CFAI text SS15 Reading 43 Problem no. 3

Hey guys, I hope I’ve referred to the right reading. This is a problem in interest rate swaps. In problem 3, it says that the the company has a floating rate obligation of $500m with a coupon payment of 2.5 times LIBOR. In the solution you will see that the NP is multiplied by 2.5! I’m confused! Anyone knows why? Why multiply the entire face value by 2.5 when only the coupon payment is 2.5 times LIBOR? Am I missing something? Please help!

I think it’s just the multiplicative property, you can move the terms around. It is still doing 2.5 x LIBOR right? rate is not multiplied by 2.5 elsewhere?

Hi, If you see the value for swap, it is actually multiplied by 2.5? Why not take $500m only? That is what I’m wondering

issues a leveraged floating-rate note you pay: $5M*2.5*LIBOR ie. $12.5M*LIBOR To offset the $12.5M*LIBOR, you enter into swap The swap You pay: 6% (fixed rate) on $12.5M You receive: LIBOR on $12.5M Net position (swap+leverage floating rate note issues) =$12.5M(LIBOR-LIBOR-6%) => you pay 6% on $12.5M As you bought a bond You receive: 7% on $12.5M Overall Position: => you pay 1% on $12.5M = $0.125M => You enter a swap of 12.5M and not 5M because you receive LIBOR from swap only and not 2.5*LIBOR. To offset the 2.5*LIBOR, you increase the NP to 5*2.5 = $12.5M

sorry typo, Overall Position: => you “receive” 1% on $12.5M = $0.125M

Thanks B_C :slight_smile:

This answer still bothers me because you’re taking in $5 million from the bonds you’ve issued but you have to purchase $12.5 million in in the 7% bond. Seems to me like you’re just earning $125,000 on a $7.5 million investment. Am I missing something?

That does seem odd.

Correct me if I’m wrong, but when you short a $5M leveraged floater to pay 2.5 x LIBOR, do you only receive $5M in proceeds ? (or do you receive the leveraged amount)

I think it would be the former, but it is counterintuitive to issue a leveraged floater if you’re financing the (leverage-1) bond out of your pocket to only earn the difference in fixed rates.

For said example, $125K for $7.5M is a 1.78% return (much less than a risk-free rate).

Face value of floater is $5 milllion.since it is leveraged 2.5xLibor it is being sold at a big premium to an instrument of similar credit and duration but with coupon of 1x libor, so the issuer will possibly even receive $12.5 million upfront for a face value of $5 million at maturity

Do not over think this. it only illustrates how a dealer might convert cash flows from an interest rate swap to his advantage Using a combination of floaters and fixed rate bonds and the swap to hedge interest rate risk on the floater, he makes 1% on a notional of 12.5 million.stop there

aiight. that seems legit although i won’t understand the motivation behind it, i do see that it is just one of many methods.