Analyse Multidimensionnelle Temps-Fréquence du MEDAF

The CAPM theory provides a measure of the sensitivity of an asset to the market called the systematic risk. The Beta of equity is estimated by its market line. According to the OLS hypothesis, it is stable over time but this is not empirically verified. Many studies are in favour with this fact (Unstable Beta), and more particularly the Beta dispersion according to the frequencies which is related to the heterogeneous behaviour of agents. We can calculate the coherence and the phase between the stock's returns and those of the market over time using the wavelets method and it is also possible to visualize it. In order to confirm the correctness of the methodology, we use three French equities with different Betas (AXA, LVMH and Orange) for the period from 2005-2015 including the crisis. We show that the wavelets coherence, associated with the phase, improve our understanding and the classification of equities according to there characteristics. Our study reveal the contagion and interdependence phenomenons between the stocks and the market. The contagion effects (from the market to the stock) is principally located on the High-Frequencies whereas the interdependence effect is located on the Low-Frequencies (Long-run investment).The link between beta and coherence-phase can help the investors to choose more efficiently the time they should invest.