Hi, I’m only providing the relevant data and including the answer to this question. My question is why is the US ask interest rate used in the numerator and the euro bid interest rate used in the denominator. I understand the FC / DC concept, but not the bid/ask interest rates. DATA: You are given the following quotes: spot exchange rate: /euro = 1.1865 - 1.1870 Three-month interest rates (percent per year): in : 5 - 5.25 in euro: 3.25 - 3.50 Q: What should the quote be for the /euro three-month forward ask exchange rate? Hint: Buying euros forward is equivalent to borrowing dollars to buy euros spot and investing the euros. Answer: (spot ask /euro) x [(1+ ask r$) / (1 + bid reuro)] = 1.1870 X [((1+(.0525/4)) / ((1+(.0325/4))] = 1.1929 Again, why is the bid euro interest rate used in the denominator and not, say, the ask euro interest rate? Thanks in advance!
because you’re borrowing euros in this transaction (i.e. selling euros forward and buying dollars forward, which is what an “ask” exchange rate entails). just like in a regular FX spot trade, when you lift the ‘ask’ price of EURUSD, you’re buying EUR for USD. but as they mention to you in the hint, a forward transaction is essentially the same only you proceed to invest the EUR and USD at their respective interest rates. when you buy EUR forward (take the ‘ask’ price, whereas selling EUR forward would be taking the ‘bid’), you essentially buy EUR spot and then put it on a EUR-paying deposit. when you give your ‘offer’ price, you want to take the lower rate (EUR bid) for calculations which means you’re paying less interest on your borrowed EUR.
thanks, but I think I am more confused now =/
I’m confused on this questions also… Since the question asks for the “forward ask exchange rate”, we use the ask fx given (1.1870) and the highest ask rate, which is given by, 1.0525/1.0325. I say the highest ask rate because from what I understand so far, when one banks asks for another bank for the bid-ask cross rates, they will always quote the highest ask and lowest bid possible. Hence, in this case, if I were to replace 1.0325 with 1.0350, my ask interest rate would be lower because the denominator is higher). Is my logic correct for this question? If not, how do they come up with that answer?
I did it like this: Think it as an example that I need 1million euro in 3 month. Then there are two ways: 1) borrow x today, exchange to euro using spot rate(S) and save the euro in the Bank x \*(1+r euro bid )/S=1,000,000 .......(1) After 3 months I will own the bank x\*(1+ r ask )…(2) 2) Enter an forward contract and exchange in 3 months by the forward rate (F) After 3 months I will borrow y and exchange : y/F=1,000,000 .......(3) Because the forward hedging, I'd own the bank the same amount of money no matter either way I choose, so y=x\*(1+r ask). Plug this in (3) and equate it to (1) x*(1+r$ ask)/F = x *(1+r euro bid )/S ==> F=(1+r$ ask)*S/(1+r euro bid ) When I look back, the trick is all inside the hint. But I can’t understand the hint intuitively without an example, just my way of thinking. Hope I have enough time to do this in the exam.
Here is how I do most FX problems which is similar to gudon’s first example. I usually do not use the formulas since they are not intuitive to me. I always think of the ask interest rate as what I need to pay the bank and the bid as what rate I can invest at. I also usually use the amounts in the bid-ask rate for my calculations. So on the Ask side if I borrow $1.1870 I can get 1 euro from that. My 1 euro will grow at the euro bid rate which is what I can invest in, so my 1 euro grows to 1.008125 euros in 3 months. By borrowing the $1.1870, I need to pay back the bank at the ask rate which is what they will lend to me at. So at the end of 3 months I will owe $1.202579 I now have 1.008125 euros but need to pay back $1.2025. Due to F/X parity, these two values need to be equal to each other. So the 3-month ask rate is 1.2025/1.008125 = 1.19288/E This same thing works on the Bid side. I can borrow 1 euro to get $1.1865. My $1.1865 will grow at the bid interest rate to $1.20133 in 3 months. On my original 1 euro loan, I will now owe 1.00875 euros. I now have $1.20133 but I owe 1.00875 euros. Again, these values should be equal due to F/X parity. So 1.20133/1.00875 = 1.1909/E I now know the 3-month forward rate should be 1.1909-1.19288$/E. Calculation not shown above: Interest Rates 3-Month Bid: 5% / 4 = 1.25% 3-Month Ask: 5.25% / 4 = 1.3125% 3-Month E Bid: 3.25% / 4 = .8125% 3-Month E Ask: 3.5% / 4 = .875%