IDEAS home Printed from https://ideas.repec.org/p/aue/wpaper/1409.html
   My bibliography  Save this paper

Factor Models of Stock Returns: GARCH Errors versus Time - Varying Betas

Author

Listed:
  • Phoebe Koundouri
  • Nikolaos Kourogenis

    (Department of Banking and Financial Management, University of Piraeus.)

  • Nikitas Pittis

    (University of Piraeus, Greece)

  • Panagiotis Samartzis

Abstract

This paper investigates the implications of time-varying betas in factor models for stock returns. It is shown that a single-factor model (SFMT) with autoregressive betas and homoscedastic errors (SFMT-AR) is capable of reproducing the most important stylized facts of stock returns. An empirical study on the major US stock market sectors shows that SFMT-AR outperforms, in terms of in-sample and out-of-sample performance, SFMT with constant betas and conditionally heteroscedastic (GARCH) errors, as well as two multivariate GARCH-type models.

Suggested Citation

  • Phoebe Koundouri & Nikolaos Kourogenis & Nikitas Pittis & Panagiotis Samartzis, 2014. "Factor Models of Stock Returns: GARCH Errors versus Time - Varying Betas," DEOS Working Papers 1409, Athens University of Economics and Business.
    • Handle: RePEc:aue:wpaper:1409
    as

    Download full text from publisher

    File URL: http://wpa.deos.aueb.gr/docs/Factor.Models.of.Stock.Returns.pdf
    File Function: First version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Ohlson, James & Rosenberg, Barr, 1982. "Systematic Risk of the CRSP Equal-weighted Common Stock Index: A History Estimated by Stochastic-Parameter Regression," The Journal of Business, University of Chicago Press, vol. 55(1), pages 121-145, January.
    3. 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.
    4. Myung Jig Kim & Charles R. Nelson & Richard Startz, 1991. "Mean Reversion in Stock Prices? A Reappraisal of the Empirical Evidence," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(3), pages 515-528.
    5. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    6. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    7. 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.
    8. Shanken, Jay, 1990. "Intertemporal asset pricing : An Empirical Investigation," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 99-120.
    9. Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(4), pages 465-487, December.
    10. Anderson, Keith & Brooks, Chris & Katsaris, Apostolos, 2010. "Speculative bubbles in the S&P 500: Was the tech bubble confined to the tech sector?," Journal of Empirical Finance, Elsevier, vol. 17(3), pages 345-361, June.
    11. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," The Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
    12. Fisher, Lawrence & Kamin, Jules H., 1985. "Forecasting Systematic Risk: Estimates of “Raw†Beta that Take Account of the Tendency of Beta to Change and the Heteroskedasticity of Residual Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 20(2), pages 127-149, June.
    13. Hagerman, Robert L, 1978. "More Evidence on the Distribution of Security Returns," Journal of Finance, American Finance Association, vol. 33(4), pages 1213-1221, September.
    14. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    15. Upton, David E & Shannon, Donald S, 1979. "The Stable Paretian Distribution, Subordinated Stochastic Processes, and Asymptotic Lognormality: An Empirical Investigation," Journal of Finance, American Finance Association, vol. 34(4), pages 1031-1039, September.
    16. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Jin Wu, 2005. "A Framework for Exploring the Macroeconomic Determinants of Systematic Risk," American Economic Review, American Economic Association, vol. 95(2), pages 398-404, May.
    17. Richardson, Matthew & Stock, James H., 1989. "Drawing inferences from statistics based on multiyear asset returns," Journal of Financial Economics, Elsevier, vol. 25(2), pages 323-348, December.
    18. Lu Zhang, 2005. "The Value Premium," Journal of Finance, American Finance Association, vol. 60(1), pages 67-103, February.
    19. N. Gregory Mankiw & David Romer & Matthew D. Shapiro, 1991. "Stock Market Forecastability and Volatility: A Statistical Appraisal," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(3), pages 455-477.
    20. Victor DeMiguel & Lorenzo Garlappi & Raman Uppal, 2009. "Optimal Versus Naive Diversification: How Inefficient is the 1-N Portfolio Strategy?," Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 1915-1953, May.
    21. Castanias, Richard P, II, 1979. "Macroinformation and the Variability of Stock Market Prices," Journal of Finance, American Finance Association, vol. 34(2), pages 439-450, May.
    22. Kon, Stanley J & Jen, Frank C, 1978. "Estimation of Time-Varying Systematic Risk and Performance for Mutual Fund Portfolios: An Application of Switching Regression," Journal of Finance, American Finance Association, vol. 33(2), pages 457-475, May.
    23. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    24. Fred D. Arditti, 1967. "Risk And The Required Return On Equity," Journal of Finance, American Finance Association, vol. 22(1), pages 19-36, March.
    25. McQueen, Grant, 1992. "Long-Horizon Mean-Reverting Stock Prices Revisited," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 27(1), pages 1-18, March.
    26. Beja, Avraham, 1972. "On Systematic and Unsystematic Components of Financial Risk," Journal of Finance, American Finance Association, vol. 27(1), pages 37-45, March.
    27. Fama, Eugene F & French, Kenneth R, 1996. "Multifactor Explanations of Asset Pricing Anomalies," Journal of Finance, American Finance Association, vol. 51(1), pages 55-84, March.
    28. Sunder, Shyam, 1980. "Stationarity of Market Risk: Random Coefficients Tests for Individual Stocks," Journal of Finance, American Finance Association, vol. 35(4), pages 883-896, September.
    29. Ang, Andrew & Chen, Joseph, 2007. "CAPM over the long run: 1926-2001," Journal of Empirical Finance, Elsevier, vol. 14(1), pages 1-40, January.
    30. Eugene F. Fama, 1968. "Risk, Return And Equilibrium: Some Clarifying Comments," Journal of Finance, American Finance Association, vol. 23(1), pages 29-40, March.
    31. Lim, Kian-Guan, 1989. "A New Test of the Three-Moment Capital Asset Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(2), pages 205-216, June.
    32. Praetz, Peter D, 1972. "The Distribution of Share Price Changes," The Journal of Business, University of Chicago Press, vol. 45(1), pages 49-55, January.
    33. Ng, Victor & Engle, Robert F. & Rothschild, Michael, 1992. "A multi-dynamic-factor model for stock returns," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 245-266.
    34. Kraus, Alan & Litzenberger, Robert H, 1976. "Skewness Preference and the Valuation of Risk Assets," Journal of Finance, American Finance Association, vol. 31(4), pages 1085-1100, September.
    35. Peter K. Clark, 1987. "The Cyclical Component of U. S. Economic Activity," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 102(4), pages 797-814.
    36. Fama, Eugene F & French, Kenneth R, 1988. "Permanent and Temporary Components of Stock Prices," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 246-273, April.
    37. Schwartz, Robert A & Whitcomb, David K, 1977. "The Time-Variance Relationship: Evidence on Autocorrelation in Common Stock Returns," Journal of Finance, American Finance Association, vol. 32(1), pages 41-55, March.
    38. Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," The Journal of Business, University of Chicago Press, vol. 47(2), pages 244-280, April.
    39. Poterba, James M. & Summers, Lawrence H., 1988. "Mean reversion in stock prices : Evidence and Implications," Journal of Financial Economics, Elsevier, vol. 22(1), pages 27-59, October.
    40. Bali, Turan G. & Mo, Hengyong & Tang, Yi, 2008. "The role of autoregressive conditional skewness and kurtosis in the estimation of conditional VaR," Journal of Banking & Finance, Elsevier, vol. 32(2), pages 269-282, February.
    41. Collins, Daniel W & Ledolter, Johannes & Rayburn, Judy Dawson, 1987. "Some Further Evidence on the Stochastic Properties of Systematic Risk," The Journal of Business, University of Chicago Press, vol. 60(3), pages 425-448, July.
    42. Bos, T & Newbold, P, 1984. "An Empirical Investigation of the Possibility of Stochastic Systematic Risk in the Market Model," The Journal of Business, University of Chicago Press, vol. 57(1), pages 35-41, January.
    43. Doron Avramov & Tarun Chordia, 2006. "Asset Pricing Models and Financial Market Anomalies," Review of Financial Studies, Society for Financial Studies, vol. 19(3), pages 1001-1040.
    44. Blume, Marshall E, 1971. "On the Assessment of Risk," Journal of Finance, American Finance Association, vol. 26(1), pages 1-10, March.
    45. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    46. Jostova, Gergana & Philipov, Alexander, 2005. "Bayesian Analysis of Stochastic Betas," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 40(4), pages 747-778, December.
    47. Petkova, Ralitsa & Zhang, Lu, 2005. "Is value riskier than growth?," Journal of Financial Economics, Elsevier, vol. 78(1), pages 187-202, October.
    48. Chang-Jin Kim & Charles R. Nelson, 1999. "State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262112388, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lioui, Abraham & Tarelli, Andrea, 2020. "Factor Investing for the Long Run," Journal of Economic Dynamics and Control, Elsevier, vol. 117(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Panagiotis Samartzis & Nikitas Pittis & Nikolaos Kourogenis & Phoebe Koundouri, 2013. "Factor Models of Stock Returns: GARCH Errors versus Autoregressive Betas," DEOS Working Papers 1318, Athens University of Economics and Business.
    2. Phoebe Koundouri & Nikolaos Kourogenis & Nikitas Pittis & Panagiotis Samartzis, 2015. "Factor Models as 'Explanatory Unifiers' versus 'Explanatory Ideals' of Empirical Regularities of Stock Returns," DEOS Working Papers 1507, Athens University of Economics and Business.
    3. Kizys, Renatas & Pierdzioch, Christian, 2011. "The changing sensitivity of realized portfolio betas to U.S. output growth: An analysis based on real-time data," Journal of Economics and Business, Elsevier, vol. 63(3), pages 168-186, May.
    4. Ortas, E. & Salvador, M. & Moneva, J.M., 2015. "Improved beta modeling and forecasting: An unobserved component approach with conditional heteroscedastic disturbances," The North American Journal of Economics and Finance, Elsevier, vol. 31(C), pages 27-51.
    5. Antypas, Antonios & Caporale, Guglielmo Maria & Kourogenis, Nikolaos & Pittis, Nikitas, 2020. "Estimation of conditional asset pricing models with integrated variables in the beta specification," Research in International Business and Finance, Elsevier, vol. 52(C).
    6. Fernando Rubio, 2005. "Eficiencia De Mercado, Administracion De Carteras De Fondos Y Behavioural Finance," Finance 0503028, University Library of Munich, Germany, revised 23 Jul 2005.
    7. Degiannakis, Stavros & Xekalaki, Evdokia, 2004. "Autoregressive Conditional Heteroskedasticity (ARCH) Models: A Review," MPRA Paper 80487, University Library of Munich, Germany.
    8. Stefano D'Addona & Mattia Ciprian, 2007. "Time Varying Sensitivities On A Grid Architecture," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 307-329.
    9. Tim Bollerslev & Robert J. Hodrick, 1992. "Financial Market Efficiency Tests," NBER Working Papers 4108, National Bureau of Economic Research, Inc.
    10. Renata Rendek, 2013. "Modeling Diversified Equity Indices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 4-2013.
    11. Malliaropulos, Dimitrios & Priestley, Richard, 1999. "Mean reversion in Southeast Asian stock markets," Journal of Empirical Finance, Elsevier, vol. 6(4), pages 355-384, October.
    12. Kim, Chang-Jin & Morley, James C. & Nelson, Charles R., 2001. "Does an intertemporal tradeoff between risk and return explain mean reversion in stock prices?," Journal of Empirical Finance, Elsevier, vol. 8(4), pages 403-426, September.
    13. Ferson, Wayne E. & Sarkissian, Sergei & Simin, Timothy, 2008. "Asset Pricing Models with Conditional Betas and Alphas: The Effects of Data Snooping and Spurious Regression," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 43(2), pages 331-353, June.
    14. Ang, Andrew & Kristensen, Dennis, 2012. "Testing conditional factor models," Journal of Financial Economics, Elsevier, vol. 106(1), pages 132-156.
    15. Shlomo Zilca, 2010. "The variance ratio and trend stationary model as extensions of a constrained autoregressive model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(5), pages 467-475.
    16. Adrian, Tobias & Franzoni, Francesco, 2009. "Learning about beta: Time-varying factor loadings, expected returns, and the conditional CAPM," Journal of Empirical Finance, Elsevier, vol. 16(4), pages 537-556, September.
    17. Malevergne, Y. & Sornette, D., 2007. "Self-consistent asset pricing models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 149-171.
    18. Liam Gallagher, 1999. "A multi-country analysis of the temporary and permanent components of stock prices," Applied Financial Economics, Taylor & Francis Journals, vol. 9(2), pages 129-142.
    19. Horváth, Lajos & Li, Bo & Li, Hemei & Liu, Zhenya, 2020. "Time-varying beta in functional factor models: Evidence from China," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    20. Bhar, Ramaprasad & Hamori, Shigeyuki, 2004. "Empirical characteristics of the permanent and transitory components of stock return: analysis in a Markov switching heteroscedasticity framework," Economics Letters, Elsevier, vol. 82(2), pages 157-165, February.

    More about this item

    Keywords

    autoregressive beta; stock returns; single factor model; conditional heteroscedasticity; in-sample performance; out-of-sample performance;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:aue:wpaper:1409. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Ekaterini Glynou (email available below). General contact details of provider: https://edirc.repec.org/data/diauegr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.