VIX and Expected Range

Continuing on trying to fight disinformation about VIX. Everyone knows that VIX index the square root of the expected 30-day variance, and if we drop mathematical precision - 30 day expected volatility of S&P index. 

Scott Bauer, on CBO's website - "the VIX Index tells us the level of expected volatility of the S&P 500 Index for the next 30 days, with a 68% confidence level",  and you can find 100s of similar explanations around the web

 

The number 68% comes from expected frequency of 1 standard deviation of normal distribution, and is of course, grossly incorrect, and I will explain why. 

While the Black-Scholes formula assumes normality of returns, this is not true of the VIX. Variance is variance but distribution is not assumed to be normal. And if you look at the returns, they are far far from normal. 

I took 21 trading day returns of SPX index, and normalized them by monthly VIX ( VIX / 100 / sqrt(252/21)  ) 

 

 These normalized returns have kurtosis over 9 ( excess kurtosis over 6 ) with long left tail. These tail affect intervals not only for 99th percentile, but closer to the center as well. The chart below overlays normal distribution for comparison.

Instead of 68%, +/- 1 VIX / sqrt(252/12) happens 85% of the time and

instead of 95%, +/- 2 VIX / sqrt(252/12) happens 99% of the time!

Please keep in mind these numbers while trading! You may be grossly underestimating your risks! 

Two important events happened since the last time I posted. First - happy belated thanksgiving to all the readers from USA. As an American I celebrate with you, and as a Ukrainian I am grateful for all the military help from the USA. Thanks to all the readers - from the US and other countries, who have called your political representatives to support Ukraine. 

The second event is the 90th anniversary of Holodomor. About 100 years ago independent Ukraine was attacked by Soviet Russia, and lost, which lead to 70 years of our occupation. To squash any resistance, and desire for independence russians engineered a famine, forcefully confiscating entire harvests, stored food, seeds, and lifestock. In the years 1922-1923 millions of Ukrainians died from starvation, while Moscow flourished and sold confiscated food to other countries.

The photo above is the memorial in DC, near Union station. The text reads: Holodomor 1932-1933. In memory of millions of innocent victims of a man-made famine in Ukraine, engineered and implemented by Stalin's totalitarian regime

All Ukrainians have heard stories from our grandparents, or great-grandparents about those terrible years. During the time of USSR russians have destroyed most of holodomor-related archival documents, falsified population statistics, and executed people for talking about the hunger. Currently russian federation continues to deny holodomor saying there was a world-wide hunger that year. This is just as ridiculous and offensive as someone saying that 9/11 was not a terrorist attack because ... other buildings around the world were also demolished in 2001.