Conversion Factors and the Invoice Price

A Treasury futures contract doesn't reference one specific bond. Instead, the short side gets to choose which of a whole basket of eligible Treasury securities to deliver at expiry — anything within a specified maturity and coupon range. Those bonds have different coupons and maturities, so they're worth different amounts, yet the futures contract trades at a single price. The mechanism that reconciles "one price, many possible bonds" is the conversion factor.

How the factor is built

Each eligible bond's conversion factor is calculated (by the exchange, in advance) as the price that bond would have per $1 face value if it were priced to yield exactly 6%, its actual coupon and remaining maturity held fixed. A bond with a coupon above 6% gets a conversion factor above 1.00 (it's worth more than a 6% bond at the same yield); a bond with a coupon below 6% gets a factor below 1.00. When a short delivers a bond, they receive an invoice price:

$$\text{Invoice price} = (\text{Futures settlement price} \times \text{Conversion factor}) + \text{Accrued interest}$$

In words: the short is paid the futures price scaled up or down by that bond's conversion factor, plus whatever coupon interest has accrued since the bond's last coupon date, exactly like buying any bond in the cash market.

Worked example

The futures settlement price is 118-16 (118.50 in decimal, per $100 face). Bond A has a conversion factor of 0.9200; Bond B has a conversion factor of 1.0450. Delivering Bond A pays an invoice price of $118.50 \times 0.9200 = 109.02$ plus accrued interest. Delivering Bond B pays $118.50 \times 1.0450 = 123.83$ plus accrued interest. Whether Bond A or Bond B is cheaper to deliver depends on comparing each bond's actual market price (what it costs to buy in the cash market) against the invoice price it would fetch: the bond with the largest gap between invoice price received and cash price paid is the cheapest to deliver, because the short profits (or loses least) by buying that bond and delivering it.

Worked example: why the factor breaks down away from 6%

Suppose yields fall to 3% across the curve. Conversion factors were computed assuming a flat 6% yield environment, so they no longer reflect the true relative value of high- versus low-coupon bonds at 3% yields — high-coupon, long-duration bonds become relatively more valuable than the 6%-yield-based factor accounts for, because at lower yields, duration effects amplify price differences. This mismatch is exactly the source of the delivery option's value: the short can wait and see which bond in the basket has drifted furthest from its conversion-factor-implied fair value, then deliver that one.

What this means in practice

Every Treasury futures trader has to compute net basis (cash price minus invoice-equivalent price) across the whole delivery basket to know which bond is currently cheapest to deliver, because the futures price itself is really tracking the CTD bond's price, scaled by that bond's own conversion factor, not some blended average of the basket.