Dispersion and Correlation Trading

Dispersion trading is a volatility strategy that compares the implied volatility of an index with the implied volatilities of the stocks inside it. The classic trade sells options (or variance) on the index and buys options on the individual stocks. It profits when the stocks move a lot individually but in different directions, so that their moves cancel out in the index. At its heart, dispersion trading is a bet on correlation: specifically, that realised correlation between the stocks will be lower than the correlation implied by option prices.

Why index volatility depends on correlation#

An index's variance depends on its members' variances and on how closely they move together:

σ²_index = Σ w_i² σ_i² + Σ_{i≠j} w_i w_j ρ_ij σ_i σ_j

If all stocks were perfectly correlated (ρ = 1), index volatility would equal the weighted average of stock volatilities. With lower correlation, index volatility is lower, because individual moves offset. See Covariance and Correlation and Diversification.

Implied correlation#

Using index and stock implied volatilities, traders back out an average implied correlation:

implied correlation ≈ (σ²_index - Σ w_i² σ_i²) / (Σ_{i≠j} w_i w_j σ_i σ_j)

Cboe publishes implied correlation indices for the S&P 500. Implied correlation has historically tended to be higher than the correlation stocks actually showed afterwards, a "correlation risk premium" that dispersion traders try to collect. Index options carry extra demand from portfolio hedgers, which pushes up index implied volatility relative to single stocks.

Building the trade#

1. Sell index volatility: short index straddles, strangles or variance swaps.
2. Buy single stock volatility: long straddles or variance swaps on the largest members.
3. Weight the legs: usually so the trade is vega neutral or so it isolates correlation.
4. Delta hedge each leg regularly.

Traders often use a subset of the largest members rather than all 500 stocks of an index, which leaves some tracking error.

When dispersion works#

• Earnings seasons, when companies move on their own news, raising individual volatility while index moves stay muted.
• Stock specific events: mergers, product launches, sector rotations.
• Calm, rotating markets where sectors move in different directions.

When it fails#

• Market crashes: correlations jump towards 1 as everything falls together. The short index volatility leg loses heavily, and stock volatility gains may not offset it. Dispersion trades suffered in 2008 and in March 2020.
• Macro driven markets: when interest rates or macro news dominate, stocks move together.

Dispersion is therefore often described as short correlation and exposed to crash risk, similar in spirit to other short volatility trades. See Theta Harvesting.

Reverse dispersion#

The opposite trade, buying index volatility and selling single stock volatility, profits when correlation rises. Some funds use it as a hedge for crisis periods, accepting a cost in normal times.

Practical difficulties#

• Many legs: trading options on dozens of stocks is costly and complex.
• Liquidity: single stock options are less liquid than index options.
• Weights change as stock prices move.
• Events: single stock earnings create jumps that affect each leg differently.

Large banks and specialist funds dominate dispersion trading. See Volatility Trading.

Frequently asked questions#

What is dispersion trading?#

A strategy that sells index volatility and buys volatility on the index's member stocks, profiting when stocks move independently rather than together.

What is implied correlation?#

The average correlation between index members implied by the difference between index option prices and single stock option prices.

What is the main risk of dispersion trading?#

A market crash, when correlations rise sharply and index volatility jumps, causing large losses on the short index leg.

Next, learn how traders exploit mispriced volatility in Volatility Arbitrage.

Sources#

• Cboe, Implied correlation indices