Time-Varying Beta Estimation: A Comparison of DCC-GARCH and Rolling-Window Methods in Turkish Industry Portfolios

Abstract

This study empirically compares the accuracy of two common methods for estimating time-varying betas in Turkish industry portfolios: rolling-window OLS regression and the DCC model. Using daily returns from 2004 to 2024, the methods are evaluated based on their alignment with CAPM predictions, specifically the insignificance of Jensen’s alpha and the significance of the market risk premium. Findings show that despite its complexity, the DCC model does not outperform the rolling-window approach. The rolling-window approach produces insignificant Jensen’s alpha estimates for more industries and yields slightly higher mean and t-statistics for the market risk premium. These findings challenge the view that rolling-window estimators are inefficient due to assuming beta constancy within short windows and suggest that the DCC model’s reliance on multiple constant parameters imposes a rigid structure that may hinder its adaptability to evolving market conditions. This study contributes to the literature by directly comparing these two widely used methods and highlighting the importance of carefully considering model assumptions when estimating time-varying betas.

Keywords

• CAPM
• Time-varying beta
• DCC
• Rolling-window
• Jensen’s alpha
• Market risk premium

Zamanla Değişen Betanın Tahmini: Türk Sektör Portföylerinde DCC-GARCH ve Rolling-Window Yöntemlerinin Karşılaştırılması

Abstract

Bu çalışma, Türk sektör portföylerinde zamanla değişen betaların tahmininde yaygın olarak kullanılan iki yöntem olan kayan pencere en küçük kareler regresyonu ile DCC modelini ampirik olarak karşılaştırmaktadır. 2004–2024 dönemine ait günlük getiriler kullanılarak, bu yöntemler CAPM öngörüleriyle özellikle Jensen alfa değerlerinin anlamsızlığı ve piyasa risk priminin anlamlılığı temelinde değerlendirilmiştir. Bulgular, karmaşıklığına rağmen DCC modelinin kayan pencere yaklaşımından daha iyi performans göstermediğini ortaya koymaktadır. Kayan pencere yaklaşımı, daha fazla sektör için istatistiksel olarak anlamsız Jensen alfa tahminleri verirken, piyasa risk primi için biraz daha yüksek ortalama ve t-istatistikleri üretmektedir. Bu bulgular, kısa pencere sürelerinde betanın sabit olduğu varsayımına dayanan kayan pencere yöntemlerinin etkin olmadığı görüşüne meydan okumakta ve DCC modelinin çok sayıda sabit parametreye dayalı yapısının, değişen piyasa koşullarına uyum sağlamasını zorlaştırabileceğini göstermektedir. Çalışma, bu iki yaygın yöntemi doğrudan karşılaştırarak ve zamanla değişen beta tahmininde model varsayımlarının dikkatli değerlendirilmesinin önemini vurgulayarak literatüre katkı sağlamaktadır.

Keywords

• SVFM
• Zamanla değişen beta
• Dinamik Koşullu Korelasyon
• Kayan pencere
• Jensen alpha
• Piyasa risk primi

References

1. Adrian, T. & Franzoni, F. (2009). Learning about beta: Time varying factor loadings, expected returns, and the conditional CAPM. Journal of Empirical Finance, 16(4), 537–556. https://doi.org/10.1016/j.jempfin.2009.02.003
2. Agrrawal, P., Gilbert, F. W. & Harkins, J. (2022). Time dependence of CAPM betas on the choice of interval frequency and return timeframes: Is there an optimum? Journal of Risk and Financial Management, 15(11), 520. https://doi.org/10.3390/jrfm15110520
3. Alexander, G. J. & Chervany, N. L. (1980). On the estimation and stability of beta. The Journal of Financial and Quantitative Analysis, 15(1), 123–137. https://doi.org/10.2307/2979022
4. Aloy, M., Laly, F., Laurent, S. & Lecourt, C. (2021). Modeling time varying conditional betas: A comparison of methods with application for REITs. In G. Dufrénot & T. Matsuki (Eds.), Recent Econo¬metric Techniques for Macroeconomic and Financial Data (pp. 229–264). Springer. https://doi.org/10.1007/978-3-030-54252-8_9
5. Baillie, R. T., Calonaci, F. & Kapetanios, G. (2022). Hierarchical time varying estimation of asset pricing models. Journal of Risk and Financial Management, 15(1), 14. https://doi.org/10.3390/jrfm15010014
6. Bali, T. G., Engle, R. & Tang, Y. (2016). Dynamic conditional beta is alive and well in the cross section of daily stock returns. Management Science, 63(11), 3760–3779. https://doi.org/10.1287/mnsc.2016.2536
7. Bauwens, L., Laurent, S. & Rombouts, J. V. K. (2006). Multi¬variate GARCH models: A survey. Journal of Applied Econometrics, 21(1), 79–109. https://doi.org/10.1002/jae.842
8. Bollerslev, T., Engle, R. F. & Wooldridge, J. M. (1988). A capital asset pricing model with time varying covariances. Journal of Political Economy, 96(1), 116–131. https://doi.org/10.1086/261527

9. Brooks, R. D., Faff, R. W. & Lee, J. H. H. (1992). The form of time variation of systematic risk: Some Australian evidence. Applied Financial Economics, 2(4), 191–198. https://doi.org/10.1080/758527100
10. Brooks, R. D., Faff R. W. & McKenzie, M. D. (1998). Time varying beta risk of Australian industry portfolios: A comparison of modelling techniques. Australian Journal of Management, 23(1), 45–66. https://doi.org/10.1177/031289629802300101
11. Caporin, M. & McAleer, M. (2012). Do we really need both BEKK and DCC? A tale of two multi¬variate GARCH models. Journal of Economic Surveys, 26(4), 736–751. https://doi.org/10.1111/j.1467-6419.2011.00683.x
12. Choudhry, T. & Wu, H. (2008). Forecasting ability of GARCH vs Kalman filter method: Evidence from daily UK time varying beta. Journal of Forecasting, 27(8), 670–689. https://doi.org/10.1002/for.1096
13. Çatık, A. N., Huyugüzel Kışla, G. & Akdeniz, C. (2020). Time varying impact of oil prices on sectoral stock returns: Evidence from Turkey. Resources Policy, 69, 101845. https://doi.org/10.1016/j.resourpol.2020.101845
14. Engle, R. (2002). Dynamic conditional correlation: A simple class of multivariate generalized auto¬regressive conditional hetero¬skedasticity models. Journal of Business & Economic Statistics, 20(3), 339–350. https://doi.org/10.1198/073500102288618487
15. Engle, R. F. (2016). Dynamic conditional beta. Journal of Financial Econometrics, 14(4), 643–667. https://doi.org/10.1093/jjfinec/nbw006
16. Engle, R. F. & Sheppard, K. (2001). Theoretical and empirical properties of dynamic conditional correlation multi¬variate GARCH (NBER Working Paper 8554). National Bureau of Economic Research. https://doi.org/10.3386/w8554
17. Esteban, M. V. & Orbe-Mandaluniz, S. (2010). A non¬parametric approach for estimating betas: The smoothed rolling estimator. Applied Economics, 42(10), 1269–1279. https://doi.org/10.1080/00036840701721257
18. Fabozzi, F. J. & Francis, J. C. (1977). Stability tests for alphas and betas over bull and bear market conditions. The Journal of Finance, 32(4), 1093–1099. https://doi.org/10.2307/2326515
19. Fama, E. F. & French, K. R. (1992). The cross-section of expected stock returns. The Journal of Finance, 47(2), 427–465. https://dx.doi.org/10.2307/2329112
20. Fama, E. F. & French, K. R. (2004). The capital asset pricing model: Theory and evidence. Journal of Economic Perspectives, 18(3), 25–46. https://dx.doi.org/10.1257/0895330042162430
21. Fama, E. F. & MacBeth, J. D. (1973). Risk, return, and equilibrium: Empirical tests. Journal of Political Economy, 81(3), 607–636. https://dx.doi.org/10.1086/260061
22. Ferson, W. E. & Harvey, C. R. (1991). The variation of economic risk premiums. Journal of Political Economy, 99(2), 385–415. https://doi.org/10.1086/261755
23. Graham, J. R. & Harvey, C. R. (2001). The theory and practice of corporate finance: Evidence from the field. Journal of Financial Economics 60(2–3), 187–243. https://doi.org/10.1016/s0304-405x(01)00044-7
24. Groenewold, N. & Fraser, P. (2000). Forecasting beta: How well does the ‘five year rule of thumb’ do? Journal of Business Finance & Accounting, 27(7–8). https://doi.org/10.1111/1468-5957.00341
25. Hwang, S., & Valls Pereira, P. L. (2006). Small sample properties of GARCH estimates and persistence. The European Journal of Finance, 12(6–7), 473–494. https://doi.org/10.1080/13518470500039436
26. İlbasmış, M. (2024). A comparison of forecasting accuracy between two dynamic conditional correlation (DCC) models. Journal of Economics Business and Political Researches, 9(23), 1–11. https://doi.org/10.25204/iktisad.1388428
27. Jagannathan, R. & Wang, Z. (1996). The conditional CAPM and the cross-section of expected returns. The Journal of Finance, 51(1), 3–53. https://doi.org/10.2307/2329301
28. Korkmaz, T., Çevik, E. I., Birkan, E. & Özataç, N. (2010). Testing CAPM using Markov switching model: The case of coal firms. Economic Research-Ekonomska Istraživanja, 23(2), 44–59. https://doi.org/10.1080/1331677X.2010.11517411
29. Lewellen, J. & Nagel, S. (2006). The conditional CAPM does not explain asset pricing anomalies. Journal of Financial Economics, 82(2), 289–314. https://doi.org/10.1016/j.jfineco.2005.05.012
30. Lettau, M. & Ludvigson, S. (2001). Resurrecting the (C)CAPM: A cross‐sectional test when risk premia are time‐varying. Journal of Political Economy, 109(6), 1238–1287. https://doi.org/10.1086/323282
31. Lintner, J. (1965). Security prices, risk, and maximal gains from diversification. The Journal of Finance, 20(4), 587–615. https://doi.org/10.2307/2977249
32. Mergner, S. & Bulla, J. (2008). Time varying beta risk of Pan-European industry portfolios: A comparison of alternative modeling techniques. The European Journal of Finance, 14(8), 771–802. https://doi.org/10.1080/13518470802173396
33. Mossin, J. (1966). Equilibrium in a capital asset market. Econometrica, 34(4), 768–783. https://doi.org/10.2307/1910098
34. Nieto, B., Orbe, S. & Zarraga, A. (2014). Time varying market beta: Does the estimation methodology matter? Statistics and Operations Research Transactions, 38(1), 13–42. http://hdl.handle.net/2117/88929
35. Shah, A. & Moonis, S. A. (2003). Testing for time-variation in beta in India. Journal of Emerging Market Finance, 2(2), 163–180. https://doi.org/10.1177/097265270300200202
36. Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. The Journal of Finance, 19(3), 425–442. https://doi.org/10.2307/2977928
37. Silvennoinen, A. & Teräsvirta, T. (2009). Multivariate GARCH models. In T. G. Andersen, R. A. Davis, J-P. Kreiß, T. Mikosch (Eds.), Handbook of Financial Time Series (pp. 201–229). Springer-Verlag. https://doi.org/10.1007/978-3-540-71297-8_9
38. Ustaoğlu, E. (2022). Time-varying beta coefficients of BIST sector indices. Muhasebe ve Finansman Dergisi, 96, 135–150. https://doi.org/10.25095/mufad.1143257