Coupon and Maturity Characteristics of the Cheapest-to-Deliver Bonds on the Treasury Bond Futures Contract

Abstract

The Treasury bond futures contract traded on the Chicago Board of Trade is based on a nominal Treasury bond with 15 years to maturity and an 8 per cent coupon. This benchmark bond may not exist during all delivery months, and even if it does, the available supply may fall short of demand for delivery on the maturing futures contract. To mitigate the potential short supply of the benchmark bond, the futures contract allows the short position to choose any bond with at least 15 years to call (or maturity) for delivery. The short position's right to choose the optimal delivery bond is called the option. The exchange has established conversion factors to determine the delivery value of the chosen bond in relation to the benchmark bond. This method of pricing alternative bonds for delivery purposes is known as pricing. Briefly, the conversion factor for the chosen bond is derived by discounting the cash flows from the bond at 8 per cent.' The conversion factor is thus based on the 8 per cent discount rate (common to all deliverable bonds) and the coupon and maturity of the bond chosen for delivery. It is not affected by the market price of the delivery bond. Factor pricing generates fair conversion rates only when the term structure of interest rates is flat and equal to 8 per cent for all bonds with 15 years or longer to call or maturity. When the term structure is not flat at 8 per cent, the conversion factor will not equal the ratio of market prices of the delivery bond to the benchmark bond. Consequently, when the term structure is rising or falling, but not equal to 8 per cent, the choice of delivery bond will generate gain or loss for the short position. The profit-maximizing short position would choose the deliverable bond that maximizes the profit from delivery. Kilcollin and Livingston have examined in detail the coupon and maturity characteristics of the cheapest-to-deliver bond on the Treasury bond futures contract.2 This note extends their work in two ways. First, it examines the coupon and maturity characteristics of the cheapest-to-deliver bond not only during the delivery month, but prior to delivery as well. Whereas previous studies have largely relied on hypothetical term structures and simulation to examine the properties of the cheapest-to-deliver bond, we use real-world data. Second, the available evidence on the variability of the cheapest-to-deliver bonds over the life of a futures contract is limited; uncertainty about which bond is the cheapest to deliver gives rise to quantity and quality risk in hedging.3 We examine the week-to-week variability of the cheapestto-deliver bonds up to 13 weeks prior to delivery, as well as the implications for hedging and speculation. The empirical results indicate that from 1977 to 1984, coupons and maturities of the cheapest-todeliver bonds varied from week to week over the last quarter of each maturing futures contract. Further examination shows, however, that the value of the quality option as well as its impact on the hedging effectiveness of the futures contract are small.