Does anyone know why the floating rate duration is 1/#of payments annually*2?? I can’t seem to figure out why the number of payments is multiplied by 2. For example, consider a 1 year swap that has quarterly payments. The duration of the party receiving floating will be (1/4*2)-(0.75*1.0)= 0.125-0.75= 0.625. Why is it not simply 1/4- 0.75=0.50???
Here in comment #3 (mwvt9), you have your answer:
http://www.analystforum.com/forums/cfa-forums/cfa-level-iii-forum/9930010
I just copied and pasted it because I think it is a good answer.
Let us know if it is still not clear.
Generally the (effective) duration of a floating rate bond is approximated as half the time between coupon payments (and reset dates). This accounts for the fact that at the reset date the price (usually) resets to par, so the greatest amount of price deviation would likely occur midway between reset dates.
Thanks for the responses! I’m a little confused though. I think this was probably covered in LI, but what is the stream of cash flows like? Consider a two year swap with semi-annual payments and a notional principal of $100 million starting on 1/1/15, with the fixed rate paying 5% and the floating paying LIBOR. If on 1/1/15 the LIBOR was at 5.25% and on 6/30/15 the LIBOR was at 5.90%, would the net payment to the floating receiver be 0.25% or 0.90%? Basically, is the cash flow determined at the beginning of the period or the end of the period? If we knew on 1/1/15 that on 6/30 we would receive $250K (0.25% of $100MM) then it effectively becomes a zero coupon bond and it’s duration should be equal to its maturity (6 months), but if we don’t know what our payment will be on 1/1/15 and it is based on the LIBOR on the day of the first payment 6/30/15 ($900K), then I don’t see how there can be any duration at all because there would be no interest rate risk (on the floating side at least)… So it seems like I’m confused on two different things; 1) Is the repricing date upfront or on the tailend(e.g. 1st payment based on LIBOR on 1/1/15 or 6/30/15) and 2) In either case how is the duration anything other than 0 or 6 months… I know I should just memorize the formula and move on but these types of things bother me until I figure them out.
Thanks for all your help!
LIBOR on the date when you entered in the contract (now) would be used to perform the payoff 6 months into your swap. (LIBOR in arrears).
1st payment is based on 1/1/2015.
You are getting that payment on day 180 - 6 months hence - so the average duration = (0 + 6 months)/2 = 3 months.