This is not a post to correct some abstract mathematical technicality, or a semantic point. Rather I hope to shed some light on widespread mis-estimation of important risk metric that I often see on the internet. For example this double-decker of ignorance popped up on my twitter feed today.
VIX as you know is an annualized measure and in order to calculate an expected daily move - that is from one trading day to another, one should use trading day count convention, and sqrt(1/252) - not 365 - as a factor.
sqrt(2/pi) ~ 0.8 is the multiplier to get the average absolute daily return, and here the author is correct.
However the range of a random walk is double that amount, 2 * sqrt(2/pi) ~ 1.6 , and in our case over 3%
Lower than 5% range we saw in S&P today, but the difference is far less dramatic than the tweet suggests.
Traders, pay attention to numbers and formulas you use in your trading. Mistakes can costs you money!
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