Correlation Swaps

A volatility swap lets you bet purely on how much a single asset wiggled, with no view on direction. A correlation swap does the same thing for how a group of assets moved relative to each other — a pure bet on whether stocks in an index rose and fell together, or went their separate ways, with no view on the index's own return or on any single stock's own volatility. Think of it as betting on how synchronized a group of dancers is, completely separate from betting on how energetic any one dancer's individual moves were.

The payoff

$$\text{Payoff} = N \times (\rho_{\text{realized}} - K_{\text{corr}}),$$

In words: $\rho_{\text{realized}}$ is the average pairwise realized correlation actually measured across all the pairs of assets in the basket over the contract's life, $K_{\text{corr}}$ is the fixed correlation level agreed at inception, and $N$ is the notional per correlation point. The long side profits if the basket's members turn out to move together more than the agreed level implied, and loses if the members turn out to be more independent of each other than expected — again, entirely separate from whether the basket's overall level went up or down.

Worked example 1 — a basic settlement

A correlation swap on a 10-stock basket has $K_{\text{corr}} = 0.30$ and notional $N$ = $40,000 per correlation point (a "point" is 0.01 of correlation). Over the contract's life, average pairwise realized correlation across all $\binom{10}{2}=45$ pairs comes in at 0.45 — the stocks moved together more than expected, perhaps because a broad macro factor (rates, a recession scare) dominated most individual stock-picking noise. That's a gap of $0.45-0.30=0.15$, or 15 points, so the payoff to the long side is $40{,}000 \times 15 =$ $600,000. If realized correlation instead came in at 0.15 (stocks moved unusually independently), the gap is $-15$ points and the long side would owe the short side $40{,}000\times15=$ $600,000 instead.

Worked example 2 — the link to dispersion trading

Correlation swaps are closely related to "dispersion trades," built from options rather than a direct swap: sell index options (short index volatility) and buy single-stock options on the index's components (long individual-stock volatility). This combination is, in effect, short correlation, because of the same portfolio-variance identity used for baskets: $\sigma_{\text{index}}^2 \approx \sum_i w_i^2\sigma_i^2 + \sum_{i\ne j} w_iw_j\rho_{ij}\sigma_i\sigma_j$. If average correlation falls, the cross terms shrink, index volatility falls relative to the components' own volatility, and the short-index/long-components position profits — the same directional bet a short correlation swap makes, just assembled from a basket of listed options rather than one OTC swap. Suppose the index's implied vol is 16% while the average single-stock implied vol across its components is 25%; back-solving the variance identity for the implied correlation consistent with those two numbers might give something like $\rho_{\text{implied}}\approx 0.35$ — that number is exactly what a correlation swap trader is implicitly comparing their own view against.

Drag the correlation slider above and picture it as the single number a correlation swap is settled against — a tighter, more line-like scatter at expiry means the basket moved together more than a looser, rounder scatter, and that's the entire payoff determinant, independent of which direction the cloud drifted.

What this means in practice

Correlation swaps are used directly by desks that have accumulated correlation exposure from other business (like selling worst-of autocallables, which are structurally short correlation) and want to hedge that exposure cleanly, without taking on unwanted volatility or directional risk in the process. They're also a standalone macro trade: correlation across most equity markets tends to spike during sell-offs (everything falls together) and fall during calm bull markets (stock-picking dominates), so a correlation swap is one of the more direct ways to express a view on "risk-on, stock-picker's market" versus "risk-off, everything's-the-same-trade" regimes.