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Estimation du Beta Tempo-fréquentiel de la Droite de Marché-Une approche par les ondelettes continues-
[Time-Frequency varying Beta Estimation -A continuous wavelets approach-]


  • MESTRE, Roman
  • TERRAZA, Michel


The Beta coefficient theorized by the CAPM is estimated by the Market Line. By hypothesis, the Beta is stable over time but empirical studies on it volatility don't confirm this fact. One of them is related to with agent heterogeneity hypothesis. In this paper; we study this hypothesis by continuous wavelets decomposition of the market line components. We use the wavelet Coherence to calculate a time-frequency Beta. We apply this methodology on three French listed stocks (AXA-LVMH-ORANGE) with different OLS beta for the daily period 2005-2015. We show that the coherence and the time-frequency Betas improve our understanding of the equity characteristics and nature according to their time and frequency dynamics. AXA and LVMH have globally an high coherence with the market whereas ORANGE coherence is low (whatever frequencies). These results can affect the time-frequency betas values. By analysing the betas we see different evolutions and dynamics which can be considered by portfolio managers to optimize their investment horizon. The continuous wavelets is a powerful tool for emphasize the time-frequency instabilities of betas. The hypothesis of heterogeneity of agents has an impact on systematic risk estimations and need to be considered in financial calculations.

Suggested Citation

  • MESTRE, Roman & TERRAZA, Michel, 2017. "Estimation du Beta Tempo-fréquentiel de la Droite de Marché-Une approche par les ondelettes continues-
    [Time-Frequency varying Beta Estimation -A continuous wavelets approach-]
    ," MPRA Paper 86335, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:86335

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    References listed on IDEAS

    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. R.W. Faff & R.D. Brooks, 1998. "Time-varying Beta Risk for Australian Industry Portfolios: An Exploratory Analysis," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 25(5&6), pages 721-745.
    3. Fabozzi, Frank J. & Francis, Jack Clark, 1978. "Beta as a Random Coefficient," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(01), pages 101-116, March.
    4. Bekiros, Stelios & Nguyen, Duc Khuong & Uddin, Gazi Salah & Sjö, Bo, 2016. "On the time scale behavior of equity-commodity links: Implications for portfolio management," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 41(C), pages 30-46.
    5. repec:mgt:youmgt:v:16:y:2018:i:2:p:141-157 is not listed on IDEAS
    6. 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.
    7. 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.
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    More about this item


    CAPM; Continuous Wavelets ; Wavelets Coherence ; Time-Frequency varying Betas;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates


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