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Variance Dispersion and Correlation Trading

Dispersion trade: trading an index volatility vs the volatility of a basket of stocks. 


Index variance < average variance of constituents --> diversification effect --> related to correlation between constituents. 


Back-testing --> IV-RV premium of index > IV-RV premium of single-stock. 

Selling variance on an index and buying variance on its members has generally been a profitable strategy. 

This can be partly explained by demand for protection at the index level. 


Realised index volatility can be thought of as arising from two factors:

(a) the volatilities of the constituents.

(b) the correlation between them. 


Realised index variance is described by the equation: Dispersion 2

These realised quantities can be observed and pairwise correls calculated and averaged to give overall correlation for index. 


Another way to express this ‘average correlation’ --> assume that correlation is the same for all pairs of stocks. 

Disp 5    or approximately (for a well diversified index): Disp 6


Advantage: average implied correlation (not directly measurable) can be backed out from IV of index and constituents. 


This implied correlation can be traded by selling index variance and buying single-stock variance --> short correl. 

To hedge out the exposure to volatility initially --> legs must be weighted with more index Nvega than single-stock Nvega

The Nvega of the constituents must be adjusted by a factor equal to the square root of implied correlation. 


Like volatility, implied correlation > realised correlation  --> candidate for carry-style trades. 

Rolling short correlation through variance dispersion performs well on average. 


Volatility and correlation are themselves correlated --> tend to spike together in a sharp sell-off.


Variance dispersion trade = short correlation

- losses can be very large as the trade becomes short volatility when both correlation and volatily go up. 

- gains are diminished as the trade becomes long volatility when both volatility and correlation go down. 


This ‘volatility-scaling effect’ helps to account for the premium of variance dispersion levels compared to correl swaps. 


Equity correlation can also be traded more directly through correlation swaps.

For technical reasons, correl swaps levels tend to trade below the levels of correl associated with variance dispersion trades. 

By dynamically trading vega-neutral variance dispersions until maturity --> almost replicate the payoff of a correl swap. 


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