I am trying to find the value of a currency swap to someone after 450 days. I have all of the necessary rates and the PV factors calculated. I also have the exchange rates. I am struggling with calculating the cash flows for the pay side and the receive side. I want to use the method where I multiply the cash flow by the PV factor to get the pv of each cash flow and then add together to find the total value of each side. Thank you!
Here is the problem. I feel like I am so close to getting it but am just slightly off somewhere.
Tommy Louie, CFA, is working as a chief financial officer in a trading firm, Tradebitz Inc. The company is based in Japan. It has its business spread over South America, North America, and Europe. The firm has chosen Mexico as the strategic location for the business. They need to raise Mexican peso (MXN) for that purpose. The cost of borrowing in MXN becomes lower if they enter into a currency swap position rather than taking a direct loan themselves. The company enters into a pay fixed- receive floating loan for a principal of 100 million Yen. Tommy enters into the swap for two years with semi-annual coupon payments.
The interest rates in Mexico and Japan are given in Exhibit 1.
Japan (%). PV Factor Mexico (%)
- 2.4 .9881 6.4 .9690
360 2.6 .9747 6.8 .9363
540 2.9 .9583 7.1 .9038
720 3.2 .9398 7.4 .8711
The currency exchange rate at the time of swap initiation was 0.1265 MXN/YEN. The interest rates after 450 days are given in Exhibit 2.
Japan (%). PV Factor Mexico (%)
90 2.8 .9930 7.1 .9826
-
2.9 .9857 7.3 .9648
-
3.1 .9773 7.6 .9461
The currency exchange rate after 450 days of swap initiation becomes 0.1288 MXN/YEN. The 180-days interest rates for Japan and Mexico after one year of swap initiation were 2.7% and 7.0% respectively. The 180-days interest rates for Japan and Mexico after 180 days from swap initiation were 2.5% and 6.7% respectively.
The exchange rate one day before the swap expiry is 0.1276 MXN/YEN.
What is the value of swap to Tommy at the end of 450 days from swap initiation? I have calculated my answer using the cash flows for each side, multiplying them by their factors, and summing. I then convert the Mexican side back to Yen to compare.
When it comes to calculating the value of currency swaps, you can do it the long way, aka what you did: calculate original SFR, now you know how much interest to pay at each settlement, you discount these cashflows back to find the value of the swap of whichever party you just calculated. Then, repeat the process for the counterparty. You have to remember the currency you’re working with, and what the question is asking for.
OR there’s a very simple way of solving the problem using the formula. Currency swap value after time T = Notional*[(SFR at initiation/# of settlements per year)*sum of all new DFs+last new DF] - counterparty
Try it for yourself.
Could you show me this equation with the numbers in it? I am messing up somewhere.
Would anyone be able to assist me with the calculation? Thank you!
https://www.analystforum.com/forums/cfa-forums/cfa-level-ii-forum/91366597
Take a look at my thread here. Number 29 is asking exactly what you are seeking.
One of the sides has to be negative when you sum both cash flows. What side is negative according to your notes and understanding?
that is what I’m asking in my other thread.
My understanding is the notional amount you originally borrow has to be negative.
Interesting - I haven’t seen this formula and have been doing it the long way. Any chance you could point us to where this formula shows up in study materials so we can go investigate further? Don’t recall seeing it Schweser and would much rather be able to solve quickly (and still correctly) vs. spending a bunch of time solving. Haven’t had issues getting to the right answer the long way, but would love to shave time where possible.
Also, what do you mean by " - counterparty"? Do you mean you run this same formula for the opposite side you’re solving for and subtract that from the value you get from the first half of the formula calculating the side we’re interested in?
Really appreciate the help.
Never mind - found it in one of the TT answers. For those searching around - look at CFAI Derivatives TT’s, number 29. It has the formula there. This was also mentioned by foshizzle above, so just doubling up here. So so so much easier to solve this way.
[quote=“Tuchsford”]
maybe schweser knows something.
[quote=“foshizzle”]
or maybe they don’t but should 
I came across this same question yesterday, but the answer doesn’t match what Konvexity provided. I am too lazy to find out why. But, I will tell you this, the formula works for CFAI TTs, Schweser, and IFT. It works on all the questions I’ve done, just not Konvexity. As mentioned above, the formula is provided by CFAI in the solution.
If you want to practice using this formula, try Schweser Practice Exam Vol. 1 Exam 2 Afternoon question 109 - 114. This set of questions is very elaborated. If you don’t have Schweser, just try the question from CFAI TT.
I still can not get the right answer even using this formula. Can anyone assist with these numbers?
Go to CFAI website, go to topic test, go to deriv, work on problems 25 - 30 by applying the formula. If you can’t get the right answer, look at the solution for problem 29.
Quick question - does this work across all types swaps? Seems like it should, but wanted to confirm. Obviously, you’d need to adjust the calculation of the counterparty side depending on the type of swap, but otherwise the first part shouldn’t change, right?
I’m not sure. But I only use this for currency swaps because the alternative method (finding cashflows then discount back) takes way too long. For plain IR swaps, I use the formula given in Schweser. For equity swaps, it’s easy enough to use the method of finding cfs.
Makes sense. Thanks and good luck on Saturday!
Can anyone confirm if this equation will work for a currency swap?
Currency swap value after time T = Notional*[(SFR at initiation/# of settlements per year)*sum of all new DFs+last new DF] - counterparty.