Sains Malaysiana 48(7)(2019): 1547–1555

http://dx.doi.org/10.17576/jsm-2019-4807-24

Dependence Modeling and Portfolio Risk Estimation using GARCH-Copula Approach

(Pemodelan Kebersandaran dan Penganggaran Risiko Portfolio menggunakan Pendekatan GARCH-Copula)

RUZANNA AB RAZAK¹* & NORISZURA ISMAIL²

¹Faculty of Management, Multimedia University, 63100 Cyberjaya, Selangor Darul Ehsan, Malaysia

²Pusat Pemodelan dan Sains Data, Fakulti Sains dan Teknologi, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor Darul Ehsan, Malaysia

Diserahkan: 21 Julai 2017/Diterima: 3 Mei 2019

ABSTRACT

Past studies have shown that linear correlation measure may result in misleading interpretations and implications of dependency when financial variables are involved. The copula approach can be adopted as an alternative for measuring dependence as it provides the solution to fat tail problems in multivariate cases which arises from the probability of large or extreme co-movements. Due to limited studies on copulas using Islamic financial data, this study set outs to obtain a clear picture on the dependence between Islamic and conventional stock markets in Malaysia. Firstly, we model the dependence between Islamic and conventional returns data using the copula-ARMA-GARCH models with normal and non-normal error distributions, and secondly, we evaluate the portfolios of Islamic and conventional indices using recent risk measures. This paper shows that, by using the copula approach for measuring the dependency between two financial variables while maintaining their true nature as described by the ARMA-GARCH models, meaningful interpretation can be made about the association of the financial variables which reflects the real association between markets. Furthermore, this study proposes a set of procedures on how portfolio risks can be estimated using VaR based on the ARMA(p,q)-GARCH(1,1)-t-copula models including backtesting via simulation.

Keywords: Copula; GARCH; risk; stock returns

ABSTRAK

Kajian lepas telah menunjukkan ukuran korelasi linear mungkin boleh menghasilkan interpretasi dan implikasi yang mengelirukan tentang kebersandaran yang melibatkan pemboleh ubah kewangan. Kaedah copula boleh diguna sebagai alternatif untuk mengukur kebersandaran. Kaedah ini memberikan penyelesaian kepada masalah ekor tebal dalam kes multivariat yang muncul daripada pergerakan bersama yang ekstrim. Kajian ini dijalankan untuk mendapatkan gambaran yang jelas berkenaan kebersandaran antara pasaran saham islam dengan konvensional di Malaysia kerana kajian berkenaan kaedah copula ke atas data kewangan islam adalah terhad. Pertama, pemodelan kebersandaran dilakukan menggunakan kaedah copula-ARMA-GARCH dengan taburan ralat normal dan tidak normal. Kedua, portfolio risiko dianggar melalui ukuran risiko yang terkini. Kajian ini menunjukkan kaedah copula boleh mengukur kebersandaran dan mengekalkan ciri sebenar pulangan saham yang diwakili oleh model ARMA-GARCH, di samping memberikan interpretasi bermakna yang mencerminkan hubungan sebenar antara pasaran saham. Selain itu, kajian ini mencadangkan prosedur penganggaran risiko menggunakan kaedah VaR yang berdasarkan model ARMA(p,q)-GARCH(1,1)-t-copula, termasuklah pengujian belakang melalui pendekatan simulasi.

Kata kunci: Copula; GARCH; pulangan saham; risiko

RUJUKAN

Ab Razak, R. & Ismail, N. 2016. Portfolio risks of bivariate financial returns using copula-VaR approach: A case study on Malaysia and U.S. stock markets. Global Journal of Pure and Applied Mathematics 12(3): 1947-1964.

Ab Razak, R. & Ismail, N. 2015. The dependence of Islamic and conventional stocks: A copula approach. AIP Conference Proceeding 1678 060012: 1-5.

Albaity, M. & Ahmad, R. 2008. Performance of Syariah and composite indices: Evidence from Bursa Malaysia. Asian Academic of Management Journal of Accounting and Finance 4(1): 23-43.

Aloui, R., Ben Aïssa, M.S., Hammoudeh, S. & Nguyen, D.K. 2014. Dependence and extreme dependence of crude oil and natural gas prices with applications to risk management. Energy Economics 42: 332-342.

Genest, C., Rémillard, B. & Beaudoin, D. 2009. Goodness-of-fit tests for copulas: A review and a power study. Insurance: Mathematics and Economics 44(2): 199-213.

Ghalanos, A. 2015. Introduction to the rugarch package (Version 1.3-1). https://cran.r-project.org/web/packages/rugarch/ vignettes/Introduction_to_the_rugarch_package.pdf. Accessed on 27 January 2016.

Hammoudeh, S., Mensi, W., Reboredo, J.C. & Nguyen, D.K. 2014. Dynamic dependence of the global Islamic equity index with global conventional equity market indices and risk factors. Pasific-Basin Finance Journal 30: 189-206.

Heinen, A. & Valdesogo, A. 2012. Copula-based volatility models. In. Handbook of Volatility Models and Their Applications, edited by Bauwens, L., Hafner, C. & Laurent, S. New Jersey: John Wiley & Sons. pp. 293-316.

Jäschke, S. 2014. Estimation of risk measures in energy portfolios using modern copula techniques. Computational Statistics and Data Analysis 76: 359-376.

Melo Mendes, B.V.D. & Aíube, C. 2011. Copula based models for serial dependence. International Journal of Managerial Finance 7(1): 68-82.

Nelson, R.B. 2006. An Introduction to Copulas. New York: Springer.

Ning, C. 2010. Dependence structure between the equity market and the foreign exchange market - A copula approach. Journal of International Money and Finance 29: 743-759.

Posedel, P. 2005. Properties and estimation of GARCH (1,1) model. Metodološki Zvezki 2(2): 243-257.

Riddles, N. 2001. A portfolio manager’s view of downside risk. In. Managing Downside Risk in Financial Markets, edited by Sortino, F. & Satchell, S. Oxford: Butterworth-Heinemann Finance. pp. 74-92.

Righi, M.B. & Ceretta, P.S. 2013. Estimating non-linear serial and cross-interdependence between financial assets. Journal of Banking and Finance 37: 837-846.

Righi, M.B. & Ceretta, P.S. 2011. Modeling risk dependence with copulas in financial market: A Latin case. European Journal of Scientific Research 59(3): 295-306.

Ruppert, D. 2011. Statistics and Data Analysis for Financial Engineering. New York: Springer.

Shamiri, A., Hamzah, N.A. & Pirmoradian, A. 2011. Tail dependence estimate in financial market risk management: Clayton-Gumbel copula approach. Sains Malaysiana 40(8): 927-935.

Stoyanov, S.V., Rachev, S.T., Racheva-Yotova, B. & Fabozzi, F.J. 2011. Fat-tailed model for risk estimation. The Journal of Portfolio Management 37(2): 107-117.

*Pengarang untuk surat-menyurat; email: ruzanna415@gmail.com