How Does Systematic Risk Impact Stocks? A Study On the French Financial Market

From the CAC40 French stock index, we induce the implied market factor’s level through the inversion of a closed form pricing formula for European calls on the CAC40. For this purpose, we assume that the CAC40 index is a disturbed observation of the actual market factor, the market factor’s diffusion following a geometric Brownian motion. All the assumptions prevailing in a Black & Scholes (1973) world are assumed to hold. Based on daily data, the results show that the level of the implied market factor and its instantaneous return’s volatility are leptokurtic distributed. Having a proxy for the systematic risk, we also study the impact of the implied market factor on a basket of French assets. First, we compute correlations of assets’ returns with the return of the implied market factor, and realize as well a VAR study and a Granger causality test. Second, we estimate regressions of French assets’ returns on the return of the implied market factor. Then, we characterize the prevailing relationship between the weekly rolling volatility of the return of the implied market factor and weekly rolling volatilities of the French assets returns. These two studies lead to mitigated results.