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.
Hi Job, Thanks very much, it’s a great explanation. On the currency swap though, you need to remember that your notional amounts (bond par values as per your example) are not the same in both currencies. The notional amounts are decided based on the exchange rate as of the date they are entered into. Great way to think about it. Thanks.
--------- 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?
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.
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.
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%.
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!
can you give post the example that you got wrong?
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!
I got positive $2,114,010 to the receive fixed
very good, thanks
Why does it look like there is only one payment for the floating?
Job…Fantastic explanation. Would you please give one example of currency and equity. Thank you so much. This is very good
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
For the currency swap, the rate used for the 3rd fixed payment should be 6.5%* (450/720) right?
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)
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…
Thanks job…This is fantastic. Do you have an example of equity?