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An investor plans to exchange $1,000 into euros now, invest the resulting euros for 12 months, and then exchange the euros back into dollars at the end of the 12-month period. The spot exchange rate is €1·415 per $1 and the euro interest rate is 2% per year. The dollar interest rate is 1·8% per year.
Compared to making a dollar investment for 12 months, at what 12-month forward exchange rate will the investor make neither a loss nor a gain?
ANSWER GIVEN:
Twelve-month forward rate
= 1·415 x (1·02/1·018)
= €1·418 per $1MY WORKING:
Convert $ to € at spot exchange rate
$1000 × 1.415 = €1415Invest € at 2% for 12 months
€1415 × 1.02 = €1443.30Invest $ at 1.8% for 12 months
$1000 × 1.018 = $1018Then,
€1443.30 / unknown value = $1018
Unknown value = €1.418Can you explain the rationale behind my working? My working is longer compared to the answer given. What happened?
What you have done is fine. It is doing what the question says and is effectively money-market hedging.
However, as I explain in my free lectures, forward rates and money market hedging give the same end result which is why it is faster to use the interest rate parity formula to calculate the forward rate.
Although what you have done takes a little bit longer, it would still get full marks (and the workings are irrelevant, especially since this would be a section A or B question and so nobody would look at your workings 🙂 )
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