Current one-year interest rates in Europe are 5%, while one-year interest rates

Question

Current one-year interest rates in Europe are 5%, while one-year interest rates in the U.S. are 2%. A customer converts $10,000 to euros and invests them in Europe. One year later, she converts the euros back to dollars. The current spot rate of the euro is $1.10.

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 $1.00, what is the percentage return from the strategy?

c. If the spot rate of the euro in one year is $1.08, what is the percentage return from the strategy?

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

Explanation / Answer

1 euro = 1.1 usd

1 USD = 1/1.1 = 0.9091 euro

Fwd USD = 0.9091 *(1+5%) / (1+2%) = 0.9358 euro

Fwd Euro = 1/0.9358 = 1.0686 USD

b&c)

10000 USD converts into = 10000 /1.1 = 9090.91 Euro

Investes at 5% gives = 9090.91 * 1.05 = 9545.45

10000 USD would have been = 10000*1.02 = 10200

b)

9545.45 Euro converts into = 9545.45 * 1.00 = 9545.45 USD

% return = (9545.45 -10200)/10000 = -6.55% (Loss)

c)

9545.45 Euro converts into = 9545.45 * 1.08 = 10309.09 USD

% return = (10309.09 -10200)/10000 = 1.09% (Profit)

d)

Successful spot rate is = 10200 / 9545.45 = 1.0686 USD (calculated in part a)

It should be above 1.0686 USD

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