Correlation Trading

Correlation trading is something that hasn't yet been discussed on this blog. In principle, one can bet on the correlation(s) among n assets of one's choice. However most commonly correlation trading is done on an index. In other words, you are betting on the correlation of the constituents of the index. You can approach a bank and ask them to quote the strike of a correlation swap for you. Then you can sit back and let the bank worry about all the dirty hedging works.

There are sound reasons not to go down this route. First, what if you want to speculate on a basket that is not a common index? That may not be readily quotable at the bank. Secondly, the strike of the correlation swap quoted by the bank is likely to have a large spread buffer to compensate for the risk they take.

An alternative is to proxy the correlation swap. The technique is generally known as dispersion trading. It's a fancy name of long-shorting an index versus its components, or vice versa.

Straddles
The most primitive way of dispersion trading is to long the index straddle and short the constituents straddles (this would be betting on the correlation among the constituents to go up). In this case, each of the straddles proxy the specific variances (of the index or of the constituents), and the long-short portfolio of straddles in turn proxies the correlation. Such a simplistic scheme would of course leave a lot to be desired (e.g. the need to rehedge, see here).

Variance Swaps
Can we do better? Absolutely. It's almost a no-brainer: replace the straddles with variance swaps! So instead of longing the index straddle and shorting the constituents straddles, you long the index variance swap and short the constituents variance swaps to bet the correlation going up. Thanks to the characteristics of variance swaps, you don't have to worry about rehedging anymore. Sounds good, doesn't it? But there is still room for improvement. Although hedging is not necessary, the weights of the variance swaps have to be dynamically maintained. As an example, suppose our (value weighted) index I has only two components A and B. Initially the the index is made up of 50% each of A and B. You try to trade correlation by longing $100 notional of variance swap on I and shorting $50 notional of variance swaps on A and B each. Over time, the underlyings move and the weights of A and B become, say, 43% and 57% respectively. You'd have to dynamically re-balance your variance swap portfolio to keep in line with the changing weights.

Note: The above discussion assumes a value weighted index.

As a side note, the strike of the long index variance swap, short constituents variance swap portfolio would in general differ from a correlation swap quote. The reason is non-zero vol-of-vol. This paper gives an in-depth investigation into the matter.

Gamma Swaps
Knowing the shortcoming of dispersion trading using variance swaps (i.e. the need for reallocation), what alternative do we have? We can use a kind of swap that 'scales' itself according to the underlying level, a feature that is provided by gamma swaps. You long the index gamma swap and short the constituents gamma swaps to bet the correlation going up. Due to the structure of a gamma swap, your exposure to each index component would in fact automatically match the desired weightings as the underlyings change.