Dispersion Trading Explained

Index volatility sits below the weighted average of single-stock volatility because of correlation, and dispersion trades are built on exactly that gap.

Dispersion trading sells volatility on an index and buys volatility on the index’s own constituents, or the reverse, expressing a view on the correlation between those constituents rather than a view on volatility itself. The mathematics of index variance decomposes into a weighted average of single-stock variances minus a term that grows with average pairwise correlation, which is exactly why index implied volatility trades below the weighted average of the single names underneath it.

Index variance can be written as the weighted sum of each constituent’s own variance, plus a cross term built from every pairwise covariance between constituents, weighted by their index weights. Collapsing every pairwise correlation to a single average, and noting that for a broad index the cross term dominates once there are more than a handful of names, the standard approximation used across dispersion desks reduces to index volatility equaling the square root of average correlation multiplied by the weighted average of single-stock implied volatility. Since the square root of any correlation below 1 is itself below 1, index implied volatility sits below the weighted average of the…

Suppose the weighted average single-stock implied volatility across an index’s constituents is 30 percent and the average pairwise implied correlation priced into the options market is 40 percent. The square root of 0.40 is roughly 0.63, so index implied volatility comes out near 19 percent, a gap of about 11 volatility points between the index level and the weighted average of the names underneath it, entirely explained by the correlation term rather than by any difference in how the index and its constituents are priced individually.

The classic dispersion structure sells index volatility, through an index variance swap or a delta-hedged short index straddle, and buys a basket of single-stock volatility positions sized to the same index weights, funding the long single-name legs with the premium collected from the short index leg. This position is long dispersion and short correlation: it profits when realised correlation between the constituents comes in below the correlation implied at the trade’s inception, because in that scenario the index realises less variance, relative to the weighted average variance the single names actually deliver, than the options market had priced. A trade put on at an implied correlation…

The reverse structure, short dispersion and long correlation, buys index volatility and sells the single-name basket, and profits in the opposite scenario, when realised correlation comes in above what was implied at inception. A desk running either side prices the trade off the CBOE-style implied correlation measure rather than off a single stock-by-stock view, since the whole position depends on the average pairwise relationship across the basket rather than on any one name.