Time-Frequency Analysis of CAPM: Application to the CAC 40

Abstract

The market line estimation implicitly assumes that its parameters are constant over time supposing whatever the investment horizon, the investors have a similar behaviour. In this paper,we discuss this hypothesis using the technique of wavelets. First, we verify the expected result concerning the statistical weaknesses of market line and the high volatility of its parameters. Second, we use the wavelets to estimate the frequency betas. We show that the classic beta (estimated with OLS) considers a short-run beta. We propose a methodology based on time-frequency analysis that leads to an overview of equities characteristics useful to portfolio managers.