Module 5 · Advanced

Cross-margining & the correlation problem

Cross-margining — offsetting margin between digital assets and traditional markets, or between any two correlated books — is a headline product for modern prime brokers. The engineering is straightforward. The risk question is not.

A margin offset between two positions is only justified if the correlation holds in the liquidation scenario. Correlations estimated on calm-period data overstate the benefit, and “correlation goes to one” is the standard failure mode — everything the client owns falls together, while the hedges that earned the offset stop hedging. Serious houses handle this three ways, usually in combination:

  • Compute the offset under stressed correlation rather than sample correlation.
  • Impose a cap on the maximum offset percentage, however good the statistics look.
  • Require the offset to survive a decorrelation scenario — a named stress in which the assumed relationships break.

If you are ever asked to design cross-margining, that caveat is the answer. Enthusiasm about capital efficiency without it is how margin models blow up.

🎛 Correlation stress lab

Long crypto vs short equity index — how much offset should the hedge earn?

10
10
70%
20%
60%
No offset (sum of standalones)
$2,899,784
Naive offset at sample ρ = 70%
$1,546,816
Under stressed ρ = 20%
$2,040,118
Margin actually charged
$2,040,118

Offset benefit granted

$859,666

Naive benefit denied by stress/cap

$493,303

The offset is only worth granting if the correlation holds in the liquidation scenario. Correlations estimated on calm data overstate it — and “correlation goes to one” (for longs) or breaks entirely (for hedges) is the standard failure mode. Serious houses charge the worst of: the sample-correlation margin, a stressed- correlation recompute, and a hard cap on the offset percentage. Set sample ρ to 90% and stressed ρ to 0% — the naive benefit is exactly the loss you'd eat when the hedge fails. Educational tool — not investment advice.

Worked example: long BTC spot, short BTC futures

The cleanest-looking cross-margin case is a client long BTC spot and short an exchange-listed BTC future. Near-perfect correlation, so near-full offset? Almost — but the residual is the point:

  • Basis risk. The two legs are correlated, not identical. The spot-futures basis moves — sometimes violently in stress — and the basis is exactly what remains after the offset. It must be charged.
  • Different venues, different settlement. The future settles through a clearing house on its schedule; the spot leg lives wherever it's custodied. A hedge you can't monetize simultaneously is a weaker hedge.
  • Different legal entities. If the legs sit in different entities of the client (or of the broker), the offset needs enforceable netting to mean anything.

Second-order but real: cross-entity margin

A global prime broker runs positions in separate legal entities — US, UK, EU, Singapore, offshore — each with its own insolvency regime. Offsetting margin across entities is only defensible where close-out netting is legally enforceable in every relevant jurisdiction: the same netting-opinion question that governs counterparty-risk netting sets. Without the opinion, the offset is a hope, not a hedge — in a default you may find yourself an unsecured creditor of one entity while owing the estate of another in full.

Things to try

  • • Sample ρ 90%, stressed ρ 0%: the “naive benefit denied” figure is precisely the loss you'd eat when the hedge fails.
  • • Set the offset cap to 90% and stressed ρ high — now the cap is doing nothing. Drop stressed ρ and watch which control binds first.
  • • Unbalance the legs ($20M vs $5M): even perfect correlation can't offset what isn't there.