Swaps made easy understand, different, presented, actually, opinion

morebeans

I had this posted a few posts into a different topic, but thought I would start a seperate topic with this as the first post. Honestly, when I see a vignette on swaps come up I am releived now. Hopefully this clears this topic up for a lot of people.

Here is how I do it. It takes an extra minute, but this method was much simplier than the ones presented in the books in my opinion. This will look like a long explanation, but it is actually pretty simple when you understand it and you can do it pretty quick.

The key is to remember that you value a fixed rate bond like you normally would. Then, you independently value a floating security. Keep in mind the floating rate security resets to par at each payment.

Now let's take this question:
A $10 million 1-year semi-annual-pay LIBOR-based interest-rate swap was initiated 90 days ago when LIBOR was 4.8%. The fixed rate on the swap is 5%, current 90-day LIBOR is 5% and 270-day LIBOR is 5.4%. The value of the swap to the fixed-rate payer is closest to:

A) $19,229.

B) $15,633.

C) $12,465.


First the fixed rate bond:
The interest rate is 5.0% semi-annually. With a notional principal of $10MM, that means two payments of $250,000. The notional principal of $10MM also is returned on the second payment. So I actually right out on the page:

$250,000 + $10,250,000

To calculate the value of the bond, you must discount each of these back. Since this is a 360 day agreement with semiannual payments, from initation payments will come at day 180 and day 360. It says you are 90 days into the agreement, which means the payments are now 90 and 270 days away.

The 90 day rate was 5.0%. That is an annual rate, so you must divide by 4 (4 = 90/360) to get how much to discount over the 90 days = 1.25%. You do the same thing with the 270 rate 5.4% = 5.4%*(270/360) = 4.05%. Now I add those underneath my cashflows:

$250,000/(1.0125) + $10,250,000/(1.0405) = $10,097,947.74
That's the value of the fixed rate security aka the value of the fixed rate receiver.

Now the floater:
Again I first figure out the cashflows but remember, it resets to par at each payment. Think of it as the bond matures and returns the principal at each payment, then issues a new security at par if that makes sense.

So they give you the initial rate of 4.8%. That is semi-annual, so the first coupon is $240,000. You have the $10MM notional principal returned with this though, so the actual cashflow is $10,240,000 in 180 days. I write down on the paper:

$10,240,000

Now 90 days later, the rate to discount it at is the same as the 90 day rate for the fixed security (5%/4 = 1.25%).

$10,240,000 / (1.0125) = $10,113,580.25 = value of floating rate bond = value of floating receiver

Now subtract the two:
$10,113,580.25 - $10,097,947.74 = $15,632.51



Let's say its a currency swap. All you do is value each bond in their respective currencies. If one or both are fixed rate, you value them like normal bonds. If one or both are floating, you use the floating method above. Then you take the value of one of the bonds, multiply it by the exchange rate, and subtract.

When I understood this method, the swap section went from being hard for me, to a very very easy chapter.

RepoToronto

Can you help please...I must have done a/some silly mistakes but can somebody tell me where I go wrong in my computation...only 2 neurones still working...

Value of fixed rate coupon = 5.15/4%*250,000,000=3,218,750
Fixed Bond = 250,000,000+3,218,750*2 =256,437,500 (A)

Floater = 1.42%*250,000,000+250,000,000 = 253,550,000 (B)

Value of swap = A-B = 2,887,500

WarrenB1

Very good explanation. Helps a great deal. I hate those questions normally.

chandsingh

Great example, however can this be used for Kellyz question asked, I think you said ￡2,114,010 to the receive fixed but how did you work out the coupon on the floating?

If you are not given the 90 day LIBOR at inception of the swap then I am right in thinking you cannot use this method? The correct answer was -￡2,250,000.

FinancialAnaly

Thanks job..This is fantastic. Do you have an example of equity?

redskins44

N/M i know what I did wrong, it should be 450/360 and 630/360 and not the other way around. I'm retarded..

needhelp1700

hmmms I keep getting something else for the fixed rate payment. I'm pretty sure i'm doing it wrong.

For the 3rd and 4th rate for the fixed payments, I did 6.5% * (450/720) and 7.0% * (630/720)

Sportsman

For the currency swap, the rate used for the 3rd fixed payment should be 6.5%* (450/720) right?

bingbingliang

Currency:

You just value each bond in its respective currency then translate into the main currency.

Let's say you want to do a $ for Yen swap with notional principal of $1,0000,000 for 2 years and semiannual payments. Current exchange rate is Y120 to $1. Let's say $ is paying fixed at 6.0% and Y is paying floating, and at initiation, 180 day rate in Japan is 5.5%.

90 days into it, the current interest rate structure is this:
USA
90 day - 4.5%
270 day - 5.5%
450 day - 6.5%
630 day - 7.0%

Japan
90 day - 4.0%
270 day - 5.0%
450 day - 6.0%
630 day - 6.5%

And the current exchange rate is Y110 to $1. What is the value to the receive Yen?

Ok first let's value receive $. This equivalent to buying a fixed rate bond in the USA and issuing a floating rate bond in Japan.

So semiannual payments at 6.0% on $1,000,000 means $30,000 semi annual payments with the $1,000,000 notional principal returning at the final payment. So here is the timeline of when you receive payments:

In 90 days $30,000
In 270 days $30,000
in 450 days $30,000
in 630 days $1,030,000

You discount the above payments in the respective $$$ rates above. So at 90 days, you take 4.5%*90/360 = 1.125% and at 270 days, you take 5.5%*(270/360) = 4.125% and so on.

When you discount the above payments add all that up, you should get $1,003,781

Now the receive Yen bond. First let's figure out the notional principal in Yen. The original exchange rate was Y120 to $1 on $1,000,000 notional principal so that equals Y$120,000,000. The Yen is floating with the first 180 day rate at 5.5% so you value this same way you value floating rate bond in my first example.

The first interest payment = 5.5%*(180/360) = 2.75%*$120,000,000 = Y3,300,000
But you also receive the notional principal back at this point so here is the timeline of cashflows

In 90 days receive Y123,300,000

The 90 day rate is currently 4.0% in Japan. You need to multiply by 90/360 though which equals 1.0%

Value of floating rate Yen bond = 123,300,000/1.01 = 122,079,208

Now convert back at the current exchange rate of Y110 to $1.

Y122,079,208/110 = $1,109,811

Now subtract the two

$1,109,811 - $1,003,781 = $106,030

ninja1024

Job..Fantastic explanation. Would you please give one example of currency and equity. Thank you so much. This is very good