Review Fear and the Fama-French Factors

Robert B. Durand, Dominic Lim and J. Kenton Zumwalt (2011) ‘Fear and the Fama-French Factors’, Financial Management, (2), p. 409.


The volatility Index (VIX) also referred to as the ‘investor fear gauge’ estimates the expected market volatility of the S&P 500 over the next 30 days. The changes in volatility ignites different actions of the investors, due to changes in the risks. The investors tend to ‘fly to quality’ when their expected risk increases. Robert, Dominic and Zumwalt (2011) investigated the investors total risk expectations based on VIX.

Data and Methodology

Fama and French (1993) three-factor model was developed as an extension of the capital asset pricing model (CAPM). Incorporating the size factor and value factor, this model has become significantly influential in the corporate finance. The fourth factor, momentum factor (Carhart 1997) has been added to evaluate the asset returns. To evaluate the market volatility using VIX, the Fama-French model is applied with the momentum factor, modeled as below:


The first factor is the market risk premuim which is related to the variance of the market. The timely variant volatility of the market returns affects the market risk premium. The second factor is the size factor (SMB), where firms with lower market capitalization has a higher-risk adjusted returns as compared to those with higher market capitalization. The third factor is the value factor (HML) which spans the value-to-growth premium. The ‘value stock are those having high book value of equity to their capitalization, while ‘growth’ are those with lower ratio. The fourth factor is the momentum factor (WML) which adds the cross-sectional returns explanation.

Results Fama & French factors

When the total riskexpectation changes, as captured by change in VIX, it affect the four risk premia of the model. The study used S&P 500 data from February 1, 1993 to July 30, 2007. The results indicated a negative correlation between market risk premium and change in VIX, and between market risk premium and HML, SMB and WML. The high negative correlation between market risk premium HML indicates flight-to-equity. The VAR results indicated that changes in VIX drives the changes observed in all the risk premia. Overall, the results indicated that changes in VIX affects all the risk premia, while the market rism premium, the SMB and HML affects the change in VIX. The impulse response function of change in VIX on HML, SMB and WML shows ‘flight to quality’ effect. The variance decomposition results indicated that change in VIX and SMB are important in HML decomposition. SMB, WML and change in VIX variations are greatly explained by their own variation.

Conclusions Fear and the Fama-French Factors

In conclusion, the risk premia (market risk premium, WML, HML and SMB) varies with the changes of VIX. There is a negative relationship between the market risk premium and the change in VIX. The changes in VIX leads the HML and WML to the theories of investors flying to quality as the expected risk increases. Therefore, the market volatility expectations as indicated by VIX influences equities through the risk premia. The fear and confidence of the investors as captured by VIX affects the securities through the changes of the risk premia factors.