# Fixed and floating rate swaps

Volume 5, Reading 38, page 530, question 3. I’m confused as to why CFAI mulitplied the facevalue by 2.5 in order to come up with coupon payments for the fixed side. the problem only says the floating rate side is coupon of 2.5 * LIBOR.

I thought the pay offf would be just (.07-.06)(5,000,000) but CFAI used (.07-.06)(5,000,000(2.5)

i think i remember this one, i think we had threads about it a long time ago, did not get anywhere, i also think i emailed cfai about it, maybe.

also something similar was done in level II !

hmmm…thanks! hopefully someone on the forum knows

Good old question… Face value is 5m*2.5

We’re all misled by the diagram on p489.

anyone else ?

Tulkuu has the correct answer. if you want to replicate 2.5x libor, you need to enter into a notional of 2.5x the market value you want to swap.

for example: you want to swap \$1 mill pay 2.5x libor

you will need to enter into a notional of \$2.5 million to pay libor, this means you receive the fixed rate on \$2.5mill

your interest rate is always libor - to pay or receive a multiple of it you need to adjust the notional.

Make sense?

I get what is needed to make the “hedge”

The problem is, where you get money for the 2.5 notional principle

YOu are asusming that selling a bond that pays 2.5 libor will bring in proceeds 2.5 times its facevalue?

While is hard to happen because it is only paying 2.5 libor, but not 2.5 its own face value at the end…

Not sure what you are saying, but as for the first part, you don’t need any money to pay for the notional. the notional is just the amount you calculate the payoff from. Whether you pay libor off 250mill or 2.5libor off 100mill it’s the same thing.

Now, as far as I know, swaps are only quoted at libor (or some other floating rate) and not multiples of it. So if you want a multiple of Libor you need to adjust your notional amount to match what multiple of Libor you need.

To simplify,

You are using 2.5 times the principal to earn a tiny amount of net interest spread.

the question is, how is it the teh proceeds from issuing a bond that pays 2.5 libor will be enough to buy bond with 2.5 times the face value of the issued bonds

the procceeds from the issue of such bonds should be less than 2.5 face value because most of the bond value comes from the final return of principle at the end

so basicly the purchased bonds will have to be selling at a discount, a big one…

guys can i bring your attention to a point:

you issed bonds with face value of 5,000,000

then you got bonds with face value of 12,500,000

so not only you won the interest CFA talked about

when it is time to pay off your long, you will pay 5,000,000, and you will get 12,500,000 when the bond you hold matures, that is a 7.5 m gain right there interest aside…CFA did not mention this gain…

so the way i am thinking it should have been is

issed bonds for 5,000,000 FP and 2.5L coupon

buy bonds with face value of 5,000,000, and whos coupon is above 15

anything above 15 you will net, because you will pay 15 to get 2.5L via swap…

You are not buying a bond you are entering into a swap agreement,

no there is a bond…

there is a original bond which is a leveraged floater.

you are trying to convert it into something more manageable - in terms of inflows and outflows - by using a Swap. By manageable - I mean convert the original floating rate into a fixed rate…

(all this because you expect the floating rate on which your original bond was linked to - is going to rise).

FinNinja is right - that in this entire analysis you are talking about a Swap - not the bond itself.

Bonds payments do figure in, because that is what you are trying to offset.

so you would be buying a Swap with a notional of 2.5 * Face Value of the Bond - and then working with that.

but noone answered my simple question, the face value of bond you buy is 2.5 times fave value of bond you issued which means when it is time to settle both, you would net the huge difference

you are buying a swap, not a bond…

“using the proceeds to purchase a bond with fixed rare of 7 percent per year”

you are issuing a bond to pay var

buying a bond that pays fixed

then exchanging the fixed you get for var to pay for the bond you issued

however you issed a bond for FP, and baught one for FP*2.5, which means at expiary you will pay 5,000,000 to the one you issued, and get 12,500,000 from the one you purchased

Action Instrument type Multiple Rate Cash flow face value

Issue Leveraged floater 2.5 Libor + 5,000,000

Invest Bond 7% (12,500,000)

(7,500,000)

I think this is what has been pointed at…Issuance of leverage floater is not entirely financing fixed rate bond or the bond is really needs to be trading at a heavy discount in order to make this cashflow outflow as nil.

Note: This is also arbitrage realted txn. So trader would not be using his on money. This money either has to be borrowed or there is a mismatch in understanding??

Yes offcourse, then to hedge we are using swaps which is involves NOTIONAL prinicpal which is not a problem to comprehend.

The original question was about why you multiply the face value of the fixed side by 2.5, and it’s because you need to enter into a swap agreement with a notional principle of 2.5 times the face value of the original bond to offset the leveraged libor payout.

In relation to the new question of: where do you get the money to purchase a bond in an arbitrage transaction of a short leveraged floater and a long fixed rate bond, I don’t think you can say face values are the same as cash flows especially since leveraged floaters are a combination of FRN’s and swaps themselves. I think if you were to actually price these out you would find the cash flows match. The book doesn’t do a very good job of explaining these cash flows, but I think the focus here is just on the mechanics of the strategy. Also, this strategy isn’t even mentioned in the LOS, so it seems that an in depth knowledge of the pricings of the two bonds is not necessary. The CFAI probably should have written something like “the exact pricing of the bonds is outside the scope of this book/material” to indicate that there is further information that is not presented in the curriculum.