A time-scale analysis of systematic risk: wavelet-based approach

The paper studies the impact of different time-scales on the market risk of individual stock market returns and of a given portfolio in Paris Stock Market by applying the wavelet analysis. To investigate the scaling properties of stock market returns and the lead/lag relationship between them at different scales, wavelet variance and crosscorrelations analyses are used. According to wavelet variance, stock returns exhibit long memory dynamics. The wavelet cross-correlation analysis shows that comovements between stock returns are stronger at higher scales (lower frequencies); scales corresponding to period of 4 months and longer, i.e. scales 7 and 8. The wavelet analysis of systematic risk shows that all individual assets and the diversified portfolio have a multi-scale behavior, which indicates that the systematic risk measured by Beta in the market model is not stable over time. The analysis of VaR at different time scales shows that risk is more concentrated at higher frequencies dynamics (lower time scales) of the data.