How do conversion factors work in Treasury bond futures, and why does the cheapest-to-deliver bond matter so much?

Treasury bond futures are unique because the short side can deliver any eligible bond (maturity 15+ years) against the contract. Since bonds have different coupons and maturities, the exchange uses conversion factors (CF) to normalize them.

Conversion Factor Mechanics:

The CF is the price at which a bond would trade if its YTM were exactly 6% (the contract's notional coupon). High-coupon bonds get CFs above 1.0; low-coupon bonds get CFs below 1.0.

The invoice price paid to the short is:

Invoice Price = (Futures Price x CF) + Accrued Interest

Why Cheapest-to-Deliver (CTD) Matters:

The short wants to minimize their cost, so they compare what they receive (invoice price) versus what each bond costs in the cash market. The CTD is the bond that maximizes:

Delivery Profit = Invoice Price - Cash Market Price

Or equivalently minimizes the basis = Cash Price - (Futures Price x CF).

Example:

Suppose the futures price is 120-00 (i.e., $120,000 per contract) and two eligible bonds exist:

Harborline is the CTD because it yields the highest delivery profit.

CTD Behavior Rules:

• When yields > 6%: Low-coupon, long-duration bonds become CTD
• When yields < 6%: High-coupon, short-duration bonds become CTD
• CTD shifts can cause sudden basis changes, creating risk for hedgers

The futures price effectively tracks the CTD bond, so understanding which bond is CTD tells you how the contract will behave when rates move. This is heavily tested on the FRM exam.

For more depth on fixed-income derivatives, explore our FRM course materials.