# Another Interest Rate (Cap) Question

A firm purchases a one-year cap with a strike rate of 4%, a notional principal of \$3 million, and semiannual settlement. The reference rate at the initiation of the cap is 5%, falls to 4.5% at the next settlement and then to 4% one year after the cap’s initiation. The total payoffs (without discounting) over the maturity of the swap would be: A) \$22,792. B) \$25,500. C) \$7,583.

messed up.

B gotta remember to look at the rate prior to the settlement date

McLeod, I keep getting 22,500 what am I doing wrong? First settlement date 3,000,000(.05-.04)(180/360)=15,000 Second settlement date 3,000,000(.045-.04)(180/360)=7,500 Total payoffs =22,500

oops…i think i goofed too

Cant seem to get any of the numbers above but A seems closest to what i get ETA: 22500 is what I get too.

I am in the same boat as mwvt9…

yeah, i’m also getting 22,500.

yeah, i get that number too looking at (did they end up discounting it even though they said not to? one thing i don’t remember from last year (level 2) is the first semi-annual payment being determined right at initiation… but i think it’s probably just bad recollection

The first payment is determined at initiation, but not paid out until the first settlement 6 months later. It is called paying in arrears.

mwvt9 Wrote: ------------------------------------------------------- > The first payment is determined at initiation, but > not paid out until the first settlement 6 months > later. It is called paying in arrears. i remember the payment in arrears from last year, i just don’t remember the first payment being determined at initiation (i realize it’s impossible to reconcile the two recollections)… anyone know the answer??

I’m not sure I agree with the answer. They say you should assume a 182 - 183 day period since none is specified. I would have just assumed 180 days if that answer worked out.

well we would have all guessed right since it was closest to our answer, unless you were dumb and read too fast ast first and picked B. I would assume 180 unless the 30-31-31- were given to me

Schweser states that days should be provided on the exzm.

Your answer: A was correct! Since the number of days is not given for each period, approximate it with 182 in the first period and 183 in the second period. Remember that payments are made in arrears. First payoff = \$ 15,167 = \$3,000,000 × max(0, 0.05 – 0.04) × (182/360). Second payoff = \$7,625 = \$3,000,000 × max(0, 0.045 – 0.04) × (183/360) Total = \$22,792 = 7,625 + 15,167

McLeod81 Wrote: ------------------------------------------------------- > I’m not sure I agree with the answer. They say > you should assume a 182 - 183 day period since > none is specified. > > I would have just assumed 180 days if that answer > worked out. i don’t have my calculator handy. what would they calculation be?? don’t we just assume half a year?? whether it’s 180/360 or 182.5/365??? which should work out almost exactly the same??

Yeah. I remember this now. They do count actual days on these things. It can lead to different payment amounts even if the underlying reference rate is the same. If you map out the first two quarter of the year I think you get 182 days and quarters 3 and 4 will be 183.

The day count is A / 360, but usually they either give you the months involved or state a given number of days.

Yeah. I don’t think we would have to worry about this on the exam. I would be really pissed if I missed something this easy due to a stupid day convention.

Q1 = 90 (or 91 on 2000, 2004, 2008 etc) Q2 = 91 Q3 = 92 Q4 = 92