What does a correlation swap pay out and how do dispersion traders use it?

Question

AcadiFi · Accepted Answer

A correlation swap pays the difference between realized average pairwise correlation of an index basket and a correlation strike.

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Example: Nordwell Prop Trading sees index implied correlation at 0.62 (derived from index vs single-name variance prices) and believes realized will be lower. They sell a correlation swap at 0.60 strike on the top-50 S&P names, $100,000 notional per correlation point. Realized comes in at 0.48, payoff to Nordwell = $100,000 × (0.60 − 0.48) × 100 = $1.2M.

```mermaid
flowchart TD
  A[Index Basket] --> B[Compute Pairwise rho]
  B --> C[Average across N*N-1/2]
  C --> D[Compare to Strike]
  D --> E[Settle x Notional]
```

Dispersion traders approximate a correlation swap by being short index variance and long single-name variance in the constituents. When correlation falls, single-name vol becomes more valuable relative to index vol (since the index diversifies away idiosyncratic vol). The P&L is driven by the correlation gap.

Correlation swaps are cleaner than dispersion trades because they isolate correlation without vol exposure. However, liquidity is thinner, and dealers charge significant bid-ask. Risks include regime shifts (correlations spike to 1 in crises) and composition changes when index constituents are reshuffled.

What does a correlation swap pay out and how do dispersion traders use it?

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