IDEAS home Printed from https://ideas.repec.org/p/fip/fednsr/193.html
   My bibliography  Save this paper

Learning about beta: time-varying factor loadings, expected returns, and the conditional CAPM

Author

Listed:
  • Tobias Adrian
  • Francesco Franzoni

Abstract

We complement the conditional capital asset pricing model (CAPM) by introducing unobservable long-run changes in risk factor loadings. In this environment, investors rationally ?learn? the long-run level of factor loading by observing realized returns. As a direct consequence of this assumption, conditional betas are modeled using the Kalman filter. Because of its focus on low-frequency variation in betas, our approach circumvents recent criticisms of the conditional CAPM. When tested on portfolios sorted by size and book-to-market ratio, our learning-augmented conditional CAPM fails to be rejected. ; Original title: Learning about beta: a new look at CAPM tests.

Suggested Citation

  • Tobias Adrian & Francesco Franzoni, 2008. "Learning about beta: time-varying factor loadings, expected returns, and the conditional CAPM," Staff Reports 193, Federal Reserve Bank of New York.
  • Handle: RePEc:fip:fednsr:193
    as

    Download full text from publisher

    File URL: https://www.newyorkfed.org/medialibrary/media/research/staff_reports/sr193.pdf
    Download Restriction: no

    File URL: https://www.newyorkfed.org/medialibrary/media/research/staff_reports/sr193.html
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    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. 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.
    8. 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.
    9. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    10. Campbell, John Y, 1996. "Understanding Risk and Return," Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 298-345, April.
    11. 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.
    12. Schwert, G William & Seguin, Paul J, 1990. "Heteroskedasticity in Stock Returns," Journal of Finance, American Finance Association, vol. 45(4), pages 1129-1155, September.
    13. 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.
    14. Tano Santos & Pietro Veronesi, 2004. "Conditional Betas," NBER Working Papers 10413, National Bureau of Economic Research, Inc.
    15. 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.
    16. 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.
    17. John Y. Campbell & Tuomo Vuolteenaho, 2004. "Bad Beta, Good Beta," American Economic Review, American Economic Association, vol. 94(5), pages 1249-1275, December.
    18. Allan G. Timmermann, 1993. "How Learning in Financial Markets Generates Excess Volatility and Predictability in Stock Prices," The Quarterly Journal of Economics, Oxford University Press, vol. 108(4), pages 1135-1145.
    19. 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.
    20. 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.
    21. Pietro Veronesi & Tano Santos, 2004. "Conditional Betas," 2004 Meeting Papers 24, Society for Economic Dynamics.
    22. 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.
    23. 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.
    24. Shanken, Jay, 1990. "Intertemporal asset pricing : An Empirical Investigation," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 99-120.
    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. 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.
    27. Barberis, Nicholas & Shleifer, Andrei, 2003. "Style investing," Journal of Financial Economics, Elsevier, vol. 68(2), pages 161-199, May.
    28. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    29. 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.
    30. 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.
    31. Ravi Bansal & Amir Yaron, 2004. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," Journal of Finance, American Finance Association, vol. 59(4), pages 1481-1509, August.
    32. 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.
    33. 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.
    34. 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.
    35. 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.
    36. 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.
    37. Ľuboš Pástor, 2000. "Portfolio Selection and Asset Pricing Models," Journal of Finance, American Finance Association, vol. 55(1), pages 179-223, February.
    38. 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.
    39. 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.
    40. Robert B. Barsky & J. Bradford De Long, 1993. "Why Does the Stock Market Fluctuate?," The Quarterly Journal of Economics, Oxford University Press, vol. 108(2), pages 291-311.
    41. 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.
    42. repec:hrv:faseco:30747193 is not listed on IDEAS
    43. 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.
    44. 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.
    45. 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.
    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. Ang, Andrew & Chen, Joseph, 2007. "CAPM over the long run: 1926-2001," Journal of Empirical Finance, Elsevier, vol. 14(1), pages 1-40, January.
    3. 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.
    4. John Y. Campbell, 2000. "Asset Pricing at the Millennium," Journal of Finance, American Finance Association, vol. 55(4), pages 1515-1567, August.
    5. 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.
    6. 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.
    7. 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.
    8. Tim Bollerslev & Sophia Zhengzi Li & Viktor Todorov, 2014. "Roughing up Beta: Continuous vs. Discontinuous Betas, and the Cross-Section of Expected Stock Returns," CREATES Research Papers 2014-48, Department of Economics and Business Economics, Aarhus University.
    9. Stefan Nagel, 2013. "Empirical Cross-Sectional Asset Pricing," Annual Review of Financial Economics, Annual Reviews, vol. 5(1), pages 167-199, November.
    10. 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.
    11. Bali, Turan G., 2008. "The intertemporal relation between expected returns and risk," Journal of Financial Economics, Elsevier, vol. 87(1), pages 101-131, January.
    12. Stefano Gubellini, 2014. "Conditioning information and cross-sectional anomalies," Review of Quantitative Finance and Accounting, Springer, vol. 43(3), pages 529-569, October.
    13. Gagliardini, Patrick & Ossola, Elisa & Scaillet, Olivier, 2019. "A diagnostic criterion for approximate factor structure," Journal of Econometrics, Elsevier, vol. 212(2), pages 503-521.
    14. 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.
    15. Vendrame, Vasco & Guermat, Cherif & Tucker, Jon, 2018. "A conditional regime switching CAPM," International Review of Financial Analysis, Elsevier, vol. 56(C), pages 1-11.
    16. Li, Yan & Yang, Liyan, 2011. "Testing conditional factor models: A nonparametric approach," Journal of Empirical Finance, Elsevier, vol. 18(5), pages 972-992.
    17. 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.
    18. 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.
    19. 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.
    20. Gregory Connor & Lisa R. Goldberg & Robert A. Korajczyk, 2010. "Portfolio Risk Analysis," Economics Books, Princeton University Press, edition 1, number 9224.

    More about this item

    Keywords

    Investments; Capital assets pricing model;

    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:fip:fednsr:193. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/frbnyus.html .

    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: (email available below). General contact details of provider: https://edirc.repec.org/data/frbnyus.html .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.