04 — Correlation & Structure

Spreads move as a family.

Daily-return correlation of 12 contemporaneous spreads (2022). Adjacent spreads run ~0.85+ together; distant ones decouple. This is exactly why a butterfly (+1 / −2 / +1) cancels the shared level and isolates pure curvature — the cheapest, lowest-margin way to trade shape. Hover any cell.

+ correlated− correlated· diagonal = 1.0

The 3-factor curve

PCA of any futures curve collapses to three orthogonal moves that explain >95% of variance:

LEVEL ·PC1 ~70% — whole curve shifts. A long spread is nearly immune (both legs move).
SLOPE ·PC2 ~15% — contango↔backwardation tilt. This is what a calendar spread trades.
CURVATURE ·PC3 ~7% — the belly bends. This is what a butterfly trades.

Because adjacent spreads correlate so tightly (our 2022 set: ρ ≈ 0.88 adjacent), a fly's net exposure to LEVEL and SLOPE ≈ 0 — you hold the cleanest signal on the curve. SPAN's inter-month credits then margin it at ~10× less capital than an outright.

DECAY

Correlation fades with distance

Adjacent month-pairs share the same storage economics and convenience yield, so they move near-lockstep. Push the tenors apart and the link decays roughly exponentially — distant spreads answer to different parts of the curve.

COINTEGRATION

The legs are tied together

The two legs of a spread are cointegrated — they wander, but not apart. That's what makes the spread itself stationary-ish and mean-reverting. Engle-Granger / Johansen formalise it; OU models the reversion.

half-life = ln 2 / θ
STRESS

Correlation breaks when it matters

In April 2020 the tidy correlation structure shattered — a physical storage squeeze, not a statistical wiggle. Any model calibrated on calm history had no signal. Risk overlays (inventory, hard stops) are non-negotiable.