Delivery Options and Treasury Bond Futures Hedge Ratios

D erivatives such as futures contracts on Treasury bonds (T-bonds) anci notes are tailorniade for hedging interest-rate risk, and in priticiple, computation of an optimal hedge ratio should be easy. The risk-minimizing number oi contracts is obtained by dividing the price value of a basis point {PVBP) ofthe underlying cash position (i.e., the change in dollar value resulting trom a I basis point change in yield) by the PVBP ofthe futures contract. While the PVBP ofthe cash position is straighttorward tor parallel yield curve shifts, the PVBP ofthe futures contract can be more difficult to calculate because of delivery options in the contract. Any Treasury bond with maturity or time to first call of at least 15 years is eligible tor delivery against the T-bond contract. Similarly, the T-note contract may be settled with any note originally issued with 10 years to maturity with remaining maturity at least 6;̂ years. However, because the conversion factors used to adjust delivery terms for the actual bond or note delivered do not perfectly reflect relative value, there is almost always one unique "cheapest-to-deliver" (CTD) bond. If the identity of that bond could be determined in advance, then the PVBP of the contract would also be easy to compute as the converted, forward PVBP of$l()(),()()() par of the CTD. Some sources employing this methodology are surveyed in Rcndleman [1999|.