Beta Risklerinin Modellenmesi ve Tahmini: Türkiye’deki Döviz Portföyü Örneği

Öz

Bu araştırmada, Türkiye’deki döviz yatırımcılarının oluşturacakları döviz portföylerini modellenmesi ve gelecek tahminin yapılması amaçlanmıştır. Bu amaç doğrultusunda, temel model olarak Sermaye Varlıkları Fiyatlandırma Modeli (SVFM) ile tutarlı ve durağan beta riskine olanak sağlayan Doğrusal Piyasa Modeli (DPM) kullanılmıştır. DPM’nin modellenmesi için En Küçük Kareler (EKK) yöntemi kullanılmıştır. İkinci model olarak ise Koşullu Sermaye Varlıkları Fiyatlandırma Modeli (K-SVFM) ile tutarlı ve zamana bağlı değişen (time-varying) beta riskine olanak sağlayan Zamana bağlı değişen Doğrusal Piyasa Modeli (Z-DPM) kullanılmıştır. Z-DPM’nin modellenmesi için tek değişkenli (GARCH) ve çok değişkenli (DCC-GARCH) GARCH-tipi modeller ve durum uzayı formundaki Kalman filtresi algoritması (KFMR) kullanılmıştır. Türkiye Cumhuriyet Merkez Bankası (TCMB)’nda gösterge niteliğindeki efektif alış-satışa konu olan 9 ülkenin son 15 yıllık dönemine ait, haftalık döviz kurlarının Türk Lirası (TL) cinsinden fiyatları ve bu fiyatlardan eşit ağırlıklı olarak oluşturulan sepet kur, araştırma verisi olarak kullanılmıştır. Araştırma verisinin modellenmesi ve bir yıllık gelecek tahmini aşamasında DPM ve Z-DPM’nin performansları karşılaştırılmıştır. Bulgulara göre, Z-DPM’nin KFMR ile modellenmesi durumunda, döviz kurlarının modellenmesi ve gelecek tahmini konusunda diğer modellere kıyasla çok daha iyi performans gösterdiği; buna karşın Z-DPM’nin GARCH ve DCC-GARCH ile modellenmesi durumunda EKK’ye göre yetersiz kaldığı görülmüştür. Döviz kurlarına ait beta risklerinin durağan olmadığı temel sonucuna ulaşılmıştır.

Anahtar Kelimeler

• Beta Riski
• DCC-GARCH
• GARCH
• Kalman Filtresi
• Sermaye Varlıkları Fiyatlandırma Modeli (SVFM)

Modeling and Forecasting of Beta Risks: The Case of Foreign Currency Portfolio in Turkey

Öz

In this study, it is aimed to perform the modeling and future estimation of the foreign currency portfolios to be established by the foreign currency investors in Turkey. For this purpose, as the benchmark model, Linear Market Model (LMM) is used which is consistent with the Capital Asset Pricing Model (CAPM) and enables the beta risk. For the modeling of LMM, Ordinary Least Squares (OLS) method is used. As a second model, Time-varying Linear Market Model (Tv-LMM) is used which is consistent with the Conditional Capital Asset Pricing Model (C-CAPM) and enables the time-varying beta risk. For the modeling of Tv-LMM, univariate (GARCH) and multivariate (DCC-GARCH) GARCH-type models and state space form via Kalman filter algorithm (KFMR) are used. The prices of the weekly foreign currency exchange rates in Turkish Liras (TL) of the period of last 15 years for 9 countries subject to effective purchase-sales as an indicator at Central Bank of Republic of Turkey (CBRT) and the currency basket formed as equally weighted based on these prices are used as the research data. At the stage of modeling of the research data and future estimation for 1 year, LMM and Tv-LMM performances are compared. According to the findings, in the case of modeling of Tv-LMM with KFMR, it is shown that it shows much better performance compared to the other models in modeling of foreign currency exchange rates and future estimation; whereas, in case of modeling of Tv-LMM with GARCH and DCC-GARCH, it is shown to be insufficient compared to OLS. It is concluded that the beta risks of exchange rates are not static.

Anahtar Kelimeler

• Beta Risk
• DCC-GARCH
• GARCH
• Kalman Filter
• Capital Asset Pricing Model (CAPM)

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