GARP Book 3 - Question 20.17

[liyi1989]

Question 20.17: Consider a currency swap where interest in British pounds at the rate of 3% is paid and interest on euros at 2% is received. The British pound principal is 1.0 million pounds and the euro principal is 1.1 million euros. The most recent exchange has just occurred and the interest is exchanged every six months. There are two years are remaining in the life of the swap. The current exchange rate is 1.15 euro/pound. The risk-free rates in pounds and euros are 2.5% and 1.5%. Value the swap by considering it as the difference between two bonds. All rates are compounded semi-annually.

Answer:


My question has nothing to do with swap. It mentions EUR/GBP=1.15. So, in the last step of the answer, which converting EUR of 1110797 to GBP, shall we use 1110797*1.15 instead of 1110797/1.15?

Well, by looking at the recent market data, EUR/GBP is indeed ~0.9. So maybe the wording in the problem "1.15 euro/pound" intended to be GBP/EUR? or it is a typo? In FRM exam, what is the convention? suppose, based on Google's historical data 1 euro always equals <1 pound. I assume based on the book,
EURGBP=EUR/GBP=0.9, correct? how about "euro/pound" in the problem?



Simply speaking, the easiest & reasonable explanation is that there is a typo in the problem, which should be pound/euro = 1.15?

Thanks!

 

[David Harper CFA FRM]

Hi @liyi1989 Exactly correct, well done and observant on your part. Unfortunately despite our feedback to be careful about FX conventions, GARP has struggled to get this right (e.g., our feedback here goes back over three years, see here a similar prior mistake on sample/exam question to which we provided feedback https://forum.bionicturtle.com/threads/garp-2017-p1-question-6-garp17-p1-6.13818/post-59661).

I'm going to agree with you. It is easiest is to infer from the solution that what the question intends is for the mathematical conversion ratio to be 1.15 Euros (EUR) per 1.0 British Pound (GBP). Because € 1,110,797 Euros are converted by dividing by 1.15, the intention is that mathematically the conversion is 1.15 Euros per 1.0 GPB. As you already know, but GARP can't seem to keep track of, this is represented by the convention base/quote of GBPEUR €1.150 or GBP/EUR €1.150.

Further, as FX practitioners know, even this might be confusing because Euro is the highest ranking currency such that your 0.90 lookup is expected: As Euro is highest rank, it will always be the base currency, and the Euro/ Pound pair will (almost) always be quoted as EUR/GBP, such that 0.90 EURGBP means 0.90 GBP (the quote currency) per 1.0 EUR (the base currency). There exists an established priority ranking of the major currencies (https://en.wikipedia.org/wiki/Currency_pair ) where the USD is not at the top because we're a young nation as nations go. The Euro is at the top and, in general therefore, will always be the base currency in a default quote convention. So really this question 20.17 should be giving the assumption very plainly (and notice how, when writing the question, I would reiterate an interpretation of the convention b/c not everybody works with this. This question is hard already, it should not bring the reader to a screeching halt trying to figure out exactly what 1.15 or 1/1.15 means) with something like this:

"The current exchange rate is EURGBP £0.870; i.e., 0.870 GBP per 1.0 EUR."

... I like to omit the "/" because it seems to encourage the ratio view (well, it clearly looks like a ratio with the "/" ...) rather than the base-quote convention. Looks like my rounding from 1/1.150 to 0.870 would alter the solution slightly to -43,302. Thank you for the helpful observation, as I'm sure it will end up informing a revision at some point!

 

[liyi1989]

Thanks @David Harper CFA FRM ! This is helpful.

I saw the practice exam's solution will also give "reasonable calculation" for wrong answers. I hope they will not test the GBP/EUR, EUR/GBP in the real exam (so that if we got wrong direction, the result is not one of the choices ).