# Duration and Swaps clarification needed please...

Study Session 15, Schweser Book 5 page 93… Bottom of page mmakes sense to me and is consistent with my understanding … " The duration of a fixed instrument , however is considerably greater than the duration of a comparable floating rate instrument" FINE… I Get the above. BUT the top of the same page it goies ont o say … " The pay-fixed side of the swap has effectively added a fixed-rate liability, so the duration for the swap in this example is negative, which reduces the duration of the overall portfolio" I dont get it, because I thought adding a fixed rate liability to a portfolio would increase the duration ???

pay fixed: short fixed bond, long floating since floating duration is small, its contribution on portfolio duration is small if you are short fixed bond because of the swap and have a portfolio of bonds, your overall duration will decrease because position size is smaller.

Pay-fix side of the swap. You are paying fix rate and receiving float, so you are shorting a fix rate “bond” and recieving a floating rate bond. True, fix instrument has larger duration than floating instrument, however, since you are shorting fix, therefore you duration in the fix instrument is negative; your floating side is smaller postive number, when you add these two number together, you get a negative number (meaning that your overall duration is decreasing) Example. (totally made up numbers) Fix side duration is 10, since you are shorting it, it becomes -10, Floating side duration is 6, since your are receving it, it is +6 You are paying fix & receiving float, so add (-10) and 6, you get -4. Therefore, this swap positon is reducing your overall portfolio duration. Helps??

Concur.

since you are shorting fix, therefore you duration in the fix instrument is negative This makes sense. But I guess this is confusing. to wrap my head around so we Pay Fixed, but this is ONLY because we Shorted a Fixed rate bond ( so before we shorted we receive fixed, but now we pay fixed) this is confusing

IH8FSA Wrote: > But I guess this is confusing. to wrap my head > around so we Pay Fixed, but this is ONLY because > we Shorted a Fixed rate bond ( so before we > shorted we receive fixed, but now we pay fixed) Example. You hold 10 million worth of fixed rate bonds. You enter into a 5 million swap contract (effectively short 5 million fixed rate bonds, long 5 million floating rate bonds). Your new position is long 5 million fixed rate bonds and long 5 million floating rate bonds. Obviously, your duration is lower.

IH8FSA Wrote: ------------------------------------------------------- > But I guess this is confusing. to wrap my head > around so we Pay Fixed, but this is ONLY because > we Shorted a Fixed rate bond ( so before we > shorted we receive fixed, but now we pay fixed) > Well, you are not exactly shorting a fix-rate bond, the swap arrangment of you paying fix gives you the same kind of interest rate exposure of shorting a bond. What happen when you are shorting a bond? You hope interest rate go to up, therefore you short position can benefit. So, in a pay-fix receive flow swap, your position benefit when interest rate go up. Make sense now?

“So, in a pay-fix receive flow swap, your position benefit when interest rate go up. Make sense now?” --------------------------------------------- Hey WS< appreciate the response. But as per SCHWESERS STATEMENT below, it simply states that it added a fixed rate liability and associates this with lower duration which is confusing, I guess they could have done a better job explaining that we have shorted a fixed rate bond, therefore shorting something with +ve duration actually means its -ve duration. Or maybe this is something I should know already this far into the program, but this Sh** has always been my weak point " The pay-fixed side of the swap has effectively added a fixed-rate liability “*”, so the duration for the swap in this example is negative, which reduces the duration of the overall portfolio"