FX Arbitrage problem

I got the right answer on this one, but feel like I took an EXTREMELY long route to get there. I remember using a much easier strategy for LI, by comparing the US rate to the forward premium/discount on the foreign currency + the foreign interest rate, but then forgot the rest… any ideas? An arbitrageur observes the following market conditions: 6-month Forward Spot Market \$1.2000/€ Market \$1.18000/€ U.S. Interest Rate 4% EU Interest Rate 6% If the arbitrageur has a \$5,000,000 line of credit with a bank, which of the following best estimates the arbitrage’s risk-free profit and the flow of funds in the spot market? ----Profit----------------- Money Flow-------- a) 35,830 --------- 35,830 from US to EU b) 71,600 --------- E 4.2 mil from EU to US c) 71,600 --------- \$5.0 mil from US to EU d) 35,830 --------- E 4.2 mil from EU to US

Is the correct logic to: a) borrow dollars b) buy euros at spot price c) invest euros at 6mo int rate d) sell euros forward for dollars to lock in rate (and to eliminate risk) You would net a profit from your euro investment and the lower int rate in the US ilvino – which rate is which? hard to tell with formatting

is this a 6 month rate?and is the second rate the forward rate?

Sorry for the formatting issues: the US annualized rate is 4% and the EU annualized rate is 6%. The contract is a 6 month forward contract.

I was more confused by the exchange rates.

I got D then. I used the formula [(1+rd)- (F/S)*(1+Rf)]*\$5mn. Adjust the annualised rates to convert them to 6 month rates. Did I get it correct?

profit is in \$, but stalla didn’t mention that in the q, only the answer. and I’m not sure what the exchange rate confusion is? it is formatted above just as it is in Stalla.

Yes you did Ruhi and that’s the formula I was looking for!!!

Great! Thanks for posting this. Nice refresher it was.

Domestic rate = 2% (roughly) Foreign rate = 3% (roughly) (1+R_f)* forward/spot = 1.01283<1.02 So we can borrow EUR for less than the 2% we’d get if invested in the US. So we must borrow EUR and convert to USD (so answer is B or D). (1.02-1.01283)*\$5m = \$35850 net proft. So D. Full action: 1) borrow equivalent of \$5m in EUR. This is EUR 4.167m @ 1.2 (so it must be B or D) 2) Convert from EUR to USD. So 4.167m*1.2 = \$5m 3) invest @ 2% to get \$5.1m 4) convert to EUR using forward @1.18 to get EUR4.322m 5) pay off loan of 1.03*4.167m = EUR4291666. We have EUR30367 left over, or \$35833.

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no problem - I (stupidly) was using the annual I-rates rather than the 6-month rates, and was coming up with weird numbers using the shorter method, so I went the long route ala rg’s post above. Thanks for saving my sanity today!

So i always do the whole transaction as chrismaths shows above, but i guess we can get the same result by multiplying the amount by the differential? that really would save some time, but i’m paranoid so i always go the long way to check the math.