Question

The following exchange rates exist on a particular day.

• Spot exchange rate: U.S. $1.400/euro
• Forward exchange rate (90 days): U.S. $1.427/euro

The following (annualized) interest rates on 90-day government bonds also exist on this day:

• Euro-denominated bonds: 8%
• U.S. dollar–denominated bonds: 16%

1. Financial investors in all countries have the expectation that the spot exchange rate in 90 days will be 0.7100 euro/U.S. dollar. Are investors expecting the euro will appreciate or depreciate during the next 90 days?

2. Consider the comparison between investments in U.S. dollar–denominated bonds and euro-denominated bonds, with any foreign investment done as uncovered foreign investment. In which direction (between the United States and the euro area) will there be an incentive for uncovered investment to flow, based on a comparison of returns? Calculate the relevant returns and explain your answer.

Answer 1

a. The spot (current) exchange rate is US $1.400/euro
Investors expect the spot rate to be 0.7100 euro/US dollar in 90 days.
0.7100 euro/US dollar is equivalent to 1/0.7100 = USD 1.4084 euro.
Therefore, the investors are expecting that the euro will appreciate against the dollar in next 90 days.

b. Suppose an investor has $1 to invest. Assume there is no compounding on the interest.
An investment of $1 in the USD-denominated bond with 16% interest rate will have the future value of $1.16 in 90 days.

If the investor exchanges his dollar to euro today at $1.400/euro (spot rate), it will be equal to 0.7143 euros.
An investment of 0.7143 euros in the euro-denominated bond with 8% interest rate will have the future value of 0.7714 euros in 90 days.
The 90-days forward exchange rate is $1.427/euro. Therefore, 0.7714 euros will be equivalent to $1.1

Therefore, the direction of the uncovered investment would be towards the United States as it fetches a higher return on a dollar investment than it does in the euro area.