This 1st Chart shows Volatility Research correlation Trend Line of %VXX vs %S&P 500 Index for year 2011.
R squared is 0.76. Slope of the trend line is minus 2.78, meaning that %VXX increases 2.78 times more than %S&P 500 Index decreases, and vice versa.
For practical purposes, it's easy to remember
(%VXX) = (-3) * (%S&P_ 500)
There were 252 daily-close data points for 2011 in this chart.
The chart above also shows that divergence of data from the trend line increases for %S&P 500 >+ 2 and <-2.
So, we decided to see if 2 trend lines might be, at least, better visual fits to the data: one for + %VXX and one for - %VXX.
This 2nd chart shows these 2 trend lines, + %VXX green, - %VXX red, and the trend line from all data in the 1st chart above as a dashed blue line.
The red line is definitely a better visual fit for - %VXX.
The green line is about 1% above the blue line and with the same slope.
For practical purposes when %VXX is negative, it's easy to remember
(%VXX) = (-1.5) * (%S&P_500 + 1)
(%VXX) = (-3 ) * (%S&P_ 500 + 1) / (2)
and use the 1st equation when %VXX is positive.
These 2 new trend lines show that a non-linear regression might produce a better correlation that any of these trend lines.
Data beneath the error bars are about 2/3rds of the data, and data outside the error bars are about 1/3rd of the 252 data points for 2011 -- >~+5% VXX and <~ -5% VXX.
This following chart shows %VXX vs %S&P 500 sorted by ascending %S&P 500 for year 2011.
The following chart shows a correlation close to our first chart above but includes data from Jan 30, 2009 thru Mar 8, 2012.
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