# Cheapest to Deliver Bond

When dealing with Treasury bond futures, locating the cheapest-to-deliver bond is a critical decision. When yields are fairly low (below 6%), as they are at present, which of the following types of bonds tend to be the cheapestto- deliver? A) Low-coupon, long maturity. B) Zero-coupon, long maturity. C) High-coupon, long maturity. D) High-coupon, short maturity I am really confused at this question.It would be of great help if someone can help me.

It seems like a silly question. Each of these bonds will have a conversion factor, and the CTD will be the one which is cheapest when the conversion factor is considered. There’s no way to know which of the conversion factors will be off by the greatest percentage (in the correct direction).

Where’d you see this question?

+1

I saw this in Schweser Q bank…I don’t think they give wrong questions…Mathematically we have to minimize (Quoted bond’s price - (Quoted Futures Price X Conversion Factor))…Basically I am having confusion to grasp this concept practically…Any thoughts…??

Yes, the conversion factor’s the thing; without it, the question is pointless.

The conversion factors are recalculated every day, with the view toward making all deliverable bonds cost the same amount. However, the process is imperfect, so there will always be a bond that is cheaper than the others (when the CF is taken into account); that one’s the CTD.

I gave an example in this thread: http://www.analystforum.com/forums/cfa-forums/cfa-level-i-forum/91330426.

This is mentioned in the 'Interest Rate Futures" chapter in Options, Futures and Other Derivatives. Hull writes, “When bond yields are in excess of 6%, the conversion factor system tends to favor delivery of low coupon long maturity bonds. When yields are less than 6%, the system tneds to favor high coupon short maturity bonds.”

He also mentions, CBOT calculates conversion factor based on assumption of 6% interest rate.

"The conversion factor for a bond is set equal to the quoted price the bond would have per dollar of principal on the first day of the delivery month on the assumption that the interest rate for all maturities equals 6% per annum.