özgür; Vedat Sarıkovanlık

doi:10.3934/QFE.2021020

Quantitative Finance and Economics

2021, Volume 5, Issue 3: 452-470. doi: 10.3934/QFE.2021020

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Research article

An application of Regular Vine copula in portfolio risk forecasting: evidence from Istanbul stock exchange

Cemile Özgür ^,,
Vedat Sarıkovanlık

School of Business, Department of Finance, Istanbul University, Istanbul, Turkey

Received: 17 February 2021 Accepted: 25 May 2021 Published: 02 June 2021
JEL Codes: C13, C15, C52, G17

In times of financial turbulence, it is a well-documented fact that the co-movement of financial returns tends to increase leading to unexpected portfolio losses. The magnitude of the losses can severely be underestimated when the characteristics of univariate return series and the dependence structure between the returns are not represented well by a risk forecasting model. From a growing literature on the available multivariate modelling tools, this paper aims to investigate daily portfolio Value at Risk and Expected Shortfall forecasting performance of elliptical as well as Regular Vine copulas. For this purpose, return series of twelve stocks that are listed in Istanbul Stock Exchange are obtained for the period of June 2010 to December 2018. The series are modelled with univariate Generalized Auto-Regressive Conditional Heteroskedasticity models with Normal and Student's t innovations. Equally weighted portfolio returns are forecasted depending on the univariate GARCH marginals and their multivariate dependence structure. Estimated daily portfolio Value at Risk and Expected Shortfall values with varying levels are compared with the traditional Variance-Covariance and Dynamic Conditional Correlation Multivariate GARCH model estimates. While the models performed well at the Value at Risk backtests, according to the applied ES backtests R-vine copula GARCH found better at yielding more accurate Expected Shortfall forecasts.
- copula theory,
- Regular Vine copula,
- value at risk,
- expected shortfall,
- risk management
Citation: Cemile Özgür, Vedat Sarıkovanlık. An application of Regular Vine copula in portfolio risk forecasting: evidence from Istanbul stock exchange[J]. Quantitative Finance and Economics, 2021, 5(3): 452-470. doi: 10.3934/QFE.2021020

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Abstract

In times of financial turbulence, it is a well-documented fact that the co-movement of financial returns tends to increase leading to unexpected portfolio losses. The magnitude of the losses can severely be underestimated when the characteristics of univariate return series and the dependence structure between the returns are not represented well by a risk forecasting model. From a growing literature on the available multivariate modelling tools, this paper aims to investigate daily portfolio Value at Risk and Expected Shortfall forecasting performance of elliptical as well as Regular Vine copulas. For this purpose, return series of twelve stocks that are listed in Istanbul Stock Exchange are obtained for the period of June 2010 to December 2018. The series are modelled with univariate Generalized Auto-Regressive Conditional Heteroskedasticity models with Normal and Student's t innovations. Equally weighted portfolio returns are forecasted depending on the univariate GARCH marginals and their multivariate dependence structure. Estimated daily portfolio Value at Risk and Expected Shortfall values with varying levels are compared with the traditional Variance-Covariance and Dynamic Conditional Correlation Multivariate GARCH model estimates. While the models performed well at the Value at Risk backtests, according to the applied ES backtests R-vine copula GARCH found better at yielding more accurate Expected Shortfall forecasts.

References

[1]	Aas K (2016) Pair-Copula Constructions for Financial Applications: A Review. Econometrics 4: 43. doi: 10.3390/econometrics4040043
[2]	Aas K, Berg D (2009) Models for construction of multivariate dependence-a comparison study. Eur J Financ 15: 639–659. doi: 10.1080/13518470802588767
[3]	Aas K, Czado C, Frigessi A, et al. (2009) Pair-copula constructions of multiple dependence. Insur Math Econ 44: 182–198. doi: 10.1016/j.insmatheco.2007.02.001
[4]	Acar EF, Czado C, Lysy M (2019) Flexible dynamic vine copula models for multivariate time series data. Econ Stat 12: 181–197.
[5]	Acerbi C, Tasche D (2002) On the coherence of expected shortfall. J Bank Financ 26: 1487–1503. doi: 10.1016/S0378-4266(02)00283-2
[6]	Allen D, McAleer M, Singh A (2017) Risk Measurement and Risk Modelling Using Applications of Vine Copulas. Sustainability 9: 1762. doi: 10.3390/su9101762
[7]	Allevi E, Boffino L, De Giuli ME, et al. (2019) Analysis of long-term natural gas contracts with vine copulas in optimization portfolio problems. Ann Oper Res 274: 1–37. doi: 10.1007/s10479-018-2932-x
[8]	Ang A, Chen J (2002) Asymmetric correlations of equity portfolios. J Financ Econ 63: 443–494. doi: 10.1016/S0304-405X(02)00068-5
[9]	Artzner P, Delbaen F, Eber JM, et al. (1999) Coherent Measures of Risk. Math Financ 9: 203–228. doi: 10.1111/1467-9965.00068
[10]	Bedford T, Cooke RM (2001) Probability Density Decomposition for Conditionally Dependent Random Variables Modeled by Vines. Ann Math Artif Intell 32: 245–268. doi: 10.1023/A:1016725902970
[11]	Bedford T, Cooke RM (2002) Vines: A New Graphical Model for Dependent Random Variables. Ann Stat 30: 1031–1068. doi: 10.1214/aos/1031689016
[12]	Boako G, Tiwari AK, Roubaud D (2019) Vine copula-based dependence and portfolio value-at-risk analysis of the cryptocurrency market. Int Econ 158: 77–90. doi: 10.1016/j.inteco.2019.03.002
[13]	Bollerslev T (1986) Generalized Autoregressive Conditional Heteroskedasticity. J Econ 31: 307–327. doi: 10.1016/0304-4076(86)90063-1
[14]	Brechmann EC, Hendrich K, Czado C (2013) Conditional copula simulation for systemic risk stress testing. Insur Math Econ 53: 722–732. doi: 10.1016/j.insmatheco.2013.09.009
[15]	Carnero MA, Peña D, Ruiz E (2012) Estimating GARCH volatility in the presence of outliers. Econ Lett 114: 86–90. doi: 10.1016/j.econlet.2011.09.023
[16]	Cherubini U, Luciano E (2001) Value-at-risk Trade-off and Capital Allocation with Copulas. Econ Notes 30: 235–256. doi: 10.1111/j.0391-5026.2001.00055.x
[17]	Christoffersen PF (1998) Evaluating Interval Forecasts. Int Econ Rev 39: 841. doi: 10.2307/2527341
[18]	Czado C (2010) Pair-Copula Constructions of Multivariate Copulas, In: Jaworski P, Durante F, Härdle W, and Rychlik T, editors, Copula Theory and Its Applications, Lecture Notes in Statistics, Springer, Berlin, Heidelberg, 198: 93–109.
[19]	Dickey DA, Fuller WA (1979) Distribution of the Estimators for Autoregressive Time Series With a Unit Root. J Am Stat Assoc 74: 427–431.
[20]	Dißmann J, Brechmann E, Czado C, et al. (2013) Selecting and estimating regular vine copulae and application to financial returns. Comput Stat Data Anal 59: 52–69. doi: 10.1016/j.csda.2012.08.010
[21]	Embrechts P, Kaufmann R, Patie P (2005) Strategic long-term financial risks: Single risk factors. Comput Optim Appl 32: 61–90. doi: 10.1007/s10589-005-2054-7
[22]	Embrechts P, McNeil A, Straumann D (2002) Correlation and Dependence in Risk Management: Properties and Pitfalls, In: Dempster MAH, editor, Risk Management: Value at Risk and Beyond, chapter 7, Cambridge University Press, Cambridge, 176–223.
[23]	Engle R (1982) Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica 50: 987. doi: 10.2307/1912773
[24]	Engle R (1984) Chapter 13 Wald, likelihood ratio, and Lagrange multiplier tests in econometrics, In: Handbook of Econometrics, North Holland, 2: 775–826.
[25]	Engle R (2002) Dynamic Conditional Correlation. J Bus Econ Stat 20: 339–350. doi: 10.1198/073500102288618487
[26]	Ghalanos A (2020) rugarch: Univariate GARCH models. R package version 1.4-4.
[27]	Hofert M, Kojadinovic I, Maechler M, et al. (2020) copula: Multivariate Dependence with Copulas. R package version 1.0-0.
[28]	Hung NT (2019) Interdependence of oil prices and exchange rates: Evidence from copula-based GARCH model. AIMS Energy 7: 465–482. doi: 10.3934/energy.2019.4.465
[29]	Joe H (1996) Families of m-Variate Distributions with Given Margins and m(m-1)/2 Bivariate Dependence Parameters. Lecture Notes-Monograph Series 28: 120–141.
[30]	Joe H (1997) Multivariate Models and Dependence Concepts, Chapman & Hall, London.
[31]	Jorion P (2000) Value at Risk: The New Benchmark for Managing Financial Risk, McGraw-Hill, New York.
[32]	Kupiec P (1995) Techniques for Verifying the Accuracy of Risk Measurement Models. J Deriv 3.
[33]	Kurowicka D, Cooke RM (2006) Uncertainty Analysis with High Dimensional Dependence Modelling, John Wiley & Sons, Chichester, UK.
[34]	Li DX (2000) On Default Correlation. J Fixed Income 9: 43–54. doi: 10.3905/jfi.2000.319253
[35]	Ljung GM, Box GEP (1978) On a measure of lack of fit in time series models. Biometrika 65: 297–303. doi: 10.1093/biomet/65.2.297
[36]	McNeil AJ, Frey R (2000) Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach. J Empir Financ 7: 271–300. doi: 10.1016/S0927-5398(00)00012-8
[37]	Messaoud SB, Aloui C (2015) Measuring Risk of Portfolio : GARCH-Copula Model. J Econ Integr 30: 172–205. doi: 10.11130/jei.2015.30.1.172
[38]	Müller FM, Righi MB (2018) Numerical comparison of multivariate models to forecasting risk measures. Risk Manage 20: 29–50. doi: 10.1057/s41283-017-0026-8
[39]	Nagler T, Bumann C, Czado C (2019a) Model selection in sparse high-dimensional vine copula models with an application to portfolio risk. J Multivar Anal 172: 180–192. doi: 10.1016/j.jmva.2019.03.004
[40]	Nagler T, Schepsmeier U, Stoeber J, et al. (2019b) VineCopula: Statistical Inference of Vine Copulas. R package version 2.3.0.
[41]	Nelsen RB (2006) An Introduction to Copulas, Springer-Verlag, New York.
[42]	Nikoloulopoulos AK, Joe H, Li H (2012) Vine copulas with asymmetric tail dependence and applications to financial return data. Comput Stat Data Anal 56: 3659–3673. doi: 10.1016/j.csda.2010.07.016
[43]	Patton AJ (2001) Modelling Time-Varying Exchange Rate Dependence using the Conditional Copula. SSRN Electron J.
[44]	Patton AJ (2012) A review of copula models for economic time series. J Multivar Anal 110: 4–18. doi: 10.1016/j.jmva.2012.02.021
[45]	R Core Team (2019). R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria.
[46]	Righi MB, Ceretta PS (2012) Predicting the risk of global portfolios considering the non-linear dependence structures. Econ Bull 32: 282–294.
[47]	Rockinger MM, Jondeau E (2001) Conditional Dependency of Financial Series: An Application of Copulas. SSRN Electron J.
[48]	Ruppert D, Matteson DS (2015) Statistics and Data Analysis for Financial Engineering, Springer Texts in Statistics, Springer New York, New York, NY.
[49]	Sklar A (1959) Fonctions de Répartition À N Dimensions et Leurs Marges. Publ Inst Stat Univ Paris 8: 229–231.
[50]	Tofoli PV, Ziegelmann FA, Candido O, et al. (2019) Dynamic D-Vine Copula Model with Applications to Value-at-Risk (VaR). J Time Ser Econ 11.
[51]	Vaz de Melo Mendes B, Mendes Semeraro M, P Câmara Leal R (2010) Pair-copulas modeling in finance. Financ Mark Portf Manag 24: 193–213. doi: 10.1007/s11408-010-0130-1
[52]	Weiß GNF, Scheffer M (2015) Mixture pair-copula-constructions. J Bank Financ 54: 175–191. doi: 10.1016/j.jbankfin.2015.01.008
[53]	Zhang B, Wei Y, Yu J, et al. (2014) Forecasting VaR and ES of stock index portfolio: A Vine copula method. Phys A 416: 112–124. doi: 10.1016/j.physa.2014.08.043

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