Estimation Of Risk Premium Parameters In The Fisher Equation By The State Space Model And Kalman Filter: Case Of Turkey

Öz

Statistical theories are universal and come into sight differently with respect to the conditions, time and societies. Therefore, the results obtained from an analysis should not be comprehended as valid for everywhere and in all conditions. A risk-increasing event in a country might have different effects in another country. What underlies the changefulness of interest rates as well as risk premiums is the expectation; thus the economical relations may have quite different appearances for various periods in different countries. In this study, the time-varying risk premium is attempted to be estimated using the Kalman filter and examining the term structure of the interests from the viewpoint of the Expectations Hypothesis (EH). Kalman filter approach takes the changefulness of interest rates, potentially permanent changes of risk premiums and overlapping errors of estimation into consideration. The study has used of the data on monthly interest rates (regarding the TL-based accounts) for the 2002:01-2018:10 period in Turkey’s economy. The most important feature of the study is that it allows us to identify how the factors causing changes in risk premiums for Turkey’s economy can be estimated in time using the Kalman filter with no predeterminations. According to the risk premium estimates obtained by using the Kalman filter, the risk premium takes positive values in some periods and negative values in other periods. The risk premium is estimated to be negative in high volatility periods and positive in low volatility periods. The results obtained provide rational investors with important and beneficial information about the uncertainties of future changes in the interest rates.

Anahtar Kelimeler

• Expectation Theory
• risk premium
• estimation of time-varying parameters
• Kalman Filter.

Fisher Denklemindeki Risk Primi Parametresinin Durum Uzay Modeli Ve Kalman Filtresi İle Tahmini: Türkiye Örneği

Öz

İktisadi teoriler evrensel olmakla birlikte koşullara, zamana ve toplumlara göre farklı görünümler alır. Bu nedenle yapılan bir analizden elde edilen sonuçların her yerde ve her koşulda geçerli olarak algılanmaması gerekir. Bir ülkede riski artıran bir gelişme başka bir ülkede aynı etkiyi yaratmayabilir. Gerek faiz oranlarındaki gerekse risk primindeki bu oynaklığın altında yatan şey beklentilerdir ki; ekonomik ilişkiler, farklı ülkelerde çeşitli dönemlerde oldukça değişik görünümler sergileyebilir. Bu çalışmada faizin vade yapısı Beklentiler Hipotezi (BH) açısından ele alınarak zamanla değişen risk primi Kalman filtresi kullanılarak tahmin edilmiştir. Kalman filtresi yaklaşımı, faiz oranındaki değişimlerin oynaklığını, risk primindeki olası kalıcı değişimleri ve üst üste gelen tahmin hatalarını dikkate almaktadır. Çalışmada Türkiye ekonomisine ait 2002:01-2018:10 dönemi için aylık faiz oranı (TL üzerinden açılan mevduatlara ilişkin faiz oranı) verilerinden yararlanılmıştır. Çalışmanın en önemli özelliği, Türkiye ekonomisi için risk primini değiştirmeye sebep olan faktörlerin zaman boyunca önceden belirlenmeksizin Kalman filtresi ile nasıl tahmin edeceğimizi sağlamasıdır. Kalman filtresi kullanılarak elde edilen risk primi tahminlerine göre, risk primi bazı dönemlerde pozitif, bazı dönemlerde ise negatif değerler almaktadır. Risk primi, oynaklığın yüksek olduğu dönemlerde negatif, oynaklığın düşük olduğu dönemlerde ise pozitif tahmin edilmiştir. Elde edilen tahmin sonuçları rasyonel yatırımcılara faiz oranlarındaki gelecek değişimlere ait belirsizlikler hakkında önemli ve yararlı bilgiler sunmaktadır.

Anahtar Kelimeler

• Beklentiler Teorisi
• risk primi
• zamana göre değişken parametrelerin tahmini
• Kalman Filtresi

Kaynakça

1. Akıncı, Ö., Gürcihan, B., Gürkaynak, R. ve Özel, Ö. (2006). Devlet İç Borçlanma Senetleri İçin Getiri Eğrisi Tahmini, Araştırma ve Para Politikası Genel Müdürlüğü Çalışma Tebliği, No: 06/08, Ankara.
2. Arslan, M. (2012). Faiz Oranlarının Vade Yapısı, Beklenti Hipotezinin Türk Sabit Getirili Menkul Kıymet Piyasasında Test Edilmesi, İşletme Araştırmaları Dergisi, 4(3), 5-19.
3. Alper, C.E., Akdemir, A. and Kazimov, K. (2004). Estimating the Term Structure of Government Securities in Turkey, Boğaziçi University Research Papers: ISS/EC-2004-03.
4. Arize, A.C., Malindretos, J. and Obi, Z.I. (2002). Long- and Short-Term Interest Rates in 19 Countries: Tests of Cointegration and Parameter Instability, Atlantic Economic Journal, 30, 105-119.
5. Breeden, D. (1986). Consumption, Production, Inflation and Interest Rates: A Synthesis, Journal of Financial Economics, 16, 3-39.
6. Brito, R.D., Duarte, A.J.M.A. and Gullien, O.T.C. (2004). Overreaction of Yield Spreads and Movements of Brazilian Interest Rates, Brazilian Review of Econometrics, 24(1), 1-56.
7. Campbell, J.Y. (1987). Stock Returns and the Term Structure, Journal of Financial Economics, 18, 373-399.
8. Campbell J.Y. (1995). Some Lessons from the Yield Curve, The Journal of Economic Perspectives, 9(3), 129-152.

9. Cook T. & Hahn, T. (1989). The Effect of Changes in the Federal Funds Rate Target on Market Interest Ratesin the 1970s, Journal of Monetary Economics, 24, 331-351.
10. Demirel, Y. (2014). Faiz Oranı Vade Yapısı: Türk Lirası Faiz Oranları Üzerinde Bir Çalışma, Bankacılar Dergisi, 90, 51-67.
11. Engle R.F. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation, Econometrica, 50, 987-1007.
12. Engle, R., Lilien, D. and Robins, R. (1987), Estimating Time-Varying Premia In The Term Structure: The ARCH-LM Model, Econometrica, 55, 391-407.
13. Engle, R., Ng, V. and Rothschild, M. (1990). Asset Pricing with a Factor ARCH Covariance Structure: Empirical Estimates for Treasury Bills, Journal of Econometrics, 45, 213–238.
14. Fama, E.F. (1996). Term Premiums and Default Premiums in Money Markets, Journal of Financial Economics, 17, 175-196.
15. Gerlach, S. & Smets, F. (1997). The Term Structure of Euro-Rates: Some Evidence in Support of the Expectation Hypothesis, Journal of International Money and Finance, 16(2), 305-321.
16. Gravelle, T., Muller, P. and Stréliski, D. (1999). Towards a New Measure of Interest Rate Expectations in Canada: Estimating a Time-Varying Term Premium In Information in Financial Asset Prices, Proceedings of a Conference Held by the Bank of Canada, 179-216.
17. Gravelle, T., & Morley, J.C. (2005). A Kalman Filter Approach To Characterizing The Canadian Term Structure of Interest Rates, Applied Financial Economics, 15, 691-705.
18. Gregory, A. & Voss, G. (1991). The Term Structure of Interest Rates: Departures from Time-Seperable Expected Utility, Canadian Journal of Economics, 24, 923-939.
19. Guillen, O.T. & Tabak, B.M. (2008). Characterizing the Brazilian Term Structure of Interest Rates, Working Paper The Banco Central do Brasil, 1-20.
20. Hardouvelis, G.A. (1994). The Term Structure Spread and Future Changes in Long and Short Rate in the G7 Countries – Is There a Puzzle?, Journal of Monetary Economics, 33, 255-283.
21. Hejazi W., Lai, H. and Yang, X. (2000). The Expectations Hypothesis, Term Premia, and the Canadian Term Structure of Interest Rates, Canadian Journal of Economics, 33, 133-148.
22. Iyer, S. (1997). Time-Varying Term Premia And The Behavior Of Forward Interest Rate Prediction Errors, Journal of Financial Research, 20, 503-507.
23. Johnson, S. (1993). Private Sector in Poland: A Small-Scale Survey, The World Bank, Washington D.C. Mimeo.
24. Kaya, H. (2010). Term Structure of Interest Rate And Macroeconomic Variables: The Turkish Case, International Journal of Economics And Finance Studies, 2(1), 77-85.
25. Kozicki, S. & Tinsley, P.A. (2002). Term Premia: Endogenous Constraints On Monetary Policy, Working Paper Federal Reserve Bank of Kansas City, 02–07.
26. Kugler, P. (1996). The Term Structure Of İnterest Rates And Regime Shifts: Some Empirical Results, Economics Letters, 50, 121–126.
27. Lee, S.S. (1995). Macroeconomic Sources of Time-Varying Risk Premia in the Term Structure of Interest Rates, Journal of Money, Credit and Banking, 27(2), 549-569.
28. Lima, A.M. & Issler, J.V. (2003). A hipótese das expectativas na estrutura a termo de taxa de juros no Brasil: uma aplicação de modelos de valor presente, Revista Brasileira de Economia, 57, 873-898.
29. Mankiw, N.G. & Miron, J. (1986). The Changing Behavior of The Term Structure of Interest Rates, Quarterly Journal of Economics, CI, 211-228.
30. Mankiw, N.G. & Summers, L.H. (1984). Do Long-Term Interest Rates Overreact to Short-Term Interest Rates?, Brookings Pagers on Economic Activity, 1, 223-242.
31. McCallum, B.T. (1994). Monetary Policy and the Term Structure of Interest Rates, NBER Working Paper, 4938, 1-26.
32. McCallum, B.T. (2006). Monetary Policy and the Term Structure of Interest Rates, Federal Reserve Bank of Richmond Economic Quarterly, 91(4), 1-21.
33. Mishkin, F. S. (1990). The Information in the Longer Maturity Term Structure About Future Inflation, The Quarterly Journal of Economics, 105(3), 815-828.
34. Nelson, C.R. (1972). The Term Structure Of Interest Rates. Basic Books, New York.
35. Paquette, J.Y. & Stréliski, D. (1998). The Use of Forward Rate Agreements in Canada, Bank of Canada Review (Spring), 57–71.
36. Pesando, J.E. (1975). Determinants of Term Premiums in the Market for United States
37. Treasury Bills, The Journal of Finance, 30, 1317-1327.
38. Pesando, J.E. (1978). On The Efficiency of The Bond Market: Some Canadian Evidence, Journal of Political Economy, 86, 1057–1076.
39. Shiler, R.J. (1979). The Volatility of Long-Term Interest Rates and Expectations Models of the Term Structure, Journal of Political Economy, 87, 1190-1219.
40. Shiller, R.J. (1990). The Term Structure of Interest Rates (Ed. B. Friedman and F.H. Hahn), Chapter 13 of Handbook of Monetary Economics, Elsevier Science, Amsterdam.
41. Tabak, B.M. & Andrade, S.C. (2003). Testing the Expectation Hypothesis for Brazilian Term Structure of Interest Rates, Revista Brasileira de Finanças, 1, 19-44.
42. Tüysüzoğlu, U. (2013). Türkiye Devlet İç Borçlanma Senetleri Getiri Eğrilerinin Geliştirilmiş Dinamik Nelson-Siegel ve Zaman Serisi Modelleri İle Öngörü Performanslarının Karşılaştırılması, TCMB Uzmanlık Tezi, Ankara.
43. Tzavalis, E. & Wickens, M.R. (1997). Explaining The Failures Of The Term Spread Models of The Rational Expectation Hypothesis of The Term Structure. Journal of Money, Credit, and Banking, 29, 364-380.
44. Özbek, L. (2017). Kalman Filtresi, Akademisyen Kitabevi.
45. Öztürk, F. ve Özbek, L. (2015). Matematiksel Modelleme ve Simülasyon, Pigeon Yayıncılık.