Correlation VXX vs S&P 500, Year 2011

July 12, 2012

Click chart to enlarge 

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.  

qPath (see also and also and also and also at end)
digit 1 today's close Quad
digit 2 yesterday's close Quad
digit 3 close Quad 2 days ago
digit 4 close Quad 3 days ago

The chart right shows these 2 trend lines, + %VXX green, - %VXX red, and the trend line from all data in the chart above dashed blue. The red line is definitely a better visual fit for - %VXX. The green line is about 1% above the blue line with the same slope. Click chart to enlarge These 2 new lines show that a non-linear regression would probably produce a better correlation that any of these lines.
Click chart to enlarge

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)

or

(%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.


Click to enlarge chart 

This 3rd chart shows all 2011 data overlaid with error bars of +- one standard deviation.

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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