# Dollar Duration of a Futures Contract

To find the numbers of futures contract needed to achieve a target duration: numbers of contract = (DDt - DDp) / (DDctd / conversion factor) Why do we need to divide DDctd by the conversion factor? Since the futures contracts that we will be receiving are the cheapest to deliver contracts and have a duration of DDctd, wouldn’t the formula (DDt - DDp) / DDctd work to find the numbers of futures contract we want? I guess I am missing / misunderstanding something. Any insights and comments are appreciated!

Future Price=CTD Price/Conversion Factor

I understand futures price = CTD Price / Conversion Factor; but conceptually, if the futures contract that you are receiving are the CTD contracts which have a duration of DDctd and the ratio (in terms of number of contracts, not price) of the original futures contract to the CTD contracts are 1 to 1; why would you still need take into account the conversion factor when calculating the number of futures needed to achieve the target duration? Would the formula (DDt - DDp) / DDctd work out?

Remember you are trading the futures contract , not some unknown CTD contract. Ultimately you as the long receive some convenient ctd contract. But the price of this one may not match the futures price , so we actualy receive either more or less based on a multiplier which serves to align the price of the futures contract to the actual ctd.

DDf = DDctd / (conversion factor). The futures’ Duration may not be equal to CTD’s. Can you confirm “Future Price=CTD Price/Conversion Factor”?

yes deriv , that is correct

Thanks, janakisri.