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

Araştırmada, Türkiye’deki döviz yatırımcılarının oluşturacakları döviz portföylerinin modellenmesi ve gelecek tahmininin yapılması için; temel model olarak, Sermaye Varlıkları Fiyatlandırma Modeli (SVFM) ile tutarlı ve durağan beta riskine olanak sağlayan, Doğrusal Piyasa Modeli (DPM) kullanılmıştır. SVFM’nin performansı ise, Koşullu Sermaye Varlıkları Fiyatlandırma Modeliyle (K- SVFM) tutarlı ve zamana bağlı değişen beta riskine olanak sağlayan Zamana bağlı değişen Doğrusal Piyasa Modeli (Z-DPM) ile karşılaştırılmıştır. Z-DPM’nin modellenmesi için, tek değişkenli (GARCH) ve çok değişkenli (DCC-GARCH) GARCH-tipi modeller ve durum uzayı formundaki Kalman filtresi (KFMR) kullanılmıştır. Türkiye Cumhuriyet Merkez Bankası’nda (TCMB) efektif alış-şatışa konu olan, 9 ülkenin son 15 yıllık haftalık döviz kurlarının Türk Lirası (TL) cinsinden fiyatları, araştırma verisi olarak kullanılmıştır. Sonuçta, Z-DPM’nin KFMR ile modellenmesi durumunda, döviz kurlarının modellenmesi ve gelecek tahmini konusunda diğerlerine karşı daha iyi performans gösterdiği; fakat Z- DPM’nin GARCH ve DCC-GARCH ile modellenmesi durumunda ise DPM’ye göre yetersiz kaldığı görülmüştür. Döviz kurlarındaki beta risklerinin durağan olmadığı temel sonucuna ulaşılmıştır.

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

In this study, Linear Market Model (LMM) is used which is consistent with the Capital Asset Pricing Model (CAPM) and enables the beta risk as the benchmark model for the purposes of perform the modeling and forecasting of the foreign currency portfolios to be established by the foreign currency investors in Turkey. Performance of Capital Asset Pricing Model is compared with the 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 the Republic of Turkey (CBRT) based on these prices are used as the research data. To sum up, 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 stable.

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