# Bond duration

Quick query: An investor wants to reduce his portfolio duration. He assums position in receive floating (reset every 3mts) position in an annual swap. Floating rate is 6% and swap rate is 5.5%. Calculate the net duration faced by the investor at first reset date.

What is the duration of the fixed here? I am guessing he will reduce his duration by .125 - Fixed duration. Not sure how to utilize the rates.

someone?

It doesn’t seem like you’ve give all the information needed to calc

i agree with not enough info… we would need to know the length of the fixed rate to give you a net duration (Fixed duration - floating duration)

Gents, do not say it can’t be done… such question is reasonable, for example, in the morning session. One must hypothesize and make assumptions. Attack the question with skill, that’s what the morning session is about! We know that the CFA curriculum states that for fixed bonds duration is approximately 70% of itss maturity, hence 0.7…(state this assumption on your answer). For floating, the max duration is 0.25 (3 months) and minimum 0, for an average of .125. (again, make your case on the exam, make the assumption). However, at first reset date, duration of floating will be at max so .25 Duration: 0.25-.70= -.45 I could also make the case that after the first reset date fixed bond has only 9 months to maturity or duration of 70% that. Duration reduced, when interest rates increase, value of portfolio increases.

Well, theres a lot of assumption that can take place here. But thats not the point. If a question needs to be answered, make sure all the facts are given. Manager might already have a certain amount of duration, so his duration has just reduced. That doesn’t mean his duration is negative like in your case for example. Also, you say 70%, I believe CFA uses 75%. And I am guessing for floating rate, we are going to be using .125 if we are not at reset date yet. So I think this question is incomplete. Will wait for the OP to get back to us. BTW, thanks for reminding me that floating rate duration is max at reset date. I would have certainly used .125 if not for your post.

why we are on the topic I am confused on duration of swaps… Can the duration of a swap be negative? Like if you receive floating and pay fixed, can the formula be (floating duration - fixed duration) which would give you a negative number? How does this work?

I saw the question as i framed it. Lets assume the duration of fixed as 3. So in this case we have 2 question: 1. Can the net duration be negative? 2. And can we assume floating duration as 0, instead of dividing it my maturity. Schweser has done this in multiple questions.

i am pretty sure that floating rate duration has to be .125. It would be 0 the day before the floating rate is paid, and .25 the day after the reset. But if you dont know where you are at in the period, CFAI says it is safe to assume half of the time period. So in this case, that would be .125. We got Schwesed on this question.

Yes, you can assume that the average duration of the floating side for quarterly payments is 0.125. So, net duration surely can be negative. For the fixed rate payer it’s normaly negative and for the fixed rate receiver it’s normaly positive. With this principle you can shorten or lengthen the duration of your bond portfolio.

thanks mcHigi… If i am paying a fixed rate swap, I am looking to receive floating, and this floating I receive will lower my duration (because the swap has negative duration for me.) So the key is to look at what i am receiving. If i am receiving fixed, i am increasing duration. Formula for duration of pay fixed is (floating duration - fixed duration). think i am good now