Nothing Special   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/hal-00587579.html
   My bibliography  Save this paper

Learning about Beta: Time-varying factor loadings, expected returns, and the Conditional CAPM

Author

Listed:
  • Francesco Franzoni

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

  • Tobias Adrian
Abstract
This paper explores the theoretical and empirical implications of time-varying and unobservable beta. Investors infer factor loadings from the history of returns via the Kalman filter. Due to learning, the history of beta matters. Even though the conditional CAPM holds, standard OLS tests can reject the model if the evolution of investor's expectations is not properly modelled. We use our methodology to explain returns on the twenty-five size and book-to-market sorted portfolios. Our learning version of the conditional CAPM produces pricing errors that are significantly smaller than standard conditional or unconditional CAPM and the model is not rejected by the data.

Suggested Citation

  • Francesco Franzoni & Tobias Adrian, 2005. "Learning about Beta: Time-varying factor loadings, expected returns, and the Conditional CAPM," Working Papers hal-00587579, HAL.
    • Handle: RePEc:hal:wpaper:hal-00587579
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Wayne E. Ferson & Campbell R. Harvey, 1999. "Conditioning Variables and the Cross Section of Stock Returns," Journal of Finance, American Finance Association, vol. 54(4), pages 1325-1360, August.
    2. 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.
    3. Hanno N. Lustig & Stijn G. Van Nieuwerburgh, 2005. "Housing Collateral, Consumption Insurance, and Risk Premia: An Empirical Perspective," Journal of Finance, American Finance Association, vol. 60(3), pages 1167-1219, June.
    4. Thomas Sargent & Noah Williams & Tao Zha, 2009. "The Conquest of South American Inflation," Journal of Political Economy, University of Chicago Press, vol. 117(2), pages 211-256, April.
    5. Schwert, G William & Seguin, Paul J, 1990. "Heteroskedasticity in Stock Returns," Journal of Finance, American Finance Association, vol. 45(4), pages 1129-1155, September.
    6. 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.
    7. Tano Santos & Pietro Veronesi, 2004. "Conditional Betas," NBER Working Papers 10413, National Bureau of Economic Research, Inc.
    8. 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..
    9. Allan G. Timmermann, 1993. "How Learning in Financial Markets Generates Excess Volatility and Predictability in Stock Prices," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(4), pages 1135-1145.
    10. John Y. Campbell & Tuomo Vuolteenaho, 2004. "Bad Beta, Good Beta," American Economic Review, American Economic Association, vol. 94(5), pages 1249-1275, December.
    11. 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.
    12. Breeden, Douglas T., 1979. "An intertemporal asset pricing model with stochastic consumption and investment opportunities," Journal of Financial Economics, Elsevier, vol. 7(3), pages 265-296, September.
    13. 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.
    14. 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.
    15. Hansen, Lars Peter & Jagannathan, Ravi, 1997. "Assessing Specification Errors in Stochastic Discount Factor Models," Journal of Finance, American Finance Association, vol. 52(2), pages 557-590, June.
    16. Engle, Robert F. & White (the late), Halbert (ed.), 1999. "Cointegration, Causality, and Forecasting: Festschrift in Honour of Clive W. J. Granger," OUP Catalogue, Oxford University Press, number 9780198296836.
    17. Jonathan Lewellen & Jay Shanken, 2002. "Learning, Asset‐Pricing Tests, and Market Efficiency," Journal of Finance, American Finance Association, vol. 57(3), pages 1113-1145, June.
    18. Nelson, Daniel B., 1992. "Filtering and forecasting with misspecified ARCH models I : Getting the right variance with the wrong model," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 61-90.
    19. Gibbons, Michael R & Ross, Stephen A & Shanken, Jay, 1989. "A Test of the Efficiency of a Given Portfolio," Econometrica, Econometric Society, vol. 57(5), pages 1121-1152, September.
    20. 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.
    21. Estrella, Arturo & Hardouvelis, Gikas A, 1991. "The Term Structure as a Predictor of Real Economic Activity," Journal of Finance, American Finance Association, vol. 46(2), pages 555-576, June.
    22. Pastor, Lubos & Stambaugh, Robert F., 2000. "Comparing asset pricing models: an investment perspective," Journal of Financial Economics, Elsevier, vol. 56(3), pages 335-381, June.
    23. Fama, Eugene F & MacBeth, James D, 1973. "Risk, Return, and Equilibrium: Empirical Tests," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 607-636, May-June.
    24. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
    25. 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.
    26. Ľuboš Pástor, 2000. "Portfolio Selection and Asset Pricing Models," Journal of Finance, American Finance Association, vol. 55(1), pages 179-223, February.
    27. Harvey, Campbell R., 1989. "Time-varying conditional covariances in tests of asset pricing models," Journal of Financial Economics, Elsevier, vol. 24(2), pages 289-317.
    28. 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.
    29. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    30. Robert B. Barsky & J. Bradford De Long, 1993. "Why Does the Stock Market Fluctuate?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(2), pages 291-311.
    31. 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.
    32. Hansen, Lars Peter & Richard, Scott F, 1987. "The Role of Conditioning Information in Deducing Testable," Econometrica, Econometric Society, vol. 55(3), pages 587-613, May.
    33. Ferson, Wayne E & Kandel, Shmuel & Stambaugh, Robert F, 1987. "Tests of Asset Pricing with Time-Varying Expected Risk Premiums and Market Betas," Journal of Finance, American Finance Association, vol. 42(2), pages 201-220, June.
    34. Campbell, John Y, 1996. "Understanding Risk and Return," Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 298-345, April.
    35. Chen, Nai-Fu & Roll, Richard & Ross, Stephen A, 1986. "Economic Forces and the Stock Market," The Journal of Business, University of Chicago Press, vol. 59(3), pages 383-403, July.
    36. Eugene F. Fama & Kenneth R. French, 2006. "The Value Premium and the CAPM," Journal of Finance, American Finance Association, vol. 61(5), pages 2163-2185, October.
    37. Pietro Veronesi & Tano Santos, 2004. "Conditional Betas," 2004 Meeting Papers 24, Society for Economic Dynamics.
    38. Shanken, Jay, 1990. "Intertemporal asset pricing : An Empirical Investigation," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 99-120.
    39. Barberis, Nicholas & Shleifer, Andrei, 2003. "Style investing," Journal of Financial Economics, Elsevier, vol. 68(2), pages 161-199, May.
    40. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    41. 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.
    42. repec:bla:jfinan:v:59:y:2004:i:4:p:1481-1509 is not listed on IDEAS
    43. 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.
    44. Cochrane, John H, 1996. "A Cross-Sectional Test of an Investment-Based Asset Pricing Model," Journal of Political Economy, University of Chicago Press, vol. 104(3), pages 572-621, June.
    45. Chan, K C & Chen, Nai-Fu, 1991. "Structural and Return Characteristics of Small and Large Firms," Journal of Finance, American Finance Association, vol. 46(4), pages 1467-1484, September.
    46. Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, vol. 55(2), pages 391-407, March.
    Full references (including those not matched with items on IDEAS)

    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. Roussanov, Nikolai, 2014. "Composition of wealth, conditioning information, and the cross-section of stock returns," Journal of Financial Economics, Elsevier, vol. 111(2), pages 352-380.
    2. John Y. Campbell, 2000. "Asset Pricing at the Millennium," Journal of Finance, American Finance Association, vol. 55(4), pages 1515-1567, August.
    3. Ang, Andrew & Chen, Joseph, 2007. "CAPM over the long run: 1926-2001," Journal of Empirical Finance, Elsevier, vol. 14(1), pages 1-40, January.
    4. Amit Goyal, 2012. "Empirical cross-sectional asset pricing: a survey," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 26(1), pages 3-38, March.
    5. Ludvigson, Sydney C., 2013. "Advances in Consumption-Based Asset Pricing: Empirical Tests," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 799-906, Elsevier.
    6. Tobias Adrian & Joshua Rosenberg, 2008. "Stock Returns and Volatility: Pricing the Short‐Run and Long‐Run Components of Market Risk," Journal of Finance, American Finance Association, vol. 63(6), pages 2997-3030, December.
    7. Stefano Gubellini, 2014. "Conditioning information and cross-sectional anomalies," Review of Quantitative Finance and Accounting, Springer, vol. 43(3), pages 529-569, October.
    8. Cooper, Michael J. & Gubellini, Stefano, 2011. "The critical role of conditioning information in determining if value is really riskier than growth," Journal of Empirical Finance, Elsevier, vol. 18(2), pages 289-305, March.
    9. Turan G. Bali & Nusret Cakici & Yi Tang, 2009. "The Conditional Beta and the Cross‐Section of Expected Returns," Financial Management, Financial Management Association International, vol. 38(1), pages 103-137, March.
    10. Boguth, Oliver & Carlson, Murray & Fisher, Adlai & Simutin, Mikhail, 2011. "Conditional risk and performance evaluation: Volatility timing, overconditioning, and new estimates of momentum alphas," Journal of Financial Economics, Elsevier, vol. 102(2), pages 363-389.
    11. Gagliardini, Patrick & Ossola, Elisa & Scaillet, Olivier, 2019. "A diagnostic criterion for approximate factor structure," Journal of Econometrics, Elsevier, vol. 212(2), pages 503-521.
    12. Stefan Nagel, 2013. "Empirical Cross-Sectional Asset Pricing," Annual Review of Financial Economics, Annual Reviews, vol. 5(1), pages 167-199, November.
    13. Vendrame, Vasco & Guermat, Cherif & Tucker, Jon, 2018. "A conditional regime switching CAPM," International Review of Financial Analysis, Elsevier, vol. 56(C), pages 1-11.
    14. Cochrane, John H., 2005. "Financial Markets and the Real Economy," Foundations and Trends(R) in Finance, now publishers, vol. 1(1), pages 1-101, July.
    15. Da, Zhi & Guo, Re-Jin & Jagannathan, Ravi, 2012. "CAPM for estimating the cost of equity capital: Interpreting the empirical evidence," Journal of Financial Economics, Elsevier, vol. 103(1), pages 204-220.
    16. Boons, M.F., 2014. "Sorting out commodity and macroeconomic risk in expected stock returns," Other publications TiSEM 1ebdac58-bf37-499d-8835-1, Tilburg University, School of Economics and Management.
    17. Maio, Paulo & Santa-Clara, Pedro, 2012. "Multifactor models and their consistency with the ICAPM," Journal of Financial Economics, Elsevier, vol. 106(3), pages 586-613.
    18. Ravi Jagannathan & Zhenyu Wang, 2002. "Empirical Evaluation of Asset‐Pricing Models: A Comparison of the SDF and Beta Methods," Journal of Finance, American Finance Association, vol. 57(5), pages 2337-2367, October.
    19. Tobias Adrian & Erkko Etula, 2010. "Funding liquidity risk and the cross-section of stock returns," Staff Reports 464, Federal Reserve Bank of New York.
    20. Committee, Nobel Prize, 2013. "Understanding Asset Prices," Nobel Prize in Economics documents 2013-1, Nobel Prize Committee.

    More about this item

    Keywords

    Asset Pricing; Bayesian Learning; CAPM Anomalies;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General

    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:hal:wpaper:hal-00587579. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.