What is dispersion trading, and why is index implied volatility typically higher than the weighted average of component volatilities?

Dispersion trading exploits the volatility spread between an index and its constituent stocks. The classic trade sells index options (typically overpriced) and buys single-stock options, profiting when realized correlation among components is lower than the correlation implied by index option prices.\n\nWhy Index Vol Trades Rich:\n\nIndex variance = weighted sum of component variances + cross-variance terms\n\nsigma_index^2 = Sum(w_i^2 x sigma_i^2) + Sum_i_!=_j(w_i x w_j x rho_ij x sigma_i x sigma_j)\n\nThe cross-variance term depends on pairwise correlations. Index option prices embed an implied correlation. If actual correlations are lower, the index will realize less volatility than implied, making the short index vol / long single-stock vol trade profitable.\n\n`mermaid\ngraph TD\n A[\"Index Options
Implied Vol = 22%
Implied Correlation = 0.65\"] --> D{\"Realized Corr < 0.65?\"}\n B[\"Stock A Options
IV = 30%\"] --> D\n C[\"Stock B Options
IV = 28%\"] --> D\n D -->|\"Yes: Corr = 0.45\"| E[\"Index realizes ~17%
Short index straddle profits
Long stock straddles offset\"]\n D -->|\"No: Corr = 0.78\"| F[\"Index realizes ~24%
Short index loses
Dispersion trade loses\"]\n`\n\nStructural Reasons for the Spread:\n1. Demand imbalance: Institutions are natural buyers of index puts (portfolio insurance), bidding up index IV\n2. Correlation risk premium: Market participants demand compensation for the risk that correlations spike during crises\n3. Convexity of correlation: When markets crash, correlations jump to 0.9+, making the short correlation trade painful in tail events\n\nWorked Example:\n\nFenwick Volatility Partners implements a 3-stock dispersion trade on the fictional Ridgeway 50 Index:\n\n| Component | Weight | Stock IV | Stock RV |\n|---|---|---|---|\n| Aldren Tech | 35% | 32% | 35% |\n| Beckford Energy | 40% | 26% | 24% |\n| Corwin Health | 25% | 29% | 31% |\n\nIndex IV = 22%, Implied correlation = 0.62\n\nRealized correlation = 0.41\n\nRealized index vol (using actual correlations): approximately 18.5%\n\nP&L components:\n- Short index straddle gain: (22% - 18.5%) exposure = +3.5% vol points on notional\n- Long Aldren straddle: (35% - 32%) = +3% vol points (realized > implied)\n- Long Beckford straddle: (24% - 26%) = -2% vol points (realized < implied)\n- Long Corwin straddle: (31% - 29%) = +2% vol points\n- Net: positive, driven by the correlation premium captured\n\nRisks:\n- Correlation spikes during market stress (2008, 2020) can cause severe losses\n- The trade has negative skew: small frequent profits vs rare large losses\n- Transaction costs across many single-stock positions are substantial\n- Vega hedging across different maturities is complex\n\nExplore advanced volatility strategies in our CFA Derivatives course.