The VIX, Rule of 16 and Realized Volatility
Two days ago, in Rule of 16 and VIX of 40, I discussed the Rule of 16 in terms of translating the (annualized) VIX number into expectations for future daily realized volatility in the S&P 500 index.
That post drew several interesting comments, which unfortunately they now reside somewhere in Disqus limbo. In one of the comments, rafaminos offered the following thoughts:
It seems that VIX is on average higher that realized volatility (based on daily returns over 30 days). I also tried to shift VIX 30 days in advance and the conclusion is the same. Since the historical ratio of the two is 1.45 (VIX/realized volatility), should not we infer from this past relationship that the implied realized volatility is more like 30 (45/1.45), meaning a 2% change 1/3 of the time?
My reply appears to be somewhere in comment purgatory as well, but the essence of my response is as follows:
Over that last 20 years, I get a VIX that is about 1.40 times the SPX 20-day realized volatility. I attribute some of the discrepancy to the high demand for SPX puts as hedges, which tends to inflate the VIX relative to realized volatility (and immediately suggests some strategic implications vis-a-vis short SPX puts strategies.)
So...given that a VIX of 32 is about 1.4x SPX realized volatility and 32/1.4 = 22.9 and 32*1.4 = 44.8, based on the historical evidence, I would conclude that:
1) VIX of 32 – 1/3 of the time the SPX is expected to have a daily change of at least 2%, but...2a) VIX of 32 – 1/3 of the time the SPX will (based on historical data) have a daily change of at least 1.4%
2b) VIX of 45 – 1/3 of the time the SPX will (based on historical data) have a daily change of at least 2%
