Multiscale Fama‐French model: application to the French market

Purpose - The purpose of this paper is to discuss a multiscale pricing model for the French stock market by combining wavelet analysis and Fama‐French three‐factor model. The objective is to examine the relationship between stock returns and Fama‐French risk factors at different time‐scales. Design/methodology/approach - Exploiting the scale separation property inherent to the maximal overlap discrete wavelet transform, the data set are decomposed into components associated with different time‐scales. This wavelet‐based decomposition scheme allows the three Fama‐French models to be tested over different investments periods. Findings - The obtained results show that the explanatory power of the Fama‐French three‐factor model becomes stronger as the wavelet scale increases. Besides, the relationship between the portfolio returns and the risk factors (i.e. the market, size and value factors) depends significantly upon the considered time‐horizon. Practical implications - The proposed methodology offers investors the opportunity to construct dynamic portfolio management strategies by taking into account the multiscale nature of risk and return. Moreover, it gives a new insight to fund rating and fund selection issues in relation to heterogeneous investments periods. Originality/value - The paper uses wavelets as a relatively new and powerful tool for statistical analysis that allows a new understanding of pricing models. The paper will be of interest not only for academics in the field of asset pricing but also for fund managers and financial market investors.