Buying Correlation

[kik92]

Hi David,

In our notes (Correlation Risk Modeling and Management), we are told that another way of buying correlation is to buy call options on an index and sell call options on individual stocks of the index.

I haven't quite understood this concept - i.e why it should result in a positive result as well as why it is considered as buying correlation. Could you kindly elaborate?

Thanks.

 

[David Harper CFA FRM]

Hi @kik92 To be honest, when I first read your question, I did not know the answer (is to suggest this correlation trade strategy is not obvious at least to me!). Below is the source, and I can see now that the key idea is they buying of call options (options are essentially volatility trades). Meissner's basic idea here appears to be: if correlation (between index components) increases, then the implied volatility of the index call option will tend to increase, and this is profitable gap between the long call option and short the individual component stocks. But I think there is much more nuance here ....

• The reference to Chapter 2 appears to be a reference to an empirically observed positive correlation between correlation level and correlation volatility (Meissner Table 2.1). The datapoints are not (to me) especially compelling. However, we do have the conventional wisdom that correlations tend to spike when markets are stressed. (although I'm not sure why the better implied, no pun intended (!), treade isn't buy index put options + selling puts on the individual stocks? ... Meissner's data more convincingly shows that correlation drops during expansions).
• We have a simple avenue to an intuition: the 2-asset portfolio variance = w(1)^2*σ(1)^2 + w(2)^2*σ(2)^2 + ρ(1,2)*w(1)*w(2)*σ(1)*σ(2), which of course extends to pairwise correlations in a matrix. Here we have the classic idea that an increase in (pairwise) correlation increases the portfolio standard deviation (volatility). This seems to me the easiest way to think about it (?!)
• However, it is still not simple: I remember almost ten years ago (I wish I could find the article) the Federal Reserve published a paper arguing that the rise in (then recent) correlations was due to a decline in volatility, citing the simple relationship: correlation = covariance/[product of volatility], where correlation and volatility are here obviously inversely related (but I'm not addressing several nuances ....)

I hope that's helpful! Thanks for a good question ....

Meissner, 1.3.2.4 Buying Call Options on an Index and Selling Call Options on Individual Components:

"1.3.2.4 Buying Call Options on an Index and Selling Call Options on Individual Components: Another way of buying correlation (i.e., benefiting from an increase in correlation) is to buy call options on an index such as the Dow Jones Industrial Average (the Dow) and sell call options on individual stocks of the Dow. As we will see in Chapter 2, there is a positive relationship between correlation and volatility. Therefore, if correlation between the stocks of the Dow increases, so will the implied volatility [note: Implied volatility is volatility derived (implied) by option prices. The higher the implied volatility, the higher the option price.] of the call on the Dow. This increase is expected to outperform the potential loss from the increase in the short call positions on the individual stocks.

Creating exposure on an index and hedging with exposure on individual components is exactly what the “London whale,” JPMorgan's London trader Bruno Iksil, did in 2012. Iksil was called the London whale because of his enormous positions in credit default swaps (CDSs). He had sold CDSs on an index of bonds, the CDX.NA.IG. 9, and hedged them by buying CDSs on individual bonds. In a recovering economy this is a promising trade: Volatility and correlation typically decrease in a recovering economy. Therefore, the sold CDSs on the index should outperform (decrease more than) the losses on the CDSs of the individual bonds.

But what can be a good trade in the medium and long term can be disastrous in the short term. The positions of the London whale were so large that hedge funds short-squeezed him: They started to aggressively buy the CDS index CDX.NA.IG. This increased the CDS values in the index and created a huge (paper) loss for the whale. JPMorgan was forced to buy back the CDS index positions at a loss of over $2 billion."

 

[Jaskarn]

Hi @David Harper CFA FRM

In official GARP reading there is a concept discussed. How can one buy a correlation. In this, it's been said that one can buy a call option on the index and simultaneously sell call on individual stocks. This will benefit in correlation increases => stock market will fall => implied vol will increase thus payoff from buying call on the index will be more than selling call on individual stocks.
My doubt is. if correlation increases=> stock market fall won't call be worthless in these first place. eg we buy call on the index with a strike price of, say x, when correlation increase then won't index value less than x as stock market will fall.

 

[David Harper CFA FRM]

@Jaskarn I moved your question, see my response above to this question from last year. I haven't given it too much thought (forum backlog) but let me know if i can try to help further with Meissner's assertion ...

 

[Hung Pham]

You don't make it clear at all.

Long call option on index is expected to be more profitable than short call option on components when correlation between components increases. Because option price reflects volatility show it could mean volatility of index would be higher. So the question is
Why correlation between components increase leading to index's volatility higher than components' volatility? Because we learn about diversification. An index would have lower volatility because of diversification.

 

[David Harper CFA FRM]

Thanks @Hung Pham Admittedly I maybe over-thought it and over-analyzed it. Perhaps the simplest explanation is the best; i.e.,

• We have a simple avenue to an intuition: the 2-asset portfolio variance = w(1)^2*σ(1)^2 + w(2)^2*σ(2)^2 + ρ(1,2)*w(1)*w(2)*σ(1)*σ(2), which of course extends to pairwise correlations in a matrix. Here we have the classic idea that an increase in (pairwise) correlation increases the portfolio standard deviation (volatility). This seems to me the easiest way to think about it (?!)

 

[Hung Pham]

The paragraph from the book does not describe the long-short action very clear. How many call options on index to long? How many call options on components to short? And with what weights?