Question

The following information is available as of today: the one-year forward rate (dollars per euro) is 1.50 ($/€) and the two-year forward rate (dollars per euro) is 2.00 ($/€). The interest rate per year for deposits in euro in the foreign country is R€ = 5.00%. A year from now your firm will generate $1.0 million that you intend to deposit in euros in the foreign country for one year. Two years from now you would like to repatriate the amount held in the deposit, i.e. whatever is accumulated in euros will be exchanges back into dollars. Obviously, one way to do this is to wait until the end of the first year, exchange the $1.0 million into euros at then prevailing dollars/euros spot exchange rate and deposit the euros; two years from now, exchange the accumulated euros into dollars at then prevailing dollars/euros spot exchange rate and repatriate the dollars. Comparing the dollars you repatriate with the initial investment ($1.0 million) you are able to calculate the return (interest rate) on your investment. With this strategy the return will be variable as it depends on the spot exchange rates a year from now and two years from now.

Part i. [10 points] Using the two available forward contract could you guarantee yourself a fixed return on the dollars invested as described above? Please provide the details of your transactions.

Part ii. [10 points] Calculate the guaranteed interest rate you would thus obtain on the $1.0 million initial investment.

Answer 1

1 year forward rate : 1.50 $ per 1 € or 1 $ for 0.6667 € ; 2 year forward rate : 2 $ per 1 € and R€ = 5%

To guarantee return on $1 million to be generated 1 year hence and then to be invested into Euro, we can do the following:

• Book forward 1 year hence to convert $1 million into Euros, and lock into the conversion rate of receiving 0.6667 € for every 1 $
• Now at the end of Year 1, the converted amount in Euro is placed in a deposit at 5% p.a. Since the future value of deposit would be known, a forward can be booked to convert the Euro back into $ at the the 2 year forward rate of 2$ per 1 Euro
• The net proceeds received after converting back into $, will be the return in USD which can be locked right now using the forward rates.

[Note that we have assumed deposit rates will not change from year to year since the question is also silent on the same. Otherwise to lock into a guaranteed rate, one should borrow the present value of Year 1 Euros at forward rate today and invest at 5% for 2 year term and use the 1 year hence $1 million cash flow to repay the loan by booking Year 1 forward simultaneously to cover.]

Return will be as below:

$ 1million convert into Euro : 1000000 * 0.6667 = 666,700.00

Invest these Euros at 5% p.a. : 666700 * (1+5%) = 700,035.00

Convert back in USD : 700,035 * 2 = $ 1,400,070.00

Return : 400,070 or 40.01%