GARP.FRM.PQ.P1 Interest rate parity (garp13-p1-6)

[Angelinelyt]

hi David

Please can you explain when do we use the following formulas for interest rate parity :

1. Ft =S0 * e(r-rf)T and
2. Forward = Spot x (1+domestic interest rate)/(1+foreign interest rate)

I am very confused as some questions use the first and some use the second and the results are different. For example from 2013 question 6, as follows:


You are examining the exchange rate between the U.S. dollar and the euro and are given the following information regarding the USD/EUR exchange rate and the respective domestic risk-free rates:

Current USD/EUR exchange rate is 1.25
Current USD-denominated 1-year risk-free interest rate is 4% per year Current EUR-denominated 1-year risk-free interest rate is 7% per year

According to the interest rate parity theorem, what is the 1-year forward USD/EUR exchange rate?

a. 0.78 b. 0.82 c. 1.21 d. 1.29

Correct answer: c
Explanation: The forward rate, FT, is given by the interest rate parity equation:

Ft =S0 * e(r-rf)T

where

S0 is the spot exchange rate,
r is the domestic (USD) risk-free rate, and rf is the foreign (EUR) risk-free rate
T is the time to delivery

 

[Deepak Chitnis]

Hi @Angelinelyt Ft =S0 * e(r-rf)T should be used when rates are continuously compounded and, Forward = Spot x (1+domestic interest rate)/(1+foreign interest rate) should be used when rates are discrete compounding (yearly, half yearly). Hope that helps you!
Thank you!

 

[Angelinelyt]

Thank you @Deepak Chitnis for the clear and succinct explanation!

 

[kansal7mba]

If the quote is given as USD/EUR, then the US Interest rate should be numerator.

 

[Angelinelyt]

Hi, thanks for the explanation above. However, i thought that USD/EUR meant 1 USD = 1.25 EUR? Which means that USD is the base currency and EUR is the quoted currency.
I memorised the formula in such a way that Ft =S0 * e(r-rf)T wherein r= quoted currency and rf = base currency and has been able to solve all problems on this except this question. This question reversed what i have learnt to say r= base currency and rf = quoted currency.

Please caa someone explain to me where have i gone wrong?

 

[Deepak Chitnis]

Hi @Angelinelyt you are assuming rate are continuously compounded, but rates are discrete compounding, read question carefully it says 4% rate per year, it means you should use formula Forward = Spot x (1+domestic interest rate)/(1+foreign interest rate), so 1.25*(1.04/1.07)=1.21495 or round to 1.21. Hope that helps!
Thank you!

 

[David Harper CFA FRM]

Hi @Angelinelyt you are correct, the above question does contain a reported flaw. USD/EUR is wrong, it should read EURUSD $1.25 with USD as the quote currency (see https://forum.bionicturtle.com/threads/2016-practice-exam-garp-q6-garp16-p1-6.9998/#post-46384). Further, you are also correct that in the expression S(0)*exp[(r-rf)*T], the (r) is the rate associated with the quote currency. This is natural and consistent with the commodity cost of carry. If the spot FX is EURUSD 1.25 then

• The base currency (EUR) is the commodity, so its own interest rate is like the dividend yield that gets subtracted with "-rf." In COC, this is directionally analogous to convenience yield of (eg) oil: the benefit conferred by commodity ownership (whether intangible convenience or tangible interest rate) is subtracted from the COC
• The quote currency (USD) is used to buy the commodity, so it is added as a cost of funding. Thanks,

 

[yuwaising]

I have a question on the base/quote currency pair. As far as I understand the readings, if stated "base/quote" would mean indirect, whereas "base per quote" means direct. Please correct me if i'm wrong as i see in the question, USD/EUR = 1.25 is a direct quote.

Question 6
6. You are examining the exchange rate between the U.S. dollar and the euro and are given the following information
regarding the USD/EUR exchange rate and the respective domestic risk-free rates:
Current USD/EUR exchange rate is 1.25
Current USD-denominated 1-year risk-free interest rate is 4% per year
Current EUR-denominated 1-year risk-free interest rate is 7% per year
According to the interest rate parity theorem, what is the 1-year forward USD/EUR exchange rate?
a. 0.78
b. 0.82
c. 1.21
d. 1.29

 

[David Harper CFA FRM]

@yuwaising I moved your question to a prior discussion; you'll notice that the question is mistaken. Earlier in the week I wrote in some detail about the FX convention here at https://forum.bionicturtle.com/threads/2016-mock-exam-question-59.21938/post-71806 i.e.,

Hi @aangermeyer Right, what you first wrote is correct:

I have been trying hard to figure out, what the phrase "at a rate of EUR 0.80 per GBP" means and how to convert it to the regular base/quote scheme. As I understand this phrase, for each pound, you get 0.80 EUR. Therefore, GBP must be the base currency, and the Euro the quote currence --> 0.80 GBP/EUR.

... that's the way of spelling it out. It very well might not be obvious to non-native-English speakers, but the "per" in "at a rate of EUR 0.80 per GBP" identifies the base currency (by implying the mathematical denominator) such that this means 0.80 (the quote) EUR per 1.0 (the base) GBP. What is confusing is that merely mathematically, as a mathematical ratio this is 0.80 EUR/1.0 GBP such that GBP 40,000,000 translates into GBP 40,000,000 * 0.80 EUR/1.0 GBP = EUR 40,000,00.

However, we do not specify the FX rate here as 0.80 EUR/GBP; i.e., what looks like the mathematical ratio is not the FX quote convention! There is an established FX convention and 0.80 EUR/GBP or 0.80 EUR/GBP signifies the base as EUR and GBP as the quote currency. So this question is mistaken, in the solution, where it should read:

• 40,000,000 GBP * 0.80 GBPEUR, or equivalently:
• 40,000,000 GBP * 0.80 GBP/EUR

We've educated GARP on the proper convention (as it was practitioner-customers who educated me, truth be told); e.g., https://forum.bionicturtle.com/thre...ures-price-cost-of-carry-mode.8005/post-41107
... i have a video that I've used to help explain (see bottom)

There is a further nuance, actually. Currencies have priority rankings. The ranking among major currencies is Euro, British Pound, Australian Dollar, New Zealand Dollar, U.S. Dollar, Canadian Dollar, Swiss Franc, Japanese Yen (source: Garner, Carley. Currency Trading in the Forex and Futures Markets (Kindle Locations 481-486). Pearson Education (US). Kindle Edition.)

That means, as Carley Garner (who is a world-class expert) says (emphasis mine),

"Knowing the order of priority tells us that the Euro versus the Pound will always be the EUR/ GBP within FX trading platforms, and the U.S. Dollar versus the Canadian Dollar will always be USD/ CAD. Once you understand that all pairs will always be quoted in the same manner (but obviously not at the same price), it is easier to grasp the concept of trading the pair. For instance, if a trader is bearish the U.S. Dollar, he wouldn’t be able to sell a USD/ EUR pair, but he could buy the Euro against the Dollar and accomplish the same feat (that is, go long the EUR/ USD). Again, when buying the EUR/ USD, the trader is purchasing the Euro and selling the Dollar simultaneously." --- Garner, Carley. Currency Trading in the Forex and Futures Markets (Kindle Locations 489-494). Pearson Education (US). Kindle Edition.

That means that, here, we should be quoting 1/0.8 = EURGBP 1.25, because the Euro ranks first and so the Euro will always be the base, and 1.25 EURGBP signifies EUR is the base and GBP is the currency, and can be expressed in English as "at a rate of GBP 1.25 per EUR." (you might notice that I have come to prefer "EURGBP" rather than "EUR/GBP" simply because the "/" might lend to the confusion that this represents a mathematical fraction!). So, you are right to be confused! But I hope this is helpful,

 

[ktrathen]

Hi,

I was working through the Part I practice exam from 2013. In question 6 they say "C" is the correct answer. I believe this might be a mistake.

Is this currency pair incorrectly quoted? Given the EUR risk free rate is higher than the USD risk free rate, the EUR forward rate should be weaker than the USD forward rate. This would translate to 1.21 only if we were talking about EUR/USD (USD per EUR).

If it is indeed USD/EUR (EUR per USD) then one USD today buys 1.25 EUR. This earns 7% to be 1.3375 EUR after one year. Dividing by 1.04 gives us a breakeven forward rate of ~1.29.

Many thanks.

 

[Nicole Seaman]

Hi,

I was working through the Part I practice exam from 2013. In question 6 they say "C" is the correct answer. I believe this might be a mistake.

Is this currency pair incorrectly quoted? Given the EUR risk free rate is higher than the USD risk free rate, the EUR forward rate should be weaker than the USD forward rate. This would translate to 1.21 only if we were talking about EUR/USD (USD per EUR).

If it is indeed USD/EUR (EUR per USD) then one USD today buys 1.25 EUR. This earns 7% to be 1.3375 EUR after one year. Dividing by 1.04 gives us a breakeven forward rate of ~1.29.

Many thanks.

Hello @ktrathen

I've moved your post to this thread, which already discusses this practice question. Please read through the discussion, as you will notice that this mistake was previously pointed out. We ask that you please use the search and tag functions in the forum to see if a question has already been discussed. This saves us time from answering duplicate questions, and it also saves you time from having to wait for someone to answer. Notice the tag at the top of this thread (garp13-p1-6: 13=year, p1=part, 6=question number). This is how all of our GARP practice questions are tagged for an easy search. Thank you