Dependence Analysis of the ISE100 Banking Sector Using Vine CopulaBükre Yıldırım Külekci, Gülden Poyraz, İsmail Gür, Ozan Evkaya
The frequently observed time-varying trends and dependence in recent years within financial markets have been essential for modeling and pricing. This study aims to analyze the dependence structure of banking sector stocks traded on the ISE100 index using time series and regular vine (R-vine) copula models. The study calculates the risk measures of value-at-risk (VaR) and expected shortfall (ES) and tests with backtesting methods for the portfolio that are constructed by equally weighting the banking stocks. This study’s findings on banking stocks specifically indicate that the application of the R-vine copula combined with the generalized auto-regressive conditional heteroskedasticity (GARCH) model improved the VaR and ES estimates compared to traditional GARCH-based approaches..
BIST100 Bankacılık Sektöründeki Bağımlılığın Asma Kopula ile İncelenmesiBükre Yıldırım Külekci, Gülden Poyraz, İsmail Gür, Ozan Evkaya
Son yıllarda sıklıkla gözlemlenen finansal piyasalar arasındaki bağımlılık ve zamana bağlı görülen değişim, modelleme ve fiyatlama açısından önem taşımaktadır. Bu çalışmada, BIST100’de işlem gören bankacılık sektörüne ait hisselerin arasındaki bağımlılık yapısının, zaman serileri ve kurallı asma (R-Vine) kopula modeli ile incelenmesi amaçlanmaktadır. Bankacılık hisselerinden eşit ağırlıklandırılarak oluşturulan portföy için, riske maruz değer (VaR) ve beklenen kayıp (ES) risk ölçütleri hesaplanmış ve geriye dönük yöntemlerle test edilmiştir. Türkiye bankacılık hisseleri özelinde yapılan bu çalışmada, GARCH ve kurallı asma kopula modellerinin birlikte uygulanmasının, geleneksel GARCH tabanlı yaklaşımlara kıyasla VaR ve ES risk ölçütü tahminlerini iyileştirdiğine dair bulgular elde edilmiştir.
Banks operating in Türkiye and traded in the ISE100 banking sector can be classified into three subsections: State banks owned by the country, private banks established by local holdings, and foreign banks that carry out their oversea activities in the country. Although they have different purposes, they are mostly affected by the same events at the same time. Each element in the banking system, especially banks themselves, cannot act individually and are affected alltogether by current economic and political factors. Therefore, one cannot expect these banking stocks that are traded in the stock market to behave independently. In addition to this, the decisions regulators and bank supervisors make regarding certain economic circumstances may also cause some simultaneous effects. Historically, the entire banking sector has been seen to contract and expand in some cases. Each stock price change can cause another related stock price to increase or decrease. In particular, sectors where a strong dependence exists, such as banking experience these co-movements more intensely.
Given the capital importance the banking sector holds in the Turkish economy, investigating the interdependence of these assets can help one better interpret these stocks both in regard to individual behaviors as well as to an integrated market setup. One can extract valuable information for this purpose using the flexibility of the vine copula approach that has been added to commonly used time series models. The underlying motivation for favoring the vine copula model over the high-dimensional copula model is to be able to consider the multivariate dependence within an unconfined approach. Due to high-dimensional copulas presenting a computational challenge, vines are more comprehensive and flexible in examining the dependency risk dynamics of portfolios under high-risk market conditions.
In this respect, the contributions of this study are twofold: First, it models the time-varying dependence structure of the 11 banking sector stocks that were traded on the ISE100 from 1/3/2018 to 9/222022, by integrating a combined generalized auto-regressive conditional heteroskedasticity (GARCH) and regular vine (R-vine) copula model. Second, the study estimates the value-at-risk (VaR) and expected shortfall (ES) risk measures of the 11-dimensional equally-weighted portfolio using a 250-day rolling window approach based on this dependence structure. An equally-weighted portfolio approach allows one to track the dependence structure, as well as to observe and measure the changes in the portfolio based on differences in dependence. This study compares the results of the proposed model with the traditional GARCH-based portfolio risk measures, providing evidence that the proposed R-vine copula-based GARCH (VGARCH) model improves the price estimations. With regard to the calculated risk measures (VaR and ES), the VGARCH model with Student’s t innovations outperforms the classical GARCH model’s results at a 95% significance level.
The results show that, while banks with a high market capitalization generally exhibit a symmetrical tail dependence (YKBNK, AKBNK, and GARAN stock listings), banks with relatively small market capitalization tend to have lower-tail dependence (ALBRK, SKBNK, TSKB, and ICBCT stock listings). The tree structure of the R-vine copula model indicates the ISCTR and VAKBN stocks to be the most interconnected central nodes. This indicates that these may be the two most important financial institutions that need to be focused on in order to achieve a faster recovery in times of financial stress. Based on the application, the survival Gumbel copula, which appears in maximum numbers, clearly also plays an important role in the dependency structure of the banking sector stocks. The prevalence of the survival Gumbel copula in the banking sector can be interpreted as a sign of the high probability that unfavorable events become extreme and easily transform into systemic risk. These results provide important implications regarding financial institutions’ economic decisions, capital regulations, the governtment’s arrangement of legislation and regulations, supervisory agencies, and investors’ risk-management decisions in the financial market.