Question

Current one-year interest rates in Europe is 2 percent, while one-year interest rates in the U.S. is 1.5 percent. You convert $100,000 to euros and invests them in France. One year later, you convert the euros back to dollars. The current spot rate of the euro is $1.28.

a. According to the IFE, what should the spot rate of the euro in one year be?

b. If the spot rate of the euro in one year is $1.20, what is your percentage return from your investment?

c. If the spot rate of the euro in one year is $1.35, what is your percentage return from your investment?

d. What must the spot rate of the euro be in one year for your strategy to be successful?

Answer 1

a). S1 = S0 x [(1 + i_U.S.) / (1 + i_Euro)]

= 1.28 x [1.015 / 1.02] = 1.28 x 0.9951 = $1.274/euro

b).

1. Convert dollars to euros: $100,000/$1.28 = €78,125.

2. Invest euros for one year and receive €78,125 × 1.02 = €79,687.50.

3. Convert euros back to dollars and receive €79,687.50 × $1.20 = $95,625

The percentage return = $95,625/$100,000 – 1 = 0.95625 – 1 = -0.0438, or -4.38%

c).

1. Convert dollars to euros: $100,000/$1.28 = €78,125.

2. Invest euros for one year and receive €78,125 × 1.02 = €79,687.50.

3. Convert euros back to dollars and receive €79,687.50 × $1.35 = $107,578.125

The percentage return = $107,578.125/$100,000 – 1 = 1.0758 – 1 = 0.0758, or 7.58%

d). The strategy would be successful if the spot rate of the euro in one year is greater than $1.274.