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L.8 · ADVANCED · 3 MIN

Dispersion Trades: Index Vol vs Single-Name Vol and the Correlation Bet

A dispersion trade is one of the most quantitatively pure structures in equity derivatives: it isolates a bet on CORRELATION between an index and its constituents while being roughly hedged against the level of single-name volatility itself. The trade is the workhorse of multi-strategy desks and dedicated vol arbitrage funds because it expresses a view (correlation will fall, or rise) that simpler vanilla structures cannot cleanly express. The intuition matters even for investors who will never execute one.

Quiz · 5 questions ↓
§ 01
LegPositionWhy
Index varianceSHORT (sell variance on the index)If correlation falls, index variance falls relative to single-name variance
Constituent variancesLONG (buy variance on a basket of single names, weighted to track the index)If correlation falls, the average single-name variance stays high while index variance falls -- the long leg wins
Net exposurePure CORRELATION bet (with second-order vol-level exposure that the structure aims to minimize)Profit if realized correlation < implied; loss if realized correlation > implied
§ 02

The mathematical identity underlying the trade: index variance = sum of weighted single-name variances + 2 × sum of weighted covariance pairs. When all stocks move together (correlation = 1), index variance equals the weighted average of single-name variance -- they cancel out. When stocks move independently (correlation = 0), the covariance pairs net to zero and index variance is much smaller than the weighted average of single-name variance -- dispersion wins. The 'implied correlation' is the correlation level that makes the equation balance at current option prices.

§ 03

Dispersion trades are highly attractive in regimes where implied correlation is structurally elevated relative to long-run averages. Implied correlation tends to spike during crises (everything moves together; index puts get heavily bid) and to settle back down during calm periods. A trader who believes correlation is mean-reverting from a crisis level has a clean fundamental thesis for the structure. The risk: another crisis arrives mid-trade, correlation spikes further, and the trade loses.

§ 04

The operational complexity of dispersion trades is significant. Holding variance on 50+ single names plus the index means managing 50+ delta hedges, margin requirements on each leg, dividend and corporate-action risk on each name, and the constant rebalancing as individual stocks move. Retail traders cannot replicate the structure with vanilla options because the variance-replication portfolio requires a strip of options across many strikes -- prohibitively expensive in retail commissions. The trade is institutional-only in practice, even though the intuition is broadly educational.

§ 05
Pull up the 30-day implied volatility on a major index (S&P 500 via SPX options or SPY proxy) and on its 5 largest constituents. The implied correlation can be roughly estimated from the index IV vs the cap-weighted-average single-name IV. When the ratio is high (index IV is close to the constituent average), implied correlation is high; when the ratio is low, implied correlation is low. Track this ratio over time to build intuition for when dispersion would be attractive vs unattractive.
§ 06

The theoretical edge in dispersion is real but small per unit of capital deployed. The trade typically targets 1-3% returns per quarter with low volatility -- attractive on a risk-adjusted basis but not heroic. The operational alpha (executing many legs efficiently, sourcing the right variance instruments, managing margin) is where dedicated vol-arb desks earn their fees. A retail trader's takeaway is conceptual: when the headlines say 'everything is moving together,' implied correlation is elevated, and a dispersion-style bet would profit from a return to differentiation between names.

§ 07

Dispersion trades isolate a bet on correlation: short index variance + long single-name variance. The trade profits if realized correlation comes in below implied correlation. The load-bearing assumption is mean-reversion of correlation -- a fragile assumption during crisis regimes. Operational complexity (multi-leg execution, margin, hedging) makes the trade institutional-only in practice, but the intuition about implied correlation is broadly useful for reading the equity vol market.

Five questions · AI feedback

Sit with the ideas.

A trader runs a classic dispersion structure: short variance on the S&P 500 index, long variance on a basket of the 50 largest constituents (weighted by index weight). The implied correlation embedded in current index vs single-name pricing is 0.60. Over the trade lifetime, realized correlation across the basket comes in at 0.45. What happens to the trade's P&L, and what is the load-bearing assumption that drove the result?

Why:
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