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.
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im having a hard time grasping the time-lines in these and figured if i saw it from someone elses prespective might make things clearer - please show your work.作者: cv4cfa 时间: 2011-7-11 19:37
Ninety days ago, LIBOR was 4.8%
Fixed Rate was 5% Semi-Annual swap - so payments are 0.025 and 1.025.
Current 90 5% --> 1/(1+0.05*90/360) = 0.98765 * 0.025 = 0.02469
Current 270 5.4% -> 1/(1+0.054*270/360)=0.96108 * 1.025 = 0.98510
Fixed side of swap is now worth = 0.02469 + 0.98510 = 1.00979
Floating side: 90 days ago was a 180 day LIBOR -> 1/(1+0.048*180/360) 0.97656
Now 90 days LIBOR = 0.98765 calculated above.
So Floating is worth 0.98765 * 1.024 = 1.01135
You are in a Pay Fixed, Receive Floating -> so -1.00979 + 1.01135 = 0.00156 per $ of investment.
You invested 10 Million => 15636
Ans B
CP作者: mp3bu 时间: 2011-7-11 19:37
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.
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.
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
Now subtract the two:
$10,113,580.25 - $10,097,947.74 = $15,632.51
When I understood this method, the swap section went from being hard for me, to a very very easy chapter.作者: tikfed 时间: 2011-7-11 19:37
job71188 - that was actually pretty straightfwd & makes a lot of sense- appreciate u taking the time作者: brainsX 时间: 2011-7-11 19:37
After re-reading Jobs posting, do you know why we value the floating rate assuming it resets to par.
I understand the effects, but only in a currency swap would this make intuitive sense.
Any ideas?作者: iteracom 时间: 2011-7-11 19:37
Great explanation Jobs - thanks!
So why is there not a second cash flow from the floating bond? At the 270-day mark.作者: giants2010 时间: 2011-7-11 19:37
The resets are 180 days ( semi-annual as given in the problem ) , not Quarterly . So there is only 180 and 360 days , no 270 days cash flow作者: Pegasus2008 时间: 2011-7-11 19:37
But we're now 90 days out from t0 - so the cash flows are now 90 days and 270 days out. Job is discounting the first one by 90 days rather than the 180.作者: jarobi04 时间: 2011-7-11 19:37
Schweser lists the two things that confuses people about swaps the most:
1) When valuing a swap, why do you include notional principal when no notional principal changes hands
2) How do you value a floating rate bond when future cash flows are unknown
I'll address both of these and hopefully it will clear this up.
1) Try to think of a swap in this manner. Person A issues a fixed rate paying bond with principal of $1,000,000 (the notional principal) at 5.0% (the swap rate). Person B buys this bond. With the $1,000,000, Person A buys a floating rate paying bond from Person B.
So the reason they say no notional principal is exchanged, is Person A would be getting $1,000,000 from Person B only to turn around and send it back to him when he buys the bond. And at the end of the swap, each person would send the other person $1,000,000. When you net these, $0 changes hands.
To value a swap though, you need to value a fixed rate bond and then value a floating rate bond. While at the end, the net notional principal that exchanges is $0, think to yourself that actually what is happening is each party pays each other the notional principal (which happens to be the par value of each bond).
That will allow you to value the bonds when you consider that each party will have to return the par value of the bond they issued to the other party at expiration.
2. Really the only thing that you need to remember about floating rate bonds is THEY RESET TO PAR AT EACH COUPON PAYMENT. The only time they deviate from par is inbetween coupon payments/reset dates. This was covered in Level 1 briefly.
So while I may not know what the cashflows are going to be past the next coupon date, I don't need to know them. We only have to worry about the cashflows that take place up until the reset date.
Look at the problem I did in my first post on how to handle floating rate bonds. You assume that at each payment, the entire bond is due (coupon payment + principal) then a new bond is issued at the new rate (which happens to be issued at par).
I forgot to mention that the method I use also works for any type of currency swap. To value the foreign bond, just multiply the notional amount by the beginning exchange rate then follow the same method. When you have the value of the foreign bond in foreign currency, multiply it by the current exchange rate to bring back to domestic currency.作者: ryanlb 时间: 2011-7-11 19:37
Right , w.r.t the original date the second rest is at 360 , w.r.t the current date the second reset is at 270 . Job is clearly showing that for fixed payment he is discounting the first at 90 days and the second at 270 days .
For the floating you don't need to do the 270 , because we do not know the rate yet. We'll only know the rate 90 days later. The floating rate is established at each reset date and determines the next cash flow .作者: tobeornottobe 时间: 2011-7-11 19:37
Got it. Thank you both for your help! I wasn't associating "reset at par" with $0 value.作者: zephyranalyst 时间: 2011-7-11 19:37
I'm sorry... I'm still having trouble with this.
I understand that the floating rate note resets to par at the reset dates. I also understand that you will not know the cash flow for the second floating payment until the coupon rate is set (in 90 days in this case).
What I don't understand is why we don't care about this other future cash flow. In 90 days, the floating rate note will pay the amount shown above. At the same time it will reset to $1. 270 days from now, there will be another floating rate payment, and the $1 principal is returned. How does this floating rate payment not have a present value which appears in our calculations of the value of the floating rate note!?!?
e.g. look at it from the perspective of someone holding the floating rate note. If I don't sell the bond, I know that I'm going to get $xxx in 90 days, and then $xxx + principal in 270 days. Regardless of how you think of the bond paying back then reissuing at par, how does this reduce the value of that second cash flow to zero?
Edited 1 time(s). Last edit at Monday, April 5, 2010 at 10:58PM by calgaryeng123.作者: profil 时间: 2011-7-11 19:37
Job great post. Made my life much easier.作者: SpyAli 时间: 2011-7-11 19:37
at the payment day - coupon has reset... so it is just the face value (1$) isn't it?
CP作者: ninja1024 时间: 2011-7-11 19:37
Yes it is....a bit confusing as you have to assume the payment on the floating side is out of the picture, but I guess that's why they say it resets on those dates.作者: bdavi77962 时间: 2011-7-11 19:37
What happens after first payment day? . Let's say you'r 10 days after first payment day? How much is the floater worth then?
I get that there is a new rate for LIBOR , set on first payment day , payable on the second payment day. Would it worth that new rate discounted by a revised LIBOR reading each day ?作者: tarunajwani 时间: 2011-7-11 19:37
at that point you know the 2nd LIBOR rate.
so the PV(2nd Libor Rate + the Full Principal) is the floating payment...
CP作者: luda002 时间: 2011-7-11 19:37
I understand all the math behind it, but I don't understand how the comparison is fair.
We are including 2 coupons from the fixed side, and only 1 coupon from the floating side. Why isn't compared 1 coupon with 1 coupon?作者: huangxiaoxie 时间: 2011-7-11 19:37
You are actually comparing (in this case) 2 coupns to 2 coupns.
as you know the fixed side doesn't reset, so you need to find the value of all the future pmts discounted at the given rates.
for the floating rate you do the same thing only you are multiplying the notional by the libor rate and then discounting it by the same libor rate which gives you a value of 1.
for example:
suppose we are at a reset date and the current 180 day libor is 5%
The floater pmt would now be .05(180/360) of the notional in 180 days or .025. now, to discount that back to the present you would divide by .05(180/360) or .025.
.025 / .025 = 1
It's easier just to add the 1 to the amount that is left untill the next reset date instead of going through this each time the floater changes.Hope that makes sense.
