Abstract
In this thesis, we study the relevance of using the wavelet methodology to improve the results of the Capital Assets Pricing Model (CAPM). The equation of this model, the Market Line, establishes a relationship between the returns of a stock and those of the Market. The Beta estimate of this Line provides the sensitivity of the stock to Market’s movements. This parameter is commonly used as a systematic measure of risk for classifying equities. Under the hypothesis of homogeneity of agents behaviours, the investors have same investment horizons, and therefore they estimate a similar Beta without considering their characteristics. Moreover, the Beta is commonly estimated by OLS supposing its stability over time. The various criticisms of the CAPM have led to extensions and improvements that are presented in a first chapter. On the one hand, it appears that, in the model, it is not possible to assess the dynamics of risk over time. On the other hand, it is also impossible to take into account the heterogeneity of the agents. The wavelet appreciation of the time-frequency instability of the CAPM Beta represents the heart of this research. The use of discrete wavelets, in the context of the CAPM, is a usefull methodology to study the risk in the time-frequency domain according differents investing horizons. The application to the French market with daily data from 2005 to 2015 is the main part of this research in the univariate (Chapter 2) and multivariate (Chapter 3) cases. Beta estimated by OLS and those estimated for various horizons, related to frequency decomposition, are significantly different. It is therefore possible to use this type of decomposition to extend the possibilities of risk analysis. The analysis of the time-frequency dynamics of the systematic risk is obtained by associating the Rolling Windows with the discrete wavelets. Despite these improvements, OLS- Betas do not have BLUE properties because of there are anomalies in the estimation residuals. The use of the ARMA-GARCH family processes partially corrects the Beta estimate. So, it is possible to to develop a simple correction of OLS-Beta. The approach developed in Chapter 3 includes the multivariate nature of the regression by considering the addition of explanatory variables in the equation as additional sources of risk. Oil and gold, selected according to an analysis of different works, associated with discrete frequency decompositions lead to the estimation of the Betas of a Time-Frequency Multi-Betas Model. The results confirm the differentiation of parameters across frequency bands and provide a lot of information for risk analysis. In this same chapter, we use continuous wavelets to study in a more precise way the CAPM and its robustness. In this context, the coherence and the phase specify the Equity-Market relationship as well as the weight of Systematic Risk in the total risk. We show that Equity-Market links are neither homogeneous nor unilateral as assumed by the CAPM. The intensity and the direction of the links depend on the time and are differentiated according to the frequencies. Therefore, we propose to use a time- frequency-variable estimation of Beta, which leads to numerous results and information on the time-frequency evolution of risk. This research opens up new perspectives on the evaluation of Systematic Risk and its insertion in new computational technologies, by their computing capacities, will greatly improve the interpretation of its results.