We have talked about the VIX Index before, and have shown that it is predictive of future VIX levels, but is it predictive of future equity returns? First, we’ll see if there is a relationship between the VIX and S&P 500 price returns on the same day. The below analysis uses data from 1/1/1990 through 3/31/2018, with both daily and monthly periodicity.
Graph 1 shows the relationship between the S&P 500’s return and the VIX’s percentage change on the same day. An example data point would be the VIX falling from 20 to 18 (a 10% decrease) and the S&P 500 return being up 1.2% on the same day. As the chart shows, while the relationship might not be linear, a linear model has decent explanatory power (R2 of 48%). However, the VIX is already quoted in percentage points, so a 5 point increase in the VIX represents an expected increase of 5 percentage points of future volatility, irrespective of VIX going from 15 to 20 or 40 to 45. Therefore, using the change in the VIX level rather than the percentage change may make more sense.
Graph 2 shows a stronger linear relationship between the S&P 500’s return and the VIX’s level change rather than the VIX’s percentage change (e.g., falling from 20 to 18 results in a -2 v. -10%) on the same day (R2 of 62% v. 48%, respectively). The relationship also holds using monthly data. Therefore, it appears the change in the VIX level, measured in points, is a better explanatory variable for same day (or month) S&P 500 returns than the percentage change in VIX.
We’ve established that there is a relationship between a day’s (or month’s) S&P 500 return and a change in the VIX during the same period. However, a more interesting (i.e., potentially profitable) phenomena would be if VIX changes were predictive of future S&P 500 Index returns. We will be evaluating if the VIX’s change (level and percentage) from t-1 to t0 is predictive of S&P 500 returns from t0 to t+1.
As can be seen from the above scatter plots, there is no relationship between the next day’s S&P 500 return and the VIX’s level’s change. Nor is there a relationship between next month’s S&P 500 return and the VIX’s level change from the previous month. This also holds if measured on the VIX’s percentage change instead of the VIX’s level change.
How about the current VIX level? Is that predictive of next month’s return?
Nope, it does not seem to be predictive. But, what you can say from Graph 7 is that it appears there is a relationship between the current VIX level (the expected future volatility) and the range (or width of the distribution) of future S&P 500 returns, providing more evidence that current expected volatility is predictive of future volatility.
While there is a relationship between the current period’s (day or month) VIX change (level or percentage) and the S&P 500 return; the change in VIX has no predictive power on next period’s S&P 500 return. However, volatility is predictive of volatility.
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