For example, certain Mark Bail provides us with the following gem of ignorance here
To convert VIX from annual to monthly volatility, one needs to divide not by 12, but by square root of 12. Likewise, if you want to find daily volatility, don't divide by 252, but by √252 ≈ 16. So in Mr Bail's example above, expected monthly return volatility of S&P 17.83 / √12 = 5.14%, and monthly price volatility 5.14% * 1240.14 = $63. Daily volatility is 1.12%, or $13.92.
As I wrote here, expected range of a random walk is 2 * √(2/π) ≈ 1.6 times the volatility. Therefore expected range for S&P for the month is 1.6 * 5.14% = 8.21%, or $101.85. Expected daily range is 1.79%, or $22.22. Expected monthly high, and low come out to $1291.06, and $1189.21. Please note the magnitude of difference between Mark Bail's forecast and mine - his expected range for the month is smaller than my daily range!!!
Now let's compare these predictions using historical data... After I wrote the previous sentence I tried to figure out when the article was written. There is no date on the article, the date that is referenced in the paragraph above is "June 19", however I could not any such date on which S&P and VIX closed at the levels reported in the article. I really do not know if the author just made a mistake or simply confabulated the numbers.
What I did find is that VIX happened to close at 17.83 on May 30th, 2008, so for comparison purposes I will use that date, dealing only with percent forecasts, since S&P level on that day differs significantly from the one in the article.
During the calendar month from 5/30/2008 to 6/30/2008 S&P index had a daily return volatility of 20.44% (annualized), which is a bit higher than the VIX, but not radically so. That month S&P had an open of 1400.38, high 1404.46, low 1272, closing at 1280. The range (1404.46-1272)/1400.38 = 9.4%, is much higher than 1.49% reported in the article, and much closer to my calculation expected range of 8.21%. Make your own conclusions from here.