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Portfolio optimization from a Copulas-GJR-GARCH-EVT-CVAR model: Empirical evidence from ASEAN stock indexes

1 Faculty of Finance, Banking University of Ho Chi Minh City, Vietnam
2 School of Banking, University of Economics Ho Chi Minh City, Vietnam

This study employs several methods to simulate and construct the portfolio from stock indexes of the six Association of Southeast Asian Nations (ASEAN) markets during the period from January 2001 to December 2017, namely, time-varying Copulas; Glosten, Jagannathan and Runkle (GJR); generalised autoregressive conditional heteroskedasticity (GARCH); extreme value theory (EVT); and conditional value at risk (CVaR). Our target is minimising the risk based on CVaR, then achieving the maximal expected return for investors. Our model also sheds further light on the role of the dependence structure among stock indexes by employing elliptical (student t) Copulas, which are incorporated for simulating the optimal portfolios. Our findings suggest that the investor should invest in the optimal portfolio, which lies in the efficiency curve. Hence, the optimal portfolio has similar time-varying characteristics across the dependence of Copulas, as well as confidence levels. The research implications can be employed practically by portfolio managers and individual investors who desire to invest in ASEAN equity markets. Therefore, our findings can draw investors' attention to constructing the portfolio with the dependence level via time-varying Copulas and minimise the risk represented by CVaR rather than traditional variance.
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Keywords GARCH models; GJR; EVT; Copulas models; CVaR; portfolio optimization

Citation: Sang Phu Nguyen, Toan Luu Duc Huynh. Portfolio optimization from a Copulas-GJR-GARCH-EVT-CVAR model: Empirical evidence from ASEAN stock indexes. Quantitative Finance and Economics, 2019, 3(3): 562-585. doi: 10.3934/QFE.2019.3.562


  • 1. Acerbi C, Tasche D (2002) On the coherence of expected shortfall. J Bank Financ 26:1487-1503.    
  • 2. Awartani BM, Corradi V (2005) Predicting the volatility of the S&P-500 stock index via GARCH models:the role of asymmetries. Int J Forecasting 21:167-183.    
  • 3. Baele L, Inghelbrecht K (2009) Time-varying integration and international diversification strategies. J Empir Financ 16:368-387.    
  • 4. Bassi F, Embrechts P, Kafetzaki M (1998) Risk management and quantile estimation. A practical guide to heavy tails, 111-130.
  • 5. Barone Adesi G (2016) VaR and CVaR implied in option prices. J Risk Financ Manage 9:2.    
  • 6. Baur DG (2013) The structure and degree of dependence:A quantile regression approach. J Bank Financ 37:786-798.    
  • 7. Black F (1976) The pricing of commodity contracts. J Financ Econ 3:167-179.    
  • 8. Burdekin RC, Hughson E, Gu J (2018) A first look at Brexit and global equity markets. Appl Econ Lett 25:136-140.    
  • 9. Burggraf T (2019) Risk-Based Portfolio Optimization in the Cryptocurrency World. Working papers.
  • 10. Bollerslev T (1986) Generalized autoregressive conditional heteroskedasticity. J Econometrics 31:307-327.    
  • 11. Brownlees CT, Engle RF, Kelly BT (2011) A practical guide to volatility forecasting through calm and storm. Available at SSRN 1502915.
  • 12. Cerrato M, Crosby J, Kim M, et al.(2015) Modeling Dependence Structure and Forecasting Market Risk with Dynamic Asymmetric Copula. Available from:https://ssrn.com/abstract=2460168.
  • 13. Chuang CC, Wang YH, Yeh TJ, et al. (2014) Backtesting VaR in consideration of the higher moments of the distribution for minimum-variance hedging portfolios. Econ Model 42:15-19.    
  • 14. Chung PJ, Liu DJ (1994) Common stochastic trends in Pacific Rim stock markets. Q Rev Econ Financ 34:241-259.    
  • 15. Christoffersen PF (1998) Evaluating interval forecasts. Int Econ Rev 39:841-862.    
  • 16. Click RW, Plummer MG (2005) Stock market integration in ASEAN after the Asian financial crisis. J Asian Econ 16:5-28.    
  • 17. Choe KI, Choi P, Nam K, et al. (2012) Testing financial contagion on heteroskedastic asset returns in time-varying conditional correlation. Pac-Basin Financ J 20:271-291.    
  • 18. Christie AA (1982) The stochastic behavior of common stock variances:Value, leverage and interest rate effects. J Financ Econ 10:407-432.    
  • 19. Coles S, Bawa J, Trenner L, et al. (2001) An introduction to statistical modeling of extreme values, Springer.
  • 20. Danielsson J, De Vries CG (2000) Value-at-risk and extreme returns. Annales d'Economie et de Statistique, 239-270.
  • 21. Deng L, Ma C, Yang W (2011) Portfolio optimization via pair copula-GARCH-EVT-CVaR model. Syst Engineering Procedia 2:171-181.    
  • 22. DeFusco RA, Geppert JM, Tsetsekos GP (1996) Long-run diversification potential in emerging stock markets. Financ Rev 31:343-363.    
  • 23. Desierto DA (2017) ASEAN Investment Treaties, RCEP, and CPTPP:Regional Strategies, Norms, Institutions, and Politics. Pac Rim L Pol'y J 27:349.
  • 24. Emamverdi G (2018) Studying the effects of Using GARCH-EVT-Copula Method to Estimate Value-at-Risk of Portfolio.Iran J Financ 2:93-119.
  • 25. Embrechts P, Höing A, Juri A (2003) Using Copulae to Bound the Value-at-Risk for Functions of Dependent Risks. Financ Stochastics 7:145-167.    
  • 26. Embrechts P, Frey R, McNeil A (2005) Quantitative risk management, Princeton Series in Finance, Princeton 10.
  • 27. Errunza V, Losq E, Padmanabhan P (1992) Tests of integration, mild segmentation and segmentation hypotheses. J Bank Financ16:949-972.
  • 28. Engle R (2002) Dynamic conditional correlation:A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. J Bus Econ Stat 20:339-350.    
  • 29. Fercoq O, Richtárik P (2015) Accelerated, parallel, and proximal coordinate descent.SIAM J Optim 25:1997-2023.    
  • 30. Fernandez V (2008a) Copula-based measures of dependence structure in assets returns. Phys A 387:3615-3628.
  • 31. Fernandez V (2008b) Multi-period hedge ratios for a multi-asset portfolio when accounting for returns co-movement. J Futures Mark 28:182-207.
  • 32. French KR, Schwert GW, Stambaugh RF (1987) Expected stock returns and volatility. J Finance Econ 19:3-29.    
  • 33. Geman H, Kharoubi C (2008) WTI crude oil futures in portfolio diversification:The time-to-maturity effect. J Bank Financ 32:2553-2559.    
  • 34. Gilli M, Këllezi E, Hysi H (2006) A data-driven optimization heuristic for downside risk minimization. Swiss Finance Institute Research Paper.
  • 35. Glosten LR, Jagannathan R, Runkle DE (1993) On the relation between the expected value and the volatility of the nominal excess return on stocks. J Financ 48:1779-1801.    
  • 36. Goodell JW (2018) Comparing normative institutionalism with intended rationality in cultural-finance research. Int Rev Financ Anal.
  • 37. Gneiting T (2011) Making and evaluating point forecasts. J Am Stat Assoc 106:746-762.    
  • 38. Hansen BE (1994) Autoregressive conditional density estimation. Int Econ Rev,705-730.
  • 39. Higgins ML, Bera AK (1992) A class of nonlinear ARCH models. Int Econ Rev, 137-158.
  • 40. Holton GA (2003) Value-at-risk, Academic Press.
  • 41. Huang CW, Hsu CP (2015) Portfolio Optimization with GARCH-EVT-Copula-CVaR Models. Bank Financ Rev 7.
  • 42. Huynh TLD, Nguyen SP, Duong D (2018) Contagion risk measured by return among cryptocurrencies, In International Econometric Conference of Vietnam,Springer, Cham, 987-998.
  • 43. Impavido G, Musalem AR, Tressel T (2002) Contractual savings institutions and banks' stability and efficiency, The World Bank.
  • 44. Jin X, Lehnert T (2018) Large portfolio risk management and optimal portfolio allocation with dynamic elliptical copulas. Dependence Model 6:19-46.    
  • 45. Joe H (1997) Multivariate models and dependence concepts, London:Chapman and Hall.
  • 46. Jondeau E, Rockinger M (2003) Conditional volatility, skewness, and kurtosis:existence, persistence, and comovements.J Econ Dyn Control 27:1699-1737.    
  • 47. Kaura V (2005) Portfolio optimization using value at risk, Imperial College London, London.
  • 48. Kotz S, Shanbhag D (1980) Some new approaches to probability distributions. Advances Appl Probability 12:903-921.    
  • 49. Laurent S, Rombouts JV, Violante F (2012) On the forecasting accuracy of multivariate GARCH models. J Appl Econometrics 27:934-955.    
  • 50. Lerche I, Mudford BS (2005) How many Monte Carlo simulations does one need to do?. Energy Explor Exploit 23:405-427.    
  • 51. Liu HH, Wang TK, Li W (2019) Dynamical Volatility and Correlation among US Stock and Treasury Bond Cash and Futures Markets in Presence of Financial Crisis:A Copula Approach. Res Int Bus Financ 48:381-396.    
  • 52. Luu Duc Huynh T (2019) Spillover Risks on Cryptocurrency Markets:A Look from VAR-SVAR Granger Causality and Student'st Copulas. J Risk Financ Manage 12:52.    
  • 53. Morgan JP (1995) RiskMetrics-Technical Document, 3rd edition, Morgan Guaranty Trust Company, New York.
  • 54. Markowitz H (1952) Portfolio selection. J Financ 7:77-91.
  • 55. 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.    
  • 56. Miller MH, Scholes M (1972) Rates of return in relation to risk:A reexamination of some recent findings. Stud Theory Capital Mark 23.
  • 57. Morgan JP (1996) Risk Metrics-Technical Document, 4th edition. J.P. Morgan, New York
  • 58. Monfared SA, Enke D (2014) Volatility forecasting using a hybrid GJR-GARCH neural network model. Procedia Comput Sci 36:246-253.    
  • 59. Mercereau B (2005) FDI Flows to Asia:Did the Dragon crowd out the Tigers?, International Monetary Fund.
  • 60. Nasir MA, Huynh TLD, Nguyen SP, et al. (2019) Forecasting cryptocurrency returns and volume using search engines. Financ Innovation 5:2.    
  • 61. Nelson DB (1991) Conditional heteroskedasticity in asset returns:A new approach. Econometrica:J Econometric Society, 347-370.
  • 62. Nelson RB (1998) An introduction to copula, New York:Springer.
  • 63. Onour IA (2010) Analysis of portfolio diversifications efficiency in emerging African stock markets. Int Res J Financ Econ 40:30-37.
  • 64. Patton AJ (2001) Modelling time-varying exchange rate dependence using the conditional copula.
  • 65. Patton AJ (2004) On the out-of-sample importance of skewness and asymmetric dependence for asset allocation. J Financ Econometrics 2:130-168.    
  • 66. Patton AJ (2006) Modelling asymmetric exchange rate dependence. Int Econ Rev 47:527-556.    
  • 67. Platen E (2006) A benchmark approach to finance. Math Financ An Int J Math Stat Financ Econ 16:131-151.
  • 68. Rigg J, Salamanca A (2009) Managing risk and vulnerability in Asia:A (re) study from Thailand, 1982-83 and 2008. Asia Pacific Viewpoint 50:255-270.    
  • 69. Rodriguez JC (2007) Measuring financial contagion:A copula approach. J Empir Financ 14:401-423.    
  • 70. Rockafellar RT, Uryasev S (2000a) Optimization of conditional value-at-risk. J Risk 2:21-42.
  • 71. Rockafellar RT, Uryasev S (2002) Conditional value-at-risk for general loss distributions. J Bank Financ 26:1443-1471.    
  • 72. Sabino da Silva, Fernando AB, Ziegelmann Flavio A (2017) Robust Portfolio Optimization with Multivariate Copulas:a Worst-Case CVaR approach.
  • 73. Sampid MG, Hasim HM, Dai H (2018) Refining Value-at-Risk estimates using a Bayesian Markov-switching GJR-GARCH Copula-EVT model. PLoS ONE 13:e0198753.    
  • 74. Singvejsakul J, Chaiboonsri C, Sriboonchitta S (2019) The Dependence Structure and Portfolio Optimization in Economic Cycles:An Application in ASEAN Stock Market, In International Symposium on Integrated Uncertainty in Knowledge Modelling and Decision Making, Springer, Cham, 161-171.
  • 75. Sklar A (1959) Fonctions de repartition an dimensions et leurs marges. Paris:Publications de l'lnstitut de statistique de l'Universite de Paris.
  • 76. Taylor SJ (1986) Modeling Financial Time Series, Chichester, UK:John Wiley and Sons.
  • 77. Wang ZR, Chen XH, Jin YB, et al. (2010) Estimating risk of foreign exchange portfolio:Using VaR and CVaR based on GARCH-EVT-Copula model. Phys A 389:4918-4928.    
  • 78. Wu Z, Chen M, Ye W, et al. (2006) Risk analysis of portfolio by Copula-GARCH. J Syst Engineering Theory Practice 2:45-52.
  • 79. Zakoian JM (1994) Threshold heteroskedastic models. J Econ Dyn Control 18:931-955.    
  • 80. Zhang N, Kang C, Xia Q, et al. (2014) Modeling conditional forecast error for wind power in generation scheduling. IEEE Tran Power Syst 29:1316-1324.    
  • 81. Zhang H, Zhou L, Ming S, et al. (2015) Empirical Research on VAR Model Based on GJR-GARCH, EVT and Copula. Sci J Appl Math Stat 3:136-143.    
  • 82. Ziegel JF (2016) Coherence and elicitability. Math Financ 26:901-918.    


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