How are interest rate futures priced and what drives the futures-spot relationship?

Question

AcadiFi · Accepted Answer

Interest rate futures are priced using a cost-of-carry framework adapted for debt instruments. For a T-bill futures contract, the theoretical price equals the spot price compounded at the repo rate minus any coupon income earned during the carry period. Take BlueRock Capital financing a $1,000,000 face 90-day T-bill at 4.2% repo while the spot yield is 3.8%. With 60 days until delivery, the futures price reflects the forward rate implied by these two yields, approximately 100 - (3.8 + (4.2-3.8) * 60/90) = 97.73 on an index basis. Positive carry (spot yield above repo) pushes futures below spot; negative carry does the opposite. Arbitrageurs enforce this by borrowing at repo, buying the underlying, and shorting futures whenever the basis deviates. In practice, delivery options, tax effects, and supply dislocations create tracking error against the model price.

```mermaid
flowchart LR
  Spot[Spot Price] --> Carry[Add Repo Cost]
  Carry --> Income[Subtract Coupon]
  Income --> Fut[Theoretical Futures]
  Fut --> Arb{Basis > 0?}
  Arb -->|Yes| Short[Short Futures]
  Arb -->|No| Long[Long Futures]
```

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How are interest rate futures priced and what drives the futures-spot relationship?

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