Realized Correlation: How Much of the Index's Calm Is Cancellation

The index, the average sector and the average large stock, each as a z-score against its own 2011+ history so three very different levels share one axis. In a crash all three rise together — that is correlation going to one, and it is why 2020 and 2022 show as a single fused spike. The configuration worth noticing is the opposite one: the blue line falling away from the orange, meaning the stocks got louder and the index got quieter at the same time.

The same three lines as a distance instead of three levels: how many times the index's own volatility the average stock and the average sector are running. A ratio rather than a gap in percentage points, because a gap widens whenever the whole market gets louder — in March 2020 every spread was enormous and none of it meant stocks had stopped moving together. The ratio strips the level out and leaves only what survives aggregation. At 1.0 the index is as volatile as its parts, which is what perfect correlation looks like.

This is nearly the same information as the correlation below, in a unit that needs no algebra: for a large equal-weighted basket ρ̄ ≈ 1/ratio². The two are not identical here, and the reason is worth knowing — this ratio divides by the CAP-WEIGHTED index, while ρ̄ is solved from the equal-weighted basket's own volatility. When a handful of names carry most of the index the two denominators come apart, so 1/ratio² has sat a median 0.04 away from the solved correlation across this history. We publish the ratio because it is the one you can check against a screen of quotes, and the correlation because it is the one that compares to what the options market prices. Neither gets its own forward-return study: that would be the section after next in different units.

One number instead of three lines. For an equal-weighted basket, N²·σ²(basket) = Σσᵢ² + ΣΣρᵢⱼσᵢσⱼ — and because the basket's own volatility is measured directly from its daily returns, everything in that identity is known except the average correlation. Solving for it gives the same quantity Cboe's implied-correlation index estimates from option prices, except computed from what actually happened.

The two baskets answer different questions. Sector correlation asks whether the market's big blocks are moving as one; stock correlation asks the same of individual companies, and sits higher because names inside a sector share its factor. They can and do diverge — a market can rotate violently between sectors while the stocks inside each one move together.

The test we run before shipping anything. Sorted into quartiles of its own history, single-stock correlation has carried no dependable directional information about SPY. The highest quartile edges the baseline at six months and the lowest quartile trails it, but the gaps are small, the buckets hold about fifty month-ends each, and the tilt has an unremarkable explanation: correlation spikes in selloffs, and selloffs mean-revert. Read this table as the reason not to trade the gauge.

Average SPY price return and share of positive outcomes from each month-end, 2011+. Observations are sampled at month-ends so the 21-session horizon does not overlap; the 63- and 126-session horizons still do, so effective sample sizes there are smaller than the counts suggest. Dividends excluded.

The configuration this page exists to name — low correlation and an index quieter than its own median — is split out below against each half on its own. It is not distinguishable from the baseline either. Calm manufactured by cancellation has not, in this record, been calm that ended badly on any schedule you could trade.

Same construction. "Quiet index" means SPY's 21-session realized volatility sat at or below its own 2011+ median on that month-end.

Per-name price history starts in 2011 for us, but the sector SPDRs reach back to 1999 — through the dot-com top, the GFC and 2020. On that longer record the same test does produce a gap, and it is the one result on this page worth arguing about: the lowest-correlation month-ends were followed by an essentially flat SPY six months later, against a clearly positive baseline.

Average SPY price return and share of positive outcomes from each month-end, 1999+, using the nine-SPDR correlation series. Same overlap caveat at 63 and 126 sessions.

One entry per month so a single quiet stretch cannot fill the table. The right-hand column is the whole argument: at the top of the record, the index and the average stock are almost the same number — there is nowhere to hide. At the bottom, the average stock runs several times the index and the index says nothing about it.