# CTD and bond futures

I am reading a chapter on bond futures in Fabozzi's book. It states that without CF (conversion factor) the CTD (cheapest to deliver) would be the bond with the longest maturity and highest coupon. Why is this? Higher coupon means higher PV (present value).

Can anyone assist?

• Can you amend your question to include the relevant quotation? – chrisaycock Jan 13 '13 at 14:53

First, I am not sure which exact statement was made. Also, you cannot just say "without CF" because you are essentially creating an artificial market with messed-up utility. In summary the cheapest-to-deliver bond is:

The bond that results in the smallest loss or greatest profit for the futures seller.

Futures sellers have to buy the bonds they are going to deliver against the contract. So, it is the bond with the lowest price relative to the invoice price. You see, you do not get around applying conversion factors if you really want to figure out the CTD bond. There is no "CFD do not apply here" type of argument.

But to come to your question, to say "It states that without CF (conversion factor) the CTD (cheapest to deliver) would be the bond with the longest maturity and highest coupon." is definitely incorrect. I highly doubt this is what Fabozzi ever said, either it was a very bad typo or you misunderstood.

The conversion factor associated with each bond the futures' delivery basket is constructed such that the invoice prices of the bonds are identical under the assumption that the yield curve is flat at the level of the futures' notional coupon. Therefore, the bond with the highest duration will be the CTD when yields are above the notional coupon and the bond with the lowest duration will be the CTD when yields are below the notional coupon. (In reality, bonds are rich or cheap vis-a-vis the yield curve--e.g., an on-the-run bond may be several basis points rich to an older bond with identical maturity and coupon--so there other factors that come into play as well, but duration is usually the dominant factor.)

This doesn't directly answer your question, which I believe to be confused. But I think it might answer the question that you really want to ask.

Ignoring the conversion factors / invoice prices, I don't know why you or Fabozzi would think that "the bond with the longest maturity and highest coupon" would be cheapest. For two bonds with identical coupons, the longer maturity bond will be cheaper; for two bonds with identical maturity, the bond with the higher coupon will be more expensive. The two properties are offsetting so there is absolutely no reason to conclude that the bond with the longest maturity and the highest coupon would be cheapest.