Evidence on aggregate volatility risk premium for the French stock market

Purpose The purpose of this paper is to examine alternative six- and seven-factor equity pricing models directed at capturing a new factor, aggregate volatility, in addition to market, size, book to market, profitability, investment premiums of the Fama and French (2015) and Fama and French's (2018) aggregate volatility augmented model. Design/methodology/approach The models are tested using a time series regression and Fama and Macbeth's (1973) methodology. Findings The authors show that both six- and seven-factor models best explain average excess returns on the French stock market. In fact, the authors outperform Fama and French's (2018) model. The authors use sensitivity of aggregate volatility of a stock VCAC as a proxy to construct the aggregate volatility risk factor. The spanning tests suggest that Fama and French's (1993, 2015, 2018) and Carhart's (1997) models do not explain the aggregate volatility risk factor FVCAC. The results show that the FVCAC factor earns significant alpha s across the different multifactor models and even after controlling for the exposure to all the other in Fama and French's (2018) model. The asset pricing tests show that it is systematically priced. In fact, the authors find a significant and negative (positive) relation between the aggregate volatility risk factor and the excess returns in the French stock market when it is rising (falling), in addition, periods with downward market movements tend to coincide with high volatility. Originality/value The authors contribute to the related literature in several ways. First, the authors test two new empirical six- and seven-factor model and the authors compare them to Fama and French's (2018) model. Second, the authors give new evidence about the VCAC, using it for the first time to the authors' knowledge, to construct a volatility risk premium.