# Price CTD vs Future contract price

I am not sure I understand correctly the application of the formula used to compute the number of future contracts needed to adjust the duration of a portfolio.

The formula is :

Nc = (Duration Target - Duration Initial) * Portfolio Initial / (Duration CTD * Price CTD) * Conversion Factor

In Mock Exam Kingsbridge Q2, (exhibit 2) the price of the future, the price of the CTD bond and the Conversion factor are given, and the formula is applied using only the price of the CTD and not using the future price, which seems logical.

However in Mock Exam Kapoor Q4, only the price of the future contract and the conversion factor are given, and the same formula is applied using the future contract in the denominator.

I do not understand why this make sense because I am expecting to use the price of the CTD Bond (which is not given in this exercise)

Can someone help me understand why it is ok to use the future price?

You’re always using the futures price.

US Treasury Bond futures are a special case, because there are a number of bonds that can be delivered against the futures contract, so you use the CTD bond in your calculation. But you’re still using the futures price; it just happens that the futures price of a US Treasury Bond futures is the CTD price.

Sorry to insist but i am not sure i understand your first sentence.

For example, in Mock Exam Kingsbridge Q2 , the future price is given at 100,500 and the CTD Bond price is 97,750. The calculation does not use the future price of 100,500 so i do not understand why you say that one is always using the future price.

From my understanding, it is US Treasury futures in both questions.

Should I understand that for Mock Exam Kapoor Q4, since only the future price is given, it imply that the CTD Bond price is the future price in this case?

Or am I completely lost and I should read the full reading 22 again?

when you have a cheapest to deliver bond - you use its price. But if that is not available - you use the futures price provided as is.

Both are futures prices.

When you have a CTD bond - you have a lower cost for the hedging operation.

Ok thanks