# Swaps

By special request from Banny… If the one year spot rate is 5 percent, the two-year spot rate is 5.5 percent, and the three year spot rate is 6 percent, the fixed rate on a 3-year annual pay swap is closest to: A) 1.99%. B) 4.50%. C) 5.96%. D) 6.47%. A \$10 million 1-year semi-annual-pay LIBOR-based interest-rate swap was initiated 90 days ago when LIBOR was 4.8 percent. The fixed rate on the swap is 5 percent, current 90-day LIBOR is 5 percent and 270-day LIBOR is 5.4 percent. The value of the swap to the fixed-rate payer is closest to: A) \$12,465. B) -\$7,667. C) \$19,229. D) \$15,633.

ok start the clock… even the 1st easy one is going to take me time.

a’ight- the fixed sh*t i think i can do. so it’s 1/1.05 + 1/1.055^2 + 1/1.06^3 and the you take 1 minus the 1/1.06^3 over that mess. I get 0.059611 moving onto the ones that crush me every time. i’m going to go curl up in a ball and draw little pictures. be back!

took me ten minutes, but i got C for part 1. now on to part 2.

1/1, nice work. The fixed rate on the swap is: [1-(1/1.063)]/[(1/1.05)+(1/1.0552)+(1/1.063)] =1-0.8396 / [0.9524 + 0.8985 + 0.8396] =0.1604/2.6905 = 5.96%

ok fixed side- 5% on the 10 mil, 500k a year, 250k b/c semiannual. so you’re 250k/1. 05 90/360 (sorry if this looks funny) and then in 270 days which is day 360 you’re principal plus the 250k back so 10,250,000/ 1 + .054 270/360 i’m getting that to be 246,913.5802 + 9,851,033.157 = 10,097,946.74 for the fixed. tell me if i screwed this up and i’m going to go work the floating now. this is where it gets nice and dicey.

part 2 is D!!!

your number looks right for the fixed side

bannisja Wrote: ------------------------------------------------------- > ok fixed side- > 5% on the 10 mil, 500k a year, 250k b/c > semiannual. > > so you’re 250k/1. 05 90/360 (sorry if this looks > funny) and then in 270 days which is day 360 > you’re principal plus the 250k back so 10,250,000/ > 1 + .054 270/360 > > i’m getting that to be 246,913.5802 + > 9,851,033.157 = 10,097,946.74 for the fixed. > > tell me if i screwed this up and i’m going to go > work the floating now. this is where it gets nice > and dicey. Yep, good so far.

i’m nervous although my answer is pretty close to one of the choices so maybe my work last night on these is starting to pay off. floating- so you just need to get to that next payment date. when you initiate the swap you know the 1st floating side- it’d be that 4.8%. so 10 mil x 4.8% = 480k/2 = 240k so then (and correct me if i mess this up)- i take the 240k/1 + .05(90/360) - now here am i right to use that 90 day rate to discount it back? my picture says yes. then what i’ve learned in my swap learning is you want to then get a discount factor and you do it with 1… not sure why yet but whatever, let’s do it. so 1/1 + .05(90/360)… b/c again, i just want to get to that 1st pay date on the floaty side for some reason. get me there get me there. anyhoo that gets me to .987654. if i multiply that x my 10 milly i get 9,876,540. add that to the 237,037 and i get a magical 10,113,577. 10,113,577 - 10,097,946 = 15,631 i’m within \$2 bucks of D and i didn’t really use great rounding here. if i’m right, I AM THE SMARTEST (WO)MAN ALIVE! i know i’ve fumbled through this and probably EVERY swap question in qbank already… but yeah, i need to keep fumbling. is the 5% right to discount back on the floaty side?

By my math Banny, you nailed it!

/borat Very nice /borat The fixed rate payments are 0.05 × (180/360) × 10,000,000 = 250,000. The present value of the remaining payments are 250,000/(1 + 0.05 × (90/360)) + 10,250,000/(1+ 0.054 × (270/360)) = \$10,097,947. The floating payment in 90 days is 0.048 × (180/360) = 240,000 and the present value is 240,000/(1 + 0.05/4) = \$237,037. The second floating-rate payment combined with 1 at the end of the swap has a present value of 1 on the first payment date. The present value of 1 is 1/(1 + 0.05 × (90/360)) = 0.987654321 so the present value of the second floating rate payment combined with the principal amount is \$9,876,543. The total value is 9,876,543 + 237,037 = \$10,113,580. The value of the swap to the fixed-rate payer is 10,113,580 – 10,097,947 = \$15,633.

Good work guys. Here’s another: Consider a \$5 million semiannual-pay floating-rate equity swap initiated when the equity index is 760 and 180-day LIBOR is 3.7 percent. After 90 days the index is at 767, 90-day LIBOR is 3.4 and 270-day LIBOR is 3.7. What is the value of the swap to the floating-rate payer? A)\$3,526. B)\$2,726. C)\$3,526. D)\$2,726.

so then what’s the next twist? equity swap? currency i’m not sure i’m ready for. plain vanilla, you are my biyyyyyatch. i think i’m going to mess up an equity one. fixed would be the same, right? but then i need to learn how to do the equity part. someone tee one up.

I do this another way using discount rates. I’m trying to see how you did it this way.

ozzy you are taking me where i need to go yes brother yes!

Happy to help. I spent all day on derivatives, so I’m working on reinforcement.

How do you get the pay variable using this method. I got fixed as: .025( .9876+.9611)+.9611 = 1.0098 (Multiplied by 10MM = 10,098,175)

answer to the last question I posted: 1.0185 = 1 + 0.037(180/360) 1.0085 = 1 + 0.034(90/360) 767/760 – 1.0185/1.0085 = 0.00070579 × 5,000,000 = \$3,526 Note: The 1.0185/1.0085 is the present value of the floating rate side after 90 days.

i am crumbling… ahhhhhh! so i wanted to do the floaty payer like i did before and say that 3.7%/2 x 5 mil = 95,200 would be paid at day 180 so take 95,200/ 1. 034(90/360) and then add that to 1/1. .034(90/360) = a discount factor of .991573, which x 5 mil is 4,957,858.205 which gets me to \$5,052,255.825 for the floating dude’s side. i feel like i’m off here already. am i off already?