Dividend Capture Correlation with SPX

To try to get a handle on what the correlation of the dividend capture strategy is with the market, I looked at BXM and PUT, two indices created by the CBOE.

PUT

The CBOE has created several interesting indices. The buy-write index, BXM, sells the first out of the money SPX call every month and owns the index. The put-write index, PUT, sells the at the money SPX put every month and holds one month and three month T bills as collateral. It is a mirror strategy to BXM since a covered call is equivalent to a short put. The difference is that BXM sells the first out of the money call and PUT sells the at the money put.

The way I am trying to capture the dividend is by selling the at the money call, or first in the money call, so that there is some time premium left in the call. That way, if the stock is called away, I’ve earned the time premium. If not, I get the dividend.

Return Comparison

Here is an interesting table of monthly data covering the period 30 June 1986 to 31 October 2008 from a paper on the CBOE micro-site PUT:

In strongly positive return months, almost half the time, the S&P 500 returns an average of 4% and the Put-Write index lags, returning a little more than half that, 2%.

In relatively unchanged months, about 22% of the months, PUT outperforms the SPX returning 1.67% compared to a -0.8%. In these two states of the market, the correlation of SPX and PUT is 0.5.

In strongly down months, the SPX loses an average of 5% and PUT does better, losing 3%. The correlation here is almost 1, perfectly correlated.

So far we have the correlation of PUT with SPX, but we are trading individual names, not the index. How do we get the correlation of a buy-write of IBM, say, with SPX?

Implied Correlation Indicator

CBOE to the rescue again. They have developed an indicator that extracts the average correlation of the fifty largest SPX components with the index. They publish two of these average correlations, ICJ and JCJ.

ICJ will expire with November options, because it looks at the implied correlation by extracting implied volatilities of the December 2009 SPX options and January 2010 options for the fifty individual names. On the next Monday KCJ will be calculated using January 2012 options.

The index implied volatility can increase in two ways, one is if the implied volatility of the individual constituents increases. The other way is if the correlation in the volatility increases. In the tails, when the market rises fast and especially when it falls fast, the correlations go to one. Everything is moving together in the same direction and vol goes through the roof. Look at KCJ, the yellow line, right between the two VIX spikes last fall. It spikes above 100 which is because the calculation isn’t perfect, but it shows that everything was moving down together. (Click on the chart to enlarge.)

Looking to the right, we see the the implied correlation is around 50%. So a basket of the fifty largest stocks has an average correlation of 50% with the index.

Correlation of ‘IBM’ with PUT

Can we put these two correlations together to extract the correlation of the average large stock in SPX, what I am calling in the header ‘IBM’, with PUT?

Here is a geometric way to look at correlation. It is the cosine of the angle between the return vectors of SPX and PUT. So if you hold up two pencils and join them at the bottom, when the tops are touching they are pointing in the same direction and the correlation (cosine of the angle between them) is one. As you move the tops apart the angle between the pencils gets larger and the cosine gets smaller and so does the correlation.

So hold the two pencils apart and think of them as SPX and PUT. Now take a third pencil and that will be ‘IBM’. We know the angle ‘IBM’ makes with SPX. What does that tell us about the angle it makes with PUT? Nothing, because ‘IBM’ can spin around SPX in a circle with a fixed angle between them and its angle with PUT varies from 0 when it bumps into PUT to 120 degrees (cos (120) = -1/2) where the correlation is -0.5.

So please comment and let me know if we have another constraint that I missed that will help us to combine the two correlations.