# The Correlation Contango-Tango

I am amazed by the CBOE implied correlation indicies' ingenuity.

We all know that a portfolio's total variance is calculated by something like

Now how about we find the implied volatility for an index and all its constituents? Once we do, we have only one unknown left to solve for - the average implied correlation coefficient which equalises the equation.

The CBOE tracks a correlation index for S&P 500 options expiring every January since 2007. I have amalgamated them all together into a linear interpolated term structure. Download here.

Maybe I should automate its generation everyday.

In any case, I haven't really looked into the implied correlation index too much before.

Just like the VIX it is mean reverting, however it does seem to be creeping up a little every year. As I always suspected in this increasingly networked world.

There are only a handful of year's data - I would love to see more a longer history - it would be a nice reflection of how the world is changing.

Usually the implied correlation index is in contango (correlation decreases as the forecast horizon gets shorter) which makes a certain amount of sense I suppose, as covariance is very similar to variance.

It's in backwardation in all the right places. When implied correlation is highest, headline grabbing information is expected to subside in the future in favour of stock specific revelations to drive prices. Therefore the correlation levels are expected to decrease in the future.