How does the cheapest-to-deliver (CTD) bond work in Treasury futures, and why does it matter for hedging?

Question

AcadiFi · Accepted Answer

Treasury futures allow the short side to deliver any bond from a basket of eligible maturities, but naturally they will choose the one that minimizes their cost. This is the **cheapest-to-deliver (CTD)** bond.

**Conversion Factor Mechanics**

The exchange assigns each deliverable bond a conversion factor (CF) that adjusts its price as though it yielded exactly 6%. The invoice price the short receives is:

> Invoice Price = Futures Settlement Price x CF + Accrued Interest

The short compares this against the market price of each deliverable bond. The bond where (Market Price - Invoice Price) is smallest — or equivalently, the bond with the highest implied repo rate — becomes the CTD.

**Example: Ridgemont Capital's Duration Hedge**

Suppose Ridgemont Capital holds $50 million in corporate bonds and wants to hedge duration using 10-year Treasury futures. They identify three deliverable bonds:

| Bond | Coupon | Maturity | CF | Market Price | Implied Repo |
|------|--------|----------|------|-------------|-------------|
| T 3.50% 2033 | 3.50% | 8.5 yr | 0.8412 | 94.25 | 4.82% |
| T 4.25% 2034 | 4.25% | 9.2 yr | 0.8891 | 98.50 | 5.15% |
| T 2.75% 2032 | 2.75% | 7.8 yr | 0.7853 | 88.60 | 4.67% |

The T 4.25% 2034 has the highest implied repo rate at 5.15%, so it is the CTD. Ridgemont should hedge using the **duration of this specific bond**, not the notional duration of the contract.

**Why CTD Shifts Create Risk**

```mermaid
flowchart TD
    A[Yield Environment Changes] --> B{Yields Rise?}
    B -- Yes --> C[Low-Coupon / Long-Duration Bonds
Become CTD]
    B -- No --> D[High-Coupon / Short-Duration Bonds
Become CTD]
    C --> E[Futures Duration Increases]
    D --> F[Futures Duration Decreases]
    E --> G[Hedge Ratio Must Be Reduced]
    F --> H[Hedge Ratio Must Be Increased]
    G --> I[Rebalancing Cost]
    H --> I
```

When yields shift, the CTD can switch from one bond to another, abruptly changing the effective duration of the futures contract. A hedger who assumed a static duration will find their position over- or under-hedged after a CTD switch.

**Key FRM takeaway:** Always compute your hedge ratio using the CTD bond's modified duration and conversion factor, not the contract's notional specs. Monitor the deliverable basket for potential CTD switches during volatile rate environments.

For more on fixed-income derivatives hedging, explore our FRM Part I course materials.

How does the cheapest-to-deliver (CTD) bond work in Treasury futures, and why does it matter for hedging?

Master Part I with our FRM Course

Related Questions

Practice Questions

Bond	Coupon	Maturity	CF	Market Price	Implied Repo
T 3.50% 2033	3.50%	8.5 yr	0.8412	94.25	4.82%
T 4.25% 2034	4.25%	9.2 yr	0.8891	98.50	5.15%
T 2.75% 2032	2.75%	7.8 yr	0.7853	88.60	4.67%