# Cheapest to Deliver or Futures Price

For hedging or reallocation if they give you both futures price and the cheapest to deliver price…how do you know which to use in the formula?

Same question I have…

Seems that there’s conflicting evidence (both ways) in different places… But if anyone could let us know where in the CFAI curriculum the “official” method was indicated (if one exists), it would be highly appreciated! This seems highly testable…

which duration did they give? thats the one you use.

Here’s an example:

Reduce the duration of the bond portfolio from the current duration of 4. The portfolio market value is currently \$20 million. The futures contract is priced at \$100,000. The duration of the cheapest-to-deliver (CTD) bond is 5 years. The conversion factor for the futures contract is 1.2. Question: How many futures contracts should you sell in order to reduce the duration of the portfolio to 2?

Let me just make up a few choices. PLEASE EXPLAIN YOUR ANSWER.

A. 80

B.88

C. 96

(The correct answer is C… If you chose C, please explain why you didn’t choose A. In other words, why did you multiply by 1.2 when the price given is the futures price, not the CTD bond price.)

# of Futures = (Target Duration - Portfolio Duration) * Portfolio Value/Dollar Duration of Futures Contract

= [(Target Duration - Portfolio Duration) * Portfolio Value/DCTD * PCTD] * [DCTD * PCTD/Dollar Duration of Futures]Contract

– First line has been multiplied and divided by PCTD * DCTD

And PCTD * DCTD / Dollar Duration of Futures Contract = Conversion Factor.of CTD Bond.

Pretty sure this is a Schweser Question - and that is why the inconsistency - sometimes they use Futures contract and at other times CTD bond.

Because the duration of CTD should be adjusted by dividing by 1.2. Alternatively you multiply 1.2 to your final answer.

(2-4)/(5/1.2) * 20M/100k

i think if they give you ctd use it with the conversion factor. if they do not then use futures price.