# Adjusting dollar duration with futures (CTD) when less than 100 bps change

Ok… so I was solving some practice tests from Schwesers 2010 book 1 Exam 3, and found two different questions that were of the same nature, that solved the problem two different ways. Rather than post the entire questions here, I will just describe the difference.

In both cases you were given a market price, face value, and a duration. In both problems the question asked how many contracts to buy or sell given a less than 100 bps change, lets call it 50 bps. Both problems involved using t-bond futures and a CTD bond to create the hedge. In one problem, the numerator dollar duration is adjusted for the fact that is less than 100 bps by multiplying the given duration by 0.005 rather than 0.01 (50 bps vs 100 bps), and the CTD dollar duration is similarly adjusted. In the other problem, the numerator (Desired DD) is adjusted, however the CTD is not.

In the first situation, the final answer will effectively be the same as for a 100 bps change because both the numerator and denominator are adjusted by the same factor (0.005), whereas in the second situation since only the numerator is adjusted, there is a discrepancy.

The exact questions are 18.4 and 15.1 (18.4 only adjusts numerator, 15.1adjusts both).

Is this an error, which one is correct? I am inclined to think you adjust both since duration implicitly assumes 100 bps moves; which should yield the same result as if you did not adjust for the fact that it is less than 100 bps since both numerator and demoniator share the same adjustment.

IMO, CTD should have been adjusted in both ques.

Only difference in text i could read out is in 15.1 it explicitly says DD of CTD for a 100 bps while in 18.4 it only gives DD of CTD is this much.

We have read that DD by definition only a change in portfolio for a 100 bps change in market yield. For any other expected BPS change in BPS it should be adjusted as rightly done in 15.1

Those are my thoughts as well. I also noted the explicit 100 bps change in 15.1, however as you have mentioned by definition unless otherwise stated duration is for 100 bps changes.

markCFAIL

Are you doing only PM session in this book or you are also attempting AM session? I asked i may take these exams too. Just wondering whether AM session here would be helpful or not

Thanks!

I do them all. They are all helpful.

markCFA, are these questions still in Schweser Practice Book1 for 2012? The question numberings have changed.

dont know, im using 2010.

Just thinking,

Is it coz in 15.1 it’s corporate bond & in 18.4 its T bond…

No. Duration effects both bonds the same way, provided they have the same duration.