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.

bdavi77962

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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.
------------

Yes but be careful not to forget to set the notional to be equivalent to original. So, if you come up with 1.25 euros as the price with the initial exchange rate at $0.89/euro, you cannot just convert the 1.25 euros using current exchange rate. What's your equivalent notional?

maryli

Dreary Wrote:
-------------------------------------------------------
> ---------
> 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.
> ------------
>
> Yes but be careful not to forget to set the
> notional to be equivalent to original. So, if you
> come up with 1.25 euros as the price with the
> initial exchange rate at $0.89/euro, you cannot
> just convert the 1.25 euros using current exchange
> rate. What's your equivalent notional?

I like your thinking sir.

MiniMe7

Yea sorry. I thought the explanation was getting long and I hoped most people would remember that.

On currency, if it's a $10,000,000 between $ and Euros, with an exchange rate of $1.25/1 Euro with both fixed, I would value $10,000,000 bond at US rates. Then I would value Euro bond with Par value of 8,000,000 Euros and use respective Euro rates.

You would go through the same steps in valuing the bonds at some point in future. Then would multiple the Euro value by the current exchange rate, and then subtract.

redskins44

Oh and the most important thing to remember for equity swaps, is payments from the equity payer is not decided until the period end. This is different from other swaps where at t=0, you know the payments of t=1.

Lets say a index pays semi annually against a fixed rate of 5%, you value the 5% bond the same way as normal. To value the equity, you take Current Value of Index/Beginning Value. That is the equivalent interest rate the person will pay on the notional principal. That is not an annualized rate though!

So if index starts at 1000 and 180 days in, it is at 1100, the equity payer makes a 10% interest payment (not 5%).

Also, notional principal is reset at each equity payment. So if at 360 days into it, index value is 1200, the interest payment would be 1200/1100 = 9.1%.

scarecrow

Job71188, thanks so much for the explanation above, it makes a lot more intuitive sense than how the CFA explains it. However, I tried applying the process above to the swaps questions on the online sample cfa exams and it didn't give me the right answer. would you mind posting 2-3 more examples, especially in the format of the sample exams or the EOC qs?

Thanks!

jarobi04

can you give post the example that you got wrong?

needhelp1700

ex:

days:
90 1.42%
180 1.84%
270 2.12%
360 3.42%

45 days later:
45 2.21%
135 2.62%
225 3.73%
315 4.92%

Notional Principle of 250M with a 5.15% fixed rate. enters into a one year pay floating LIBOR (rates above) and receive fixed interest rate w/quarterly pmts.

Thank you!

RepoToronto

I got positive $2,114,010 to the receive fixed

19831985

godlike explanation.