Revisiting Fama-French’s Asset Pricing Model with an MCB Volatility Risk Factor

Since the introduction of VIX to measure the spot volatility in the stock market, VIX and its futures have been widely considered to be the standard of underlying investor sentiment. We introduce the term structure of VIX to Fama-French’s Asset Pricing Model. The magnitude of contango or backwardation (MCB volatility risk factor) derived from VIX and VIX3M identifies underlying configurations of investor sentiment. The sensitivities to this timing indicator will significantly relate to returns across individual stocks or portfolios. 

The term structure of VIX futures implies the overall investors’ risk sentiment into the future. As suggested by CBOE, using the VIX3M and VIX indices together provides useful insight into the term structure of VIX futures.  Although some theoretical research has been done on the importance of the VIX and its applications to investment and portfolio management strategies, there is little research done to examine the effect of VIX relativity (VIX3M and VIX) on individual or portfolio stock returns.

This paper focuses on the statistical inference of three defined MCB risk factors when cross-examined with Fama-French's five factors: the market factor Rm-Rf, the size factor SMB, the value factor HML, the profitability factor RMW, and the investing factor CMA. As the first study adding the magnitude of contango or backwardation to asset pricing models, our cross-regression analysis among the six factors indicates that the addition of an MCB factor indeed improves the explanatory power for the variations of the total market return (less Rf) and the intercept gets smaller but is still statistically significant. It is also true once the alternative and more in-time HML-Dev factor (Asness, 2014) is applied in the cross-regression analysis.

In addition, the MCB factor is found to have a strong and negative correlation with the value factor HML or HML-Dev, which implies that under a more relaxed and complacent market, derived from an increasing MCB factor, value portfolio usually underperforms to a greater extent. We also find that the investing factor CMA sometimes displays a significant and positive relationship with the new MCB factor, which might be counter intuitive. However, given an increasing MCB factor from the low end may indicate a recovery of market volatility sentiment from an extreme panic mood, e.g., (VIX3M/VIX)t increases from 0.70 to 0.80. Such a significant and positive explanatory relationship may not be surprising since less invested firms usually outperform under such scenarios when the market is still stressed, though with relatively less panic. Certainly, if an increasing (VIX3M/VIX)t, which implies an increasing MCB risk factor, stems from the high end (e.g., from 1.20 to 1.30), a negative correlation will prevail. It is noticeable, though, that such a significant relationship does not exist if the HML-Dev factor is used in cross-examinations. Therefore, more detailed cross-sectional and firm-level analysis is needed in the future to shed more light on the implications of an MCB risk factor in asset pricing models.

Also, in this research, robustness checks are performed on a daily basis using a daily MA(50) instead of a monthly MA(20), as a daily MA(50) is the benchmark of moving average for daily trends. The results from the daily cross-examinations are largely similar with the monthly results, except that there are significant negative correlations between the MCB factor and the profitability factor RMW, implying that value firms tend to underperform their less profitable peers in an increasingly calm market (an increasing MCB risk factor) due to their lower growth potentials.