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Time-varying betas and the cross-sectional return-risk relation: evidence from the UK


  • Patricia Fraser
  • Foort Hamelink
  • Martin Hoesli
  • Bryan Macgregor


The seminal study by Fama and MacBeth in 1973 initiated a stream of papers testing for the cross-sectional relation between return and risk. The debate as to whether beta is a valid measure of risk was reanimated by Fama and French and subsequent studies. Rather than focusing on exogenous variables that have a larger explanatory power than an asset's beta in cross-sectional tests, the matrix of variances-covariances is assumed to follow a time varying ARCH process. Using monthly data from the UK market from February 1975 to December 1996, the cross-sectional return-risk relations obtained with an unconditional specification for assets' betas are compared to those obtained when the estimated betas are based on an ARCH model. The approach taken by Pettengill, Sundaram and Mathur, which allows a negative cross sectional return-risk relation in periods in which the market portfolio yields a negative return relative to the risk free rate, was also investigated. These tests are also carried out on samples pertaining to a specific month and on samples from which a particular month is removed. Results suggest that the CAPM holds better in downward moving markets than in upward moving markets hence beta is a more appropriate measure of risk in bear markets.

Suggested Citation

  • Patricia Fraser & Foort Hamelink & Martin Hoesli & Bryan Macgregor, 2004. "Time-varying betas and the cross-sectional return-risk relation: evidence from the UK," The European Journal of Finance, Taylor & Francis Journals, vol. 10(4), pages 255-276.
  • Handle: RePEc:taf:eurjfi:v:10:y:2004:i:4:p:255-276 DOI: 10.1080/13518470110053407

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    References listed on IDEAS

    1. Clare, A. D. & Priestley, R. & Thomas, S. H., 1998. "Reports of beta's death are premature: Evidence from the UK," Journal of Banking & Finance, Elsevier, vol. 22(9), pages 1207-1229, September.
    2. Nicolaas Groenewold, 1997. "Share Prices and Macroeconomic Factors," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 24(9&10), pages 1367-1383.
    3. Andrew Clare & Raymond O'Brien & Stephen Thomas & Michael Wickens, "undated". "Macroeconomic Shocks and the Domestic CAPM: Evidence from the UK Stock Market," Discussion Papers 94/10, Department of Economics, University of York.
    4. Gourieroux, Christian & Monfort, Alain, 1992. "Qualitative threshold ARCH models," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 159-199.
    5. Engel, Charles & Rodrigues, Anthony P, 1989. "Tests of International CAPM with Time-Varying Covariances," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(2), pages 119-138, April-Jun.
    6. Fama, Eugene F, 1991. " Efficient Capital Markets: II," Journal of Finance, American Finance Association, vol. 46(5), pages 1575-1617, December.
    7. 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.
    8. Pettengill, Glenn N. & Sundaram, Sridhar & Mathur, Ike, 1995. "The Conditional Relation between Beta and Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 30(01), pages 101-116, March.
    9. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
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    Cited by:

    1. Syed ali, Raza & Syed tehseen, jawaid & Imtiaz, arif & Fahim, qazi, 2011. "Validity of capital asset pricing model: evidence from Karachi stock exchange," MPRA Paper 32737, University Library of Munich, Germany.
    2. Joliet, Robert & Hubner, Georges, 2008. "Corporate international diversification and the cost of equity: European evidence," Journal of International Money and Finance, Elsevier, vol. 27(1), pages 102-123, February.
    3. Dr. Ibrahim Onour, "undated". "The Global Financial Crisis and Equity Markets in Middle East Oil Exporting Countries," API-Working Paper Series 1009, Arab Planning Institute - Kuwait, Information Center.
    4. Durand, Robert B. & Lan, Yihui & Ng, Andrew, 2011. "Conditional beta: Evidence from Asian emerging markets," Global Finance Journal, Elsevier, vol. 22(2), pages 130-153.

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    CAPM; QTARCH; return-risk relation; UK market;


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