Bond Futures and Cheapest-to-Deliver
Price a government bond futures contract from the bond the short will deliver: accrued interest today and at delivery, the carried full price, the conversion factor and the invoice amount, then check the market price for cash-and-carry and find the cheapest-to-deliver bond in the basket.
Learning focus: the quoted futures price is the cheapest-to-deliver bond's quoted forward price divided by its conversion factor, so the short delivers whichever bond costs least once its price is set against the futures price times its conversion factor.
An approximation of the exchange's method: semiannual coupons discounted at the notional yield. With an odd quarter left, the bond is valued 3 months ahead, discounted back 3 months and the accrued coupon is taken off. Exchanges publish the official factors.
The futures price is above its no-arbitrage value. Cash-and-carry locks in the gap: borrow to buy the bond at its full price, sell the futures, and deliver the bond at expiry for the invoice amount.
The check treats the futures as a forward on this bond and ignores the short's delivery options (which bond and when), which lower the fair futures price a little.
Using 90 days to delivery.
| Bond | CF used | Cost of delivering | Invoice per 100 | Full price | Implied repo rate |
|---|---|---|---|---|---|
| A CTD | 0.8960 | −0.4332 | 113.3665 | 111.6833 | 6.03%(highest) |
| B | 1.0595(computed) | 0.1118 | 134.2965 | 132.7833 | 4.56% |
| C | 0.7383(computed) | 3.4985 | 93.3682 | 95.8667 | −10.42% |
Cost of delivering = quoted price − market futures price × CF, per 100 par; the cheapest-to-deliver (CTD) bond has the lowest. Leave the CF blank to compute it from the coupon and years left at the notional yield. With both accrued interest (AI) figures, the implied repo rate is (invoice amount ÷ full price − 1) × 360 ÷ days, where the invoice is F × CF + AI at delivery and the full price is the quoted price + AI today. It assumes no coupon before delivery, judged from the months since the last coupon and to expiry of the bond above, which the basket is taken to share. The bond with the highest implied repo rate is usually the CTD.
Each bond's price today is recomputed at its yield plus the shift, as if delivery were today, with semiannual coupons on half-year steps back from maturity; the futures price is set where it converges at delivery, the lowest price ÷ CF in the basket, so the CTD's cost is zero and these costs differ from the table above, which uses the market futures price; rising yields tend to favour longer-duration bonds and falling yields shorter ones (CTD by shift: bond A from −200 bp, bond B from +50 bp, bond C from +150 bp).