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

Received: 21 July 2017/Accepted: 3 May 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

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*Corresponding author; email: ruzanna415@gmail.com