Recently some dealers in the City of London were reported as saying that hedge funds and prop trading desks of banks may have missed out on the spike in the implied correlation amongst stocks following the bomb attacks in London. In fact it is learnt that some hedge funds ha actually entered into dispersion trades designed to take long correlation positions but may have unwound them completely shortly before the bombings with very little profit.

Also, from our discussions with some dealers in Tokyo and elsewhere we have learnt that some hedge funds have unwound (a special type of) dispersion trades, whereby they typically traded single stock variance swaps against index variance swaps. It is interesting to note that there is a small minority of traders who prefer to call dispersion trades as "correlation" trades, as they believe what they are doing is either buying or selling correlation, as opposed to betting on volatility. But by and large, dispersion trading goes by the pseudonym of "volatility arbitrage".

What are dispersion trades? How could a big event, such as the London terrorist bombings, 9/11, etc. create a perfect opportunity for a dispersion trade? Before we understand dispersion trading we need to understand what is "dispersion" Dispersion, or dispersion spread, is the difference between the average variance of a basket (of stocks) and the variance of the constituent index, when correlation between the stocks approaches one.

Let us say that an equity index (which has traded options available on it, like Hang Seng, SP500, Nikkei, etc.) is comprised of n number of stocks. Further, assume that all these stocks have traded options on them and one can calculate the implied volatilities of the stocks from the market prices of the options. Also, one can easily find the implied volatility of the index from observing the price of the traded options on the index. (Remember this index is actually a basket of stocks, and the index option is actually a basket option).

Now say, that a trader artificially constructs a basket of stocks S from the same n stocks which comprise the index, keeping in mind their weights w in the index. The composition of the basket is:

The variance of the basket is:

And the volatility of the basket will be:

An interesting point to note is that the volatility of the basket as given above (what we mean is the implied volatility as well as the historical volatility) will be different from the volatility of the index. This is due to the correlation between all the stocks (correlation matrix). Though the index is comprised of all the constituent stocks which have a correlation amongst themselves, it still trades as one asset, and hence has one unique value for implied volatility and historical volatility. On the other hand the basket of stocks is created synthetically (all stocks trade independently and have their unique values of volatilities) and therefore, to calculate the volatility of the basket we have to take into account the correlation matrix of the stocks.

However, if the correlation of the stocks becomes one, all stocks are perfectly correlated with each other and the correlation matrix is simply an identity matrix, then the volatility of the basket should theoretically be equal to the weighted sum of the individual volatilities. And since in creating the basket the trader has used exactly the same weights as the index's composition, theoretically speaking, if correlation is one then the volatility of the index should be equal to the volatility of the basket. This is the measure of the dispersion, or dispersion spread, D. It is mathematically expressed as:

Therefore, the dispersion will have an upper bound of D and a lower bound of zero and hence a position can be taken on the spread.

A long dispersion trade is therefore, where the trader is:

- Long the volatility of each constituent; and
- Short the volatility of the index;

However, the above can also be looked upon as a long correlation trade, i.e. the trader is betting that the correlation is going to increase (move towards one) thereby causing the dispersion to move to its upper bound D.

What the hedge fund managers and prop traders, mentioned above, were actually doing was to go long on equity correlation. However, they unwound their trades too soon - possibly because they waited too long without seeing any sign of an increasing correlation.

But the London bombings caused a general spike in implied correlation - implied correlations are derived from option prices as well - which meant that the dispersion D, had suddenly moved closer to its upper bound.

A lot of equity (both cash and derivatives) sales traders have recently complained that it had become harder to pitch the trades to their clients with levels of implied volatility and implied correlation at historical lows, as has been the case for the last few years. However, with the London bombings two weeks back implied correlation spiked as stock fell across all sectors in reaction to the bombs and this gave rise to volatility arbitrage trading by going long correlation.

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