A Visualization of VIX Implied S&P 500 Movement

U.S. Equities have taken a hit in the first four weeks of October with the S&P 500 declining as much as -9%. The VIX has risen ~108% this month up to 25.23 as of the close yesterday.

As we have noted previously, a VIX of 25 seems a bit low given the magnitude of the daily movements. Below you can see daily S&P 500 returns and their corresponding VIX values on the big sell-off days 10/10/18 (-3.3%) and 10/24/18 (-3.1%).

Based on this historical data, we could reasonably expect VIX to be trading in the 30-45 range. However, the market is apparently not expecting large rallies over the next month.

Recall that the VIX is an expression of expected annualized market volatility over the next 30 days.  A VIX of 25 means annualized move (up or down) of 25%. That value can be converted to monthly terms by dividing by the square root of 12, which yields an expected dispersion of the S&P 500 of 7.2%, or an implied range of 2463-2848.

We can convert that to a weekly and daily basis as well (divide by the square root of 52) to get a weekly dispersion of 3.5%, giving an implied range of 2558 to 2748 from yesterday's close. Interestingly, the 1-week dispersion target for $SPX based on $VIX after Oct 11th was 2820 (it came as high as 2817).

So perhaps $VIX isn't "too low" based on the magnitude of moves. Instead, it's more that investors don't expect a swift rally. Charting out the implied dispersion we can visualize the market's short-term expectations:

We can expect VIX to adjust accordingly as S&P 500 rises and falls. I'll provide updates within the Twitter thread on the subject.

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