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Key Takeaways
- Long dispersion combines short index volatility with long volatility on a basket of constituents.
- Index variance includes both each stock’s own variance and the covariance between stocks.
- Calculate implied correlation from both terms, using consistent weights, expirations and volatility inputs.
- Size each option leg using its contract multiplier and chosen dollar-vega or variance target.
- Calculate total profit from every option, hedge and cost in the position.
What is dispersion trading?
Dispersion trading is an options strategy that trades index volatility against the volatility of the index’s constituent stocks. The classic long-dispersion position sells index volatility and buys constituent volatility, using options or variance contracts to express that relative view. Because index variance rises with the correlation between its stocks, long dispersion carries short-correlation exposure.
How does dispersion trading work?
Index variance contains two contributions: each stock’s own weighted variance and the covariance between stocks. Holding component volatility fixed, a lower correlation reduces the covariance contribution and the index’s volatility. This gives the classic long-dispersion position its short-correlation exposure.
Formula
Index variance = D + rho × C; D = Σ w_i² σ_i²; C = (Σ w_i σ_i)² − D; implied rho = (σ_index² − D) / C.- Weights sum to one in the worked 50-stock index.
- The example uses a common pairwise correlation and 22% volatility for every constituent.
- For 50 equal weights, D = 0.000968 and C = 0.04743.
- The squared volatility-ratio shortcut drops the diagonal term.
Dispersion trading example: implied vs realized correlation
A stylized index has 50 equally weighted constituents. At entry, each has 22% implied volatility and the index has 14%. For the realized scenario, specify 22% realized volatility for every constituent and common pairwise correlation of 0.25.
- Each stock weight = 1 / 50 = 0.02
- Diagonal variance D = 50 × 0.02² × 0.22² = 0.000968
- Cross-product coefficient C = 0.22² − 0.000968 = 0.04743
- Implied correlation = (0.14² − 0.000968) / 0.04743 = 0.39
- Scenario index variance = 0.000968 + 0.25 × 0.04743 = 0.01283
- Scenario index volatility = √0.01283 = 11.33%
With constituent volatility fixed at 22%, the lower correlation produces 11.33% index volatility against 14% implied at entry. The calculation identifies the variance relationship. Calculate the position’s dollar result from its specified option premiums, quantities, hedges and costs.
For the realized scenario, set each stock’s realized volatility to 22% and their common pairwise correlation to 0.25. Index variance becomes 0.01283, giving 11.33% volatility. The full calculation retains the individual-stock variance contribution.
How to size dispersion trade legs
A listed-option structure combines a short index straddle with long constituent straddles. Choose quantities from a defined dollar-vega target using each option’s sensitivity and contract multiplier. SPX option points convert to dollars through its multiplier; standard equity options generally control 100 shares.
Measure and rebalance each position’s delta. Track option marks, stock or futures hedges, trade quantities and costs. The book’s total profit is the sum of those transactions and valuations.
How traders use implied correlation and DSPX
Read implied correlation alongside index and single-stock IV. Cboe’s DSPX provides a separate 30-day dispersion reference. Match the expiration and basket before comparing the readings.
Options flow shows activity in the index and the relevant stocks; the options profit calculator compares individual structures, and the full position ledger evaluates the combined book.
Risks and limitations of dispersion trading
- Price every driver of the result. Beyond correlation, the result depends on each stock’s realized volatility, the delta hedges, and the cost of every leg.
- Size the book for a broad selloff. Stock correlations tend to rise then, which is when the short index leg loses the most.
- Use the full variance identity. The squared volatility-ratio shortcut drops the diagonal term and misstates implied correlation, and the full identity needs consistent weights, expirations and volatility inputs.
- Use the index’s actual weights and correlations. The worked example uses equal weights, one volatility and one common correlation, while real indexes have unequal weights and pairwise correlations that differ by stock.
- Budget for execution costs and tracking error. Dozens of single-stock legs each carry their own bid-ask spread and rebalancing trades, and a basket that holds fewer names than the index leaves tracking error.
Bottom line
Dispersion trading turns the gap between index and single-stock option prices into a position on correlation: long dispersion gains when realized correlation comes in below the implied level, other things equal. Size the legs by dollar vega, use the full variance identity, and judge the result from every option, hedge and cost in the book.
Clear answers
Frequently Asked Questions
Sources and Further Reading
- Cboe: S&P 500 Dispersion Index (DSPX)
- Cboe: The Impact of Dispersion on Market Expectations and Volatility
- OIC: Volatility and the Greeks
How entries are sourced, calculated and updated: editorial methodology.