This paper focuses on a methodology aimed at analyzing the Carhart multifactor model (Carhart, 1997) over various time horizons in the French Stock Market. The suggested approach exploits the decomposition scheme inherent to the wavelet-based Multiresolution Analysis, allowing one to investigate the time scale relationships between stock returns and risk factors. The empirical results show that the explanatory power of the wavelet-based four factor model is scale-sensitive. The market factor is highly significant over the range of time scales and positively effects intermediate and long-term investment horizons. Besides, the size factor is found to be negative for the portfolios constructed by small capitalization assets. The size risk also becomes negative for big portfolios at the largest time scale. The value proxy HML, which is rejected for the unitary (single) scale model is, however, significant over a large array of resolution levels (investment periods). Finally, it is found that the momentum factor, within the multiscale framework, has a significant impact on the expected stock returns.

Over the last 15 years, criticism addressed to the single-factor Sharpe-Lintner Capital Asset Pricing Model (CAPM) has led to the development of multifactor asset pricing models, motivated by Ross’s (1976) Arbitrage Pricing Theory (APT). The basic methodology has been to consider supplementary risk factors in addition to the systematic risk, in order to explain the expected excess returns. Fama and French (1993) propose three factors as surrogates for risk: the market, the size and the value factors. Adding a fourth factor which is the momentum anomaly, Carhart (1997) introduces an alternative multifactor pricing model.

Though these models have been the subject of theoretical and empirical investigation and have shown practical importance, they fail, however, to take into account, the tendency of investors to hold stocks over different periods of time. The reason is that classical pricing models are restricted in a single scale perspective. In this paper, we exploit the time scale localization property of wavelet functions to develop a multiscale Carhart four-factor model, aimed at analyzing the relationships between stock returns and risk factors at different investment periods within the French Stock Market.

This paper is structured as follows: First, it presents a short overview on the Carhart four-factor pricing model, followed by the delineation of wavelet techniques in time-series analysis, an introduction of the multiscale Carhart four-factor model, data description, empirical results drawn from the implementation of the single-scale and the multiscale pricing models, before arrising at the conclusion.

Financial Risk Management Journal, Multiscale Carhart Four-Factor Pricing Model, French Stock Market, Small Capitalization Assets, Asset Pricing Models, Arbitrage Pricing Theory, Empirical Investigation, Classical Pricing Models, Market Equilibrium Model, Maximal Overlap Discrete Wavelet Transform, Multiresolution Analysis, Wavelet Techniques, Investment Strategies.