The question states that the current USD/EUR rate is 1.25. You are asked to calculate the 1 year forward rate where USD risk free rate is 4% and EUR risk free rate is 7%.
The answer should be 1.29 but the given answer is 1.21.
In order for it to be 1.21 then the quoted exchange rate should be for EUR/USD (which is market convention) rather than USD/EUR.
Am I wrong about this? I hope they don’t make these kind of mistakes in the actual exam!
It is not a mistake.The solution is correct.The formula is
Forward Rate(Domestic/Foreign)=Spot Rate(Domestic/Foreign) X [(1 + Rd)/(1+Rf)]^n.
Here Spot(Domestic/Foreign) =1.25
Rd=4%
Rf=7%
n=1
Therefore, Forward(Domestic/Foreign)=1.25 X (1.04/1.07) = 1.21.
Here Domestic currency is USD and Foreign currency is EUR as per the normal standards.
There are 2 ways to guarantee an exchange rate in 1 years time.
Take 1 USD and convert now to 1.25 EUR. Invest the EUR for 1 year at 7%. This gives you 1.3375 EUR.
Or agree a forward rate now (F) and invest the USD at 4% for 1 year to give you 1.04 USD. When you convert your 1.04 USD to EUR at your agreed forward rate (F) you must end up with exactly 1.3375 EUR. If you do not then an arbitrage opportunity exists which would be exploited by the market and will soon disapear.
This means F = 1.3375/1.04 = approx 1.29.
As I mentioned in my original post, they got the market convention wrong for this currency pair. Had they said the EUR/USD = 1.25 then all would be well. However they said that USD/EUR = 1.25 and so we have this error.
[quote=“Saffer”]
There are 2 ways to guarantee an exchange rate in 1 years time.
Take 1 USD and convert now to 1.25 EUR. Invest the EUR for 1 year at 7%. This gives you 1.3375 EUR.
Or agree a forward rate now (F) and invest the USD at 4% for 1 year to give you 1.04 USD. When you convert your 1.04 USD to EUR at your agreed forward rate (F) you must end up with exactly 1.3375 EUR. If you do not then an arbitrage opportunity exists which would be exploited by the market and will soon disapear.
This means F = 1.3375/1.04 = approx 1.29.
As I mentioned in my original post, they got the market convention wrong for this currency pair. Had they said the EUR/USD = 1.25 then all would be well. However they said that USD/EUR = 1.25 and so we have this error.
You cannot convert USD to 1.25 EUR.The spot rate is 1.25 USD/EUR.So 1 USD will be converted to 0.8 EUR and not 1 EUR.If you make this correction in your first statement then you will reach the correct solution…
Viraj, as I have stated in both my posts, they have quoted it as USD/EUR. When currency is quoted this way, the left side is called the base currency and the right side is called the term or quote currency. USD/EUR can be read as the price of a USD in terms of EUR. Or 1.25 EUR for every USD.
Market convention (as you have correctly identified) is to quote EUR/USD. Notice how I have flipped the currency pair. When quoted this way, it means the price of a EUR in terms of USD. Had they quoted it in this way then the answer they have given (and you calculated) would be correct. But they quoted it the other way and so it is wrong.
Hello Saffer You are right about this . . The currency convention has been written incorrectly. But still the answer is correct Because if you see the books of GARP as well as Schweser carefully you’ll fnd that the interpretation of a currency pair has been twisted sometimes. Here if USD/EUR rate is given as 1.25 . . they are interpreting it like this - 1.25 USD per EUR or 1.25 Dollars per unit of Euro . . which is exactly the opposite of the market convention . . . Now if we consider interest rate parity, that country’s currency is expected to depreciate where the interest rates are higher . . which means that the Euro is expected to depreciate . . And the answer 1.21 is completely in line with this . . because if forward rate is USD/EUR = 1.21, it means 1.21 USD per EUR (according to their interpretation), which means forward rate predicts that 1 Euro is will be worth lesser number of dollars and hence it will depreciate . .
And the formula which has been stated in the other comment Forward Rate(Domestic/Foreign)=Spot Rate(Domestic/Foreign) X [(1 + Rd)/(1+Rf)]^n works with the wrong convention, and not the market convention I think the formula should be applied with great caution considering the rules of interest rate parity, because in terms of convention, I’ve seen that they have left a lot of room for confusion . . .
IRP = Spot (Base) / Spot (Price) x (1 + IR Price) / (1 + IR Base). This is a common approach.
CFAI has opposite approach
IRP = Spot (Price) / Spot (Base) x (1 + IR Price) / (1 + IR Base).
I rather use terms Base and Pricing (Quote) currency than Domestic and Foreign which is confusing.