Estimation du Beta Tempo-fréquentiel de la Droite de Marché-Une approche par les ondelettes continues-

MESTRE, Roman and TERRAZA, Michel (2017): Estimation du Beta Tempo-fréquentiel de la Droite de Marché-Une approche par les ondelettes continues-.

Abstract

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.

• Item Type: MPRA Paper
• English Title: Time-Frequency varying Beta Estimation -A continuous wavelets approach-
• Language: French
• Keywords: CAPM; Continuous Wavelets ; Wavelets Coherence ; Time-Frequency varying Betas
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C58 - Financial Econometrics; G - Financial Economics > G1 - General Financial Markets > G11 - Portfolio Choice ; Investment Decisions; G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates

References

Auth C.,Continuous Wavelet Transform and Wavelet Coherence- Implementation and Application to the Diversification Analysis of Hedge Funds Returns, 2013.

Black F. and Jensen M. and Scholes M., The Capital Asset Pricing Model : Some Empirical Test ; Studies in the Theory of Capital Markets, M. Jensen ed., New York : Praeger Publishers, 1972, pp 79-121.

Bekiros S., Nguyen D.K. and Uddin G.S, On time scale behavior of equity commodity links : implications for portfolio management, Journal of International Financial Market Institutions and Money, vol 41, 2016, pp 79-121.

Bollerserv T., Engel R and Wooldridge J. A capital asset pricing model with time-varying covariances, Journal of Political Economic, vol 96, issue 11, 1988, pp 116-131.

Bos T. and Newbold P., An empirical investigation of the possiblity of stochastic systematic risk in the market model, Journal of Business, vol 57, issue 1, 1984, pp 37-41.

Daubechies I., Ten lectures on wavelets, Conference Series of Applied mathematics in Philadelphia, Society for industrial and applied mathematics, 1992.

Groenwold N. and Fraser P., Time-Varying Betas and macroeconomic influences, Discussion Paper 97.09, 1997.

Grossmann A. and Morlet J., Decomposition of Hardy functions into square integrable wavelets of constant shape, SIAM Journal on mathematical analysis, vol 15, issue 4, 1984, pp 723-736.

Fabozzi F.J, Francis J.C, Beta as a random coefficient, Journal of Financial and Quantitative Analysis, vol 3, 1978, pp 101-116.

Brooks R., Fa_ R. and McKenzie M. Time-varying beta risk for australian industry portfolio : a comparison of modelling techniques, Australian Journal of Managment, vol 23, issue 1, 1998, pp 101-116.

Fama E. and French K., The Cross-Section of Expected Stock Returns , Journal of Finance, vol 47, issue 2, 1992, pp 427-465.

Farge M., Wavelets transforms and their applications to turbulence, Annual Review of fluid Mechanics, vol 47, issue 2, 1992, pp 427-465.

Gençay R. and Selçuk F. and Whitcher B., Multiscale systematic risk,Journal of internationnal Money and Finance, vol 24, 2005, pp 55-70.

Lau K.M Weng H., Climate Signal detection using Wavelet transform :How to make a time series sing., Bulletin of the American Meteorological Society, vol 76, issue 12 1995, pp 2391-2402.

Mallat S., A Theory for Multiresolution Signal Decomposition : The Wavelet Representation, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol 11, issue 7, july 1989.

Mallat S., Une exploration des signaux en ondelettes, Ecole polytechnique, 2009.

Mallat S., Wavelet tour of signal processing : the sparse way, AcademicPress, 2009.

Mestre R. and Terraza M., Time-frequencies analysis of CAPM-Application to the CAC 40, Accepted for publication in Managing Global Transitons Internationnal Research Journal, 2017.

Mestre R. and Terraza M., Multidimensional Time-Frequency Analysis of the CAPM, ITISE 2017 Conference Proceedings, Issue 2, pp 1187-1200, 2017.

Meyer Y., Jaffard S.,Rioul O., L'analyse par ondelettes, 1986.

Sharpe W. , Capital Asset Prices : a Theory of Market Equilibrium Under risk, Journal of Finance, Canberra. ed. Western Australia : Modelling and Simulation Society of Australia and New Zealand Inc. , vol 19, issue 3, Sept 1964, pp 425-442.

Torrence C. Compo G.P., A pratical guide to wavelet analysis, Bulletin of the American Meteorological Society, vol 79, issue 1, 1998, pp 61-78.

Torrence C. Webster P.J., I nterdecadal Changes in the ENSO-Monsoon System, Journal of Climate, vol 12, 1999, pp 2679-2690.