# Duration question

I ran across a question that gave all the info to find duration for a 120 bp change. The problem is, the question asked for 100 bp change. The answer was the same as figuring it out for a 120 bp change. Is this b/c 20 bp isn’t much? I think we discussed this before with 50 bp vs. 100 bps. Wondering if I can assume this on an exam. I don’t have the question, sorry, just the explanation and answer.

Duration is same, whether you do it using interest rate shocks of 50 bps or 100 or 200. But the interpretation of duration is what is tricky. It always means that duration is the % price change due to 100 bps change. i hope i am correct now (lately i am unsure of myself A LOT!)

Duration can be thought of, besides as the % change in price at 100bp change in interest rate, as the period of time necessary to recover the cost of a bond (PV of all coupons and of principal received in the future). It is going to be the same, no matter the shock in the interest rate (up or down at 50 or at 100 or at 120). The problem is that for very low shocks, like say 2 bp, duration gives no meaningful information, the shock is too small for a true reaction. And once you discovered what’s the % change in price for a certain shock, other than 100bp, the calculus of the % change in price is symmetrical.

Thanks map!

amber, no thanks to me? lol I guess i wasn’t clear.

oops, I meant to say thanks to you the first time, I swear! You both explained it well!

pepp Wrote: ------------------------------------------------------- > Duration is same, whether you do it using interest > rate shocks of 50 bps or 100 or 200. > But the interpretation of duration is what is > tricky. It always means that duration is the % > price change due to 100 bps change. > > i hope i am correct now (lately i am unsure of > myself A LOT!) Nope. First off you’re calculating effective duration here and there is no reason at all to believe that shocking +50 gives the same answer as +200.

to explain further more. let’s say you calculate duration, using 5bps shock. what you get as the answer is a % that you know price moves if the yield changes 100. now if the yield only change 25 bps, then what you do is multiply the duration % by 1/4 and use that to find the price change due to 25 bps. remember duration is a linear approximation, so any % price change due to 100 bps can be used to determine the %price change for any other bps. :). I am very numb these days, any advice, the studies are JUST TOOOO MUCH to do… been slacking off in APRIL.

JoeyDVivre Wrote: ------------------------------------------------------- > pepp Wrote: > -------------------------------------------------- > ----- > > Duration is same, whether you do it using > interest > > rate shocks of 50 bps or 100 or 200. > > But the interpretation of duration is what is > > tricky. It always means that duration is the % > > price change due to 100 bps change. > > > > i hope i am correct now (lately i am unsure of > > myself A LOT!) > > > Nope. > > First off you’re calculating effective duration > here and there is no reason at all to believe that > shocking +50 gives the same answer as +200. then tell the answer already.