Question

Suppose that the euro exchange rate is $1.15/euro. The continuously compounded dollar interest rate is at 3% and the continuously compounded euro interest rate is at 2%. Suppose that you borrow euros and lend dollars for 1 year, without using futures for hedging, and your initial cash flow is zero.

(a) At what exchange rate in 1 year will you break even on this position?

(b) If the exchange rate in 1 year is $1.20, what is your profit (per 1000 euros borrowed at time 0)?

(c) If the exchange rate in 1 year is $1.12, what is your profit (per 1000 euros borrowed at time 0)?

***Please don't answer again if you've already done it. I'm getting a second opinion on this. Thanks.***

Answer 1

1.
Breakeven exchange rate occurs when exchange rate in one yeat=current exchange rate*e^(dollar interest rate*t)/e^(euro interest rate*t)
=1.15*e^(3%*1)/e^(2%*1)=1.16

2.
Profit=amount in euros*(current exchange rate*e^(dollar interest rate*t)-e^(euro interest rate*t)*exchange rate in one year))
=1000*(1.15*e^(3%*1)-e^(2%*1)*1.2)=-39.22

3.
Profit=amount in euros*(current exchange rate*e^(dollar interest rate*t)-e^(euro interest rate*t)*exchange rate in one year))
=1000*(1.15*e^(3%*1)-e^(2%*1)*1.12)=42.40