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Flexible Time-Varying Betas in a Novel Mixture Innovation Factor Model with Latent Threshold

Author

Listed:
  • Mehmet Balcilar

    (Department of Economics, Eastern Mediterranean University, Northern Cyprus, via Mersin 10, Famagusta 99450, Turkey)

  • Riza Demirer

    (Department of Economics and Finance, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1102, USA)

  • Festus V. Bekun

    (Faculty of Economics Administrative and Social Sciences, Istanbul Gelisim University, Istanbul 34310, Turkey)

Abstract
This paper introduces a new methodology to estimate time-varying alphas and betas in conditional factor models, which allows substantial flexibility in a time-varying framework. To circumvent problems associated with the previous approaches, we introduce a Bayesian time-varying parameter model where innovations of the state equation have a spike-and-slab mixture distribution. The mixture distribution specifies two states with a specific probability. In the first state, the innovation variance is set close to zero with a certain probability and parameters stay relatively constant. In the second state, the innovation variance is large and the change in parameters is normally distributed with mean zero and a given variance. The latent state is specified with a threshold that governs the state change. We allow a separate threshold for each parameter; thus, the parameters may shift in an unsynchronized manner such that the model moves from one state to another when the change in the parameter exceeds the threshold and vice versa. This approach offers great flexibility and nests a plethora of other time-varying model specifications, allowing us to assess whether the betas of conditional factor models evolve gradually over time or display infrequent, but large, shifts. We apply the proposed methodology to industry portfolios within a five-factor model setting and show that the threshold Capital Asset Pricing Model (CAPM) provides robust beta estimates coupled with smaller pricing errors compared to the alternative approaches. The results have significant implications for the implementation of smart beta strategies that rely heavily on the accuracy and stability of factor betas and yields.

Suggested Citation

  • Mehmet Balcilar & Riza Demirer & Festus V. Bekun, 2021. "Flexible Time-Varying Betas in a Novel Mixture Innovation Factor Model with Latent Threshold," Mathematics, MDPI, vol. 9(8), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:8:p:915-:d:539853
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    References listed on IDEAS

    as
    1. Pagan, Adrian, 1980. "Some identification and estimation results for regression models with stochastically varying coefficients," Journal of Econometrics, Elsevier, vol. 13(3), pages 341-363, August.
    2. Fama, Eugene F & French, Kenneth R, 1992. "The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-465, June.
    3. Jagannathan, Ravi & Wang, Zhenyu, 1996. "The Conditional CAPM and the Cross-Section of Expected Returns," Journal of Finance, American Finance Association, vol. 51(1), pages 3-53, March.
    4. Ang, Andrew & Kristensen, Dennis, 2012. "Testing conditional factor models," Journal of Financial Economics, Elsevier, vol. 106(1), pages 132-156.
    5. Fama, Eugene F. & French, Kenneth R., 2017. "International tests of a five-factor asset pricing model," Journal of Financial Economics, Elsevier, vol. 123(3), pages 441-463.
    6. Novy-Marx, Robert, 2013. "The other side of value: The gross profitability premium," Journal of Financial Economics, Elsevier, vol. 108(1), pages 1-28.
    7. Zhou, Jian, 2013. "Conditional market beta for REITs: A comparison of modeling techniques," Economic Modelling, Elsevier, vol. 30(C), pages 196-204.
    8. Goodness C. Aye & Mehmet Balcilar & Rangan Gupta, 2017. "International stock return predictability: Is the role of U.S. time-varying?," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 44(1), pages 121-146, February.
    9. repec:bla:jfinan:v:53:y:1998:i:2:p:549-573 is not listed on IDEAS
    10. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    11. Hameed, Allaudeen, 1997. "Time-Varying Factors and Cross-Autocorrelations in Short-Horizon Stock Returns," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 20(4), pages 435-458, Winter.
    12. Massimiliano Caporin & Michael McAleer, 2013. "Ten Things you should know about DCC," Tinbergen Institute Discussion Papers 13-048/III, Tinbergen Institute.
    13. Satish Kumar & Riza Demirer & Aviral Kumar Tiwari, 2020. "Oil and risk premia in equity markets," Studies in Economics and Finance, Emerald Group Publishing Limited, vol. 37(4), pages 697-723, September.
    14. Hollstein, Fabian, 2020. "Estimating beta: The international evidence," Journal of Banking & Finance, Elsevier, vol. 121(C).
    15. Chen, Liang & Dolado, Juan J. & Gonzalo, Jesús, 2014. "Detecting big structural breaks in large factor models," Journal of Econometrics, Elsevier, vol. 180(1), pages 30-48.
    16. Gary Koop & Simon M. Potter, 2007. "Estimation and Forecasting in Models with Multiple Breaks," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(3), pages 763-789.
    17. Giordani, Paolo & Kohn, Robert, 2008. "Efficient Bayesian Inference for Multiple Change-Point and Mixture Innovation Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 66-77, January.
    18. Ferson, Wayne E & Harvey, Campbell R, 1991. "The Variation of Economic Risk Premiums," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 385-415, April.
    19. Ang, Andrew & Chen, Joseph, 2007. "CAPM over the long run: 1926-2001," Journal of Empirical Finance, Elsevier, vol. 14(1), pages 1-40, January.
    20. Markus Ebner & Thorsten Neumann, 2005. "Time-Varying Betas of German Stock Returns," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 19(1), pages 29-46, June.
    21. Carhart, Mark M, 1997. "On Persistence in Mutual Fund Performance," Journal of Finance, American Finance Association, vol. 52(1), pages 57-82, March.
    22. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    23. M. Hashem Pesaran & Davide Pettenuzzo & Allan Timmermann, 2006. "Forecasting Time Series Subject to Multiple Structural Breaks," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(4), pages 1057-1084.
    24. Aslanidis, Nektarios & Hartigan, Luke, 2021. "Is the assumption of constant factor loadings too strong in practice?," Economic Modelling, Elsevier, vol. 98(C), pages 100-108.
    25. Michael J. Cooper & Huseyin Gulen & Michael J. Schill, 2008. "Asset Growth and the Cross‐Section of Stock Returns," Journal of Finance, American Finance Association, vol. 63(4), pages 1609-1651, August.
    26. Massimiliano Caporin & Michael McAleer, 2013. "Ten Things You Should Know about the Dynamic Conditional Correlation Representation," Econometrics, MDPI, vol. 1(1), pages 1-12, June.
    27. Fama, Eugene F. & French, Kenneth R., 2012. "Size, value, and momentum in international stock returns," Journal of Financial Economics, Elsevier, vol. 105(3), pages 457-472.
    28. Gonzalo, Jesus & Pitarakis, Jean-Yves, 2002. "Estimation and model selection based inference in single and multiple threshold models," Journal of Econometrics, Elsevier, vol. 110(2), pages 319-352, October.
    29. Guo, Bin & Zhang, Wei & Zhang, Yongjie & Zhang, Han, 2017. "The five-factor asset pricing model tests for the Chinese stock market," Pacific-Basin Finance Journal, Elsevier, vol. 43(C), pages 84-106.
    30. Mardy Chiah & Daniel Chai & Angel Zhong & Song Li, 2016. "A Better Model? An Empirical Investigation of the Fama–French Five-factor Model in Australia," International Review of Finance, International Review of Finance Ltd., vol. 16(4), pages 595-638, December.
    31. Ball, Ray & Gerakos, Joseph & Linnainmaa, Juhani T. & Nikolaev, Valeri, 2016. "Accruals, cash flows, and operating profitability in the cross section of stock returns," Journal of Financial Economics, Elsevier, vol. 121(1), pages 28-45.
    32. Wang, Lu, 2021. "Time-varying conditional beta, return spillovers, and dynamic bank diversification strategies," The Quarterly Review of Economics and Finance, Elsevier, vol. 79(C), pages 272-280.
    33. Fama, Eugene F & French, Kenneth R, 1995. "Size and Book-to-Market Factors in Earnings and Returns," Journal of Finance, American Finance Association, vol. 50(1), pages 131-155, March.
    34. Han, Xu & Inoue, Atsushi, 2015. "Tests For Parameter Instability In Dynamic Factor Models," Econometric Theory, Cambridge University Press, vol. 31(5), pages 1117-1152, October.
    35. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-131, February.
    36. Shanken, Jay, 1990. "Intertemporal asset pricing : An Empirical Investigation," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 99-120.
    37. Lewellen, Jonathan & Nagel, Stefan, 2006. "The conditional CAPM does not explain asset-pricing anomalies," Journal of Financial Economics, Elsevier, vol. 82(2), pages 289-314, November.
    38. Allaudeen Hameed, 1997. "Time-Varying Factors And Cross-Autocorrelations In Short-Horizon Stock Returns," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 20(4), pages 435-458, December.
    39. Syed Abuzar Moonis & Ajay Shah, 2003. "Testing for Time-variation in Beta in India," Journal of Emerging Market Finance, Institute for Financial Management and Research, vol. 2(2), pages 163-180, May.
    40. Kewei Hou & Chen Xue & Lu Zhang, 2015. "Editor's Choice Digesting Anomalies: An Investment Approach," The Review of Financial Studies, Society for Financial Studies, vol. 28(3), pages 650-705.
    41. Rapach, David E. & Wohar, Mark E. & Rangvid, Jesper, 2005. "Macro variables and international stock return predictability," International Journal of Forecasting, Elsevier, vol. 21(1), pages 137-166.
    42. Fama, Eugene F. & French, Kenneth R., 2015. "A five-factor asset pricing model," Journal of Financial Economics, Elsevier, vol. 116(1), pages 1-22.
    43. Koop, Gary & Leon-Gonzalez, Roberto & Strachan, Rodney W., 2009. "On the evolution of the monetary policy transmission mechanism," Journal of Economic Dynamics and Control, Elsevier, vol. 33(4), pages 997-1017, April.
    44. Martin Lettau & Sydney Ludvigson, 2001. "Resurrecting the (C)CAPM: A Cross-Sectional Test When Risk Premia Are Time-Varying," Journal of Political Economy, University of Chicago Press, vol. 109(6), pages 1238-1287, December.
    45. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    46. Taufiq Choudhry & Hao Wu, 2008. "Forecasting ability of GARCH vs Kalman filter method: evidence from daily UK time-varying beta," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(8), pages 670-689.
    47. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    48. Becker, Janis & Hollstein, Fabian & Prokopczuk, Marcel & Sibbertsen, Philipp, 2021. "The memory of beta," Journal of Banking & Finance, Elsevier, vol. 124(C).
    49. Sascha Mergner & Jan Bulla, 2008. "Time-varying beta risk of Pan-European industry portfolios: A comparison of alternative modeling techniques," The European Journal of Finance, Taylor & Francis Journals, vol. 14(8), pages 771-802.
    50. Robert W. Faff & David Hillier & Joseph Hillier, 2000. "Time Varying Beta Risk: An Analysis of Alternative Modelling Techniques," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 27(5‐6), pages 523-554, June.
    51. Levi, Yaron & Welch, Ivo, 2017. "Best Practice for Cost-of-Capital Estimates," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 52(2), pages 427-463, April.
    52. Jiang, Chonghui & Du, Jiangze & An, Yunbi & Zhang, Jinqing, 2021. "Factor tracking: A new smart beta strategy that outperforms naïve diversification," Economic Modelling, Elsevier, vol. 96(C), pages 396-408.
    53. Su, Liangjun & Wang, Xia, 2017. "On time-varying factor models: Estimation and testing," Journal of Econometrics, Elsevier, vol. 198(1), pages 84-101.
    54. Maria Victoria Esteban & Susan Orbe-Mandaluniz, 2010. "A nonparametric approach for estimating betas: the smoothed rolling estimator," Applied Economics, Taylor & Francis Journals, vol. 42(10), pages 1269-1279.
    55. Chib, Siddhartha, 1998. "Estimation and comparison of multiple change-point models," Journal of Econometrics, Elsevier, vol. 86(2), pages 221-241, June.
    56. Sousa, Ricardo M. & Vivian, Andrew & Wohar, Mark E., 2016. "Predicting asset returns in the BRICS: The role of macroeconomic and fundamental predictors," International Review of Economics & Finance, Elsevier, vol. 41(C), pages 122-143.
    57. Gary Koop & Simon M. Potter, 2009. "Prior Elicitation In Multiple Change-Point Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 50(3), pages 751-772, August.
    58. Balcilar, Mehmet & Ozdemir, Zeynel Abidin, 2019. "The volatility effect on precious metals price returns in a stochastic volatility in mean model with time-varying parameters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    59. Arshanapalli, Bala & Fabozzi, Frank J. & Nelson, William, 2006. "The value, size, and momentum spread during distressed economic periods," Finance Research Letters, Elsevier, vol. 3(4), pages 244-252, December.
    60. Li, Yan & Yang, Liyan, 2011. "Testing conditional factor models: A nonparametric approach," Journal of Empirical Finance, Elsevier, vol. 18(5), pages 972-992.
    61. Ng, Lilian, 1991. "Tests of the CAPM with Time-Varying Covariances: A Multivariate GARCH Approach," Journal of Finance, American Finance Association, vol. 46(4), pages 1507-1521, September.
    62. Jesús Crespo Cuaresma & Gernot Doppelhofer & Martin Feldkircher & Florian Huber, 2019. "Spillovers from US monetary policy: evidence from a time varying parameter global vector auto‐regressive model," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 182(3), pages 831-861, June.
    63. Yu, Honghai & Fang, Libing & Du, Donglei & Yan, Panpan, 2017. "How EPU drives long-term industry beta," Finance Research Letters, Elsevier, vol. 22(C), pages 249-258.
    64. Jegadeesh, Narasimhan & Titman, Sheridan, 1993. "Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency," Journal of Finance, American Finance Association, vol. 48(1), pages 65-91, March.
    65. Robert W. Faff & David Hillier & Joseph Hillier, 2000. "Time Varying Beta Risk: An Analysis of Alternative Modelling Techniques," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 27(5‐6), pages 523-554, June.
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