Given the following information: The forward rate between dollars and pounds is 1.66$/GBP. The current spot rate is 1.543 $/GBP. The UK interest rate is 5.77%. The interest rate in the United States is 5.976%. Assume a U.S. investor can borrow pounds or dollars. What is the covered interest rate differential? A) −0.07814. B) 0.6786. C) 0.07661. . . . . . . . . . . . . . ------ So, I do the triangle and I go $1000 USD --> 648.90 GBP —> Add in a year of interest, 685.48 GBP —> Bring it back, $1137.9 USD Then you have the cost of borrowing USD: $1059.76 1137.9 - 1059.76 = $78.14 arbitrage profit. Great. Not an answer choice. Ok… 78.14/1000 = .07814 --> Still not an answer choice. Why is the answer negative? What am I missing?
The correct answer is A, here is how I get there: First compute the arbitrage free forward price as: F=$1.543/GBP*(1.05976/1.0577)=$1.546/GBP, next compare this to the prevailing forward rate ($1.66/GBP) this tells you that the GBP is overvalued relative to the dollar, hence you want to borrow dollars, so: Today: Borrow $1, convert to GBP at spot so you have .648GBP. Invest this amount at 5.77% for one period while locking in your future exchange rate via the sale of a forward contract. One period later: Collect .648GBP*1.0577=.6854GBP, convert back to dollars at forward rate that you locked in to get $1.66/GBP*.6854GBP=$1.137764, use the funds to pay off the loan and interest that you took out at time zero (equal to 1.05976), the difference is your arb. profit=1.137764-1.05976=.078 (if you don’t round you get the exact answer). I think this is correct, please let me know if it is not.
adavydov7: Correct answer is A. I agree with you completely on how you got your answer. However, why is the answer negative. That’s the part I can’t figure out.
Oh, my browser showed answer A as −0.07814 so I didn’t realize what negative sign you were talking about. Basically, to get the negative sign just do everything in reverse, arbitrage profits/losses are symmetrical so it shouldn’t matter which direction you do it in the answer should be the same value, but if you get a negative value then you just know you need to go the other direction to make an arb. profit of the same magnitude.
I hate this triangular arbitrage crap. I say a little prayer each night after I have closed my books and put on my pyjamas that it won’t be in the exam.
I was confused with the concepts in economics, so i traditionally stuck to few formulas in this chapter rather than inferring answers logically and this helped me… I want to ask you guys if this is right approach? You have this formula to check for which country’s currency you need to borrow or lend to extract the arbitrage profit If 1+ R(domestic) > (1 +R(foreign))*Forward/ Spot It implies that we need to borrow the foreign currency and lend the domestic currency The converse is also true for the less than sign, which translates to borrow domestic and lend foreign. Plugging in the variables: (1.66/1.543)*1.0577 gives us 1.1379 So 13.79 - R(domestic) = 13.79 - 5.98 = 7.81 is the interest rate differential Thanx in advance
1.0579 < 1.13790149 Borrow 100USD - payback 105.79 1000USD -> 64.808814GBP Lend 64.808814GBP -> getback 68.54828257GBP convert and get 113.7901491USD 113.7901491-105.79 = 8.0001491 i.e 0.080001491
Is it a wrong approach then?? I used the same approach while practicing Q bank, it worked.