Dispersion Trading

Dispersion trading is a strategy that sets the volatility of a stock index against the volatility of the individual shares in it. In its usual form the trader sells options on the index and buys options on the component stocks. The position gains if the shares move a great deal individually but in different directions, so that their moves largely cancel in the index. This is what dispersion means: the spreading apart of individual returns.

Because index volatility depends on how closely the components move together, the strategy is in effect a position on correlation. Selling index volatility and buying single-stock volatility is a short correlation trade. It is practiced mainly by bank trading desks and hedge funds that specialize in volatility trading, and it requires the ability to trade and hedge options on many names at once.

The variance of an index is determined by the weights, volatilities and pairwise correlations of its members. If all pairs are assumed to share one average correlation $\rho$, index variance is approximately:

• $\sigma_I$ is the volatility of the index.
• $w_i$ and $\sigma_i$ are the weight and volatility of stock $i$.
• $\rho$ is the average correlation between pairs of stocks.

For an index with many members the second term is small, which gives a convenient rule of thumb:

When the volatilities used are those implied by option prices, the result is the implied correlation: the level of correlation that option markets are pricing in.

Suppose index options trade at an implied volatility of 16 percent, and the weighted average implied volatility of the component stocks is 25 percent. Implied correlation is roughly (16 ÷ 25)² = 0.64² = 0.41.

A trader believes actual correlation over the coming months will be nearer 0.30. If the stocks do realize an average volatility of 25 percent with a correlation of 0.30, the index will realize a volatility of about 25 × √0.30 = 25 × 0.548 = 13.7 percent. Having sold index volatility at 16 and bought stock volatility at 25, the trader breaks even on the stock side and earns the gap between 16 and 13.7 on the index side. If correlation instead rises to 0.60, index volatility comes in near 25 × √0.60 = 19.4 percent and the trade loses.

The classic construction sells a straddle or strangle on the index and buys straddles or strangles on the components. Each leg is kept delta neutral through delta hedging, so that the result depends on volatility and not on the direction of prices. The amounts are sized so that the overall position has little net vega: a general rise or fall in all volatilities should leave it roughly unchanged, with only the relationship between index and stock volatility mattering.

Hedging dozens of option positions every day is laborious, and the exposure of a straddle fades as the price moves away from the strike. Many desks therefore use variance swaps, contracts that pay the difference between realized variance and a fixed level, which give a cleaner exposure with no hedging of the underlying.

Index options have historically traded at implied volatilities above the volatility later realized by a wider margin than single-stock options have. The usual explanation is supply and demand. Investors buy index puts to protect portfolios, which pushes index implied volatility up. At the same time, holders of individual shares sell calls against them through covered call programs, which adds supply of single-stock volatility. The outcome is an implied correlation that tends to sit above realized correlation. The difference is described as a correlation risk premium and is related to the wider volatility risk premium.

The premium can also be read as payment for risk. The trade loses when correlation jumps, and correlation jumps in crises, when losses are hardest to bear.

The main risk of the standard trade is a sharp rise in correlation. In a stock market crash, shares fall together, index volatility surges, and a short index volatility position loses heavily while the long stock positions gain less. The periods around the 2008 financial crisis and the market fall of March 2020 produced large losses for short correlation positions.

Other risks are more routine. A single component can move for reasons of its own, such as a takeover or a profit warning, and if the trader does not hold options on that name the exposure is unhedged. The position is short gamma on the index, so a sudden index move is costly before any adjustment can be made. Bid-ask spreads on single-stock options are wide, and the transaction costs of trading and hedging many legs can consume the expected edge.

The opposite position, buying index volatility and selling stock volatility, is a long correlation trade. It is used as a hedge against market stress or when implied correlation looks unusually low. Exchanges publish implied correlation indices calculated from option prices on an index and its largest members, which traders follow as a gauge of how the market is pricing the relationship. As with any strategy that depends on realized volatility differing from what is implied, past premiums are no assurance of future profit.