# duration of a floater

Since the amount due is known in advance, the duration equals time to reset. However, the text also defines an average duration? What does this mean conceptually. For a quarterly paying-floating position the duration should be .25. Why do they say that the avg. duration is .125?

because in the case you’re thinking of we don’t know how long until the next payment (i.e quarterly reset but are we 1 month or 2 months into the quarter or at the very start?)… if its the very start it would be .25 i think, otherwise they just use an average for the swaps duration… or am i off?

the duration of the floater right before payment is due is 0, duration at the start of the period is the time of the period, so for qaurterly floater on day 0 duration is .25 and on the last day its 0, CFAI tells us just to average them so its (0+.25)/2 = .125 for semiannul it would be .5/2 = .25 and so on

Yea I was wondering the same thing. Maybe the average duration of a quarterly pay assets is inbetween beginning and end that is why they use half of .25? i.e. they assume it is half way (average) to reset.

average in this case is just an approximation, nothing more

volkovv Wrote: ------------------------------------------------------- > average in this case is just an approximation, > nothing more This doesnt help. I can understand the other answers.

volkovv is right. If you have monthly floating payments, then: max time to cash flows=1/12 (start of the month, right after the reset date) min time to cash flows=0 (end of the month, at the reset date) average duration of the floating side=(1/12 - 0) / 2 = 1/24 We are not exact, again like volkovv said, but the approximation works here.

Yes… from what I remember, if not specifically mentioned… Floating Rate = 50% of the payment interval So if the payment interval is monthly or 1/12 it would be 1/12 * 50% = 1/24 For fixed rate bonds it’s 75% of the term. So a 2 year would be 1.50 duration. Someone please confirm… Thanks PJStyles

for fixed rate bond 75% of the term assumption is a bit of a strech in CFAI Book 5, reading 40, p. 224 they use one-year fixed rate bond with quarterly payments and say that duration is somewhere between 0.6 and 1.0, and then go ahead and assume 0.75; however, if frequency of coupons is differnent or term to maturity is longer than a year, then 75% of the term assumption won’t really work. My guess, they would give you duration of the fixed rate bond, like they do in practice problem 2 (p. 270)