Question

Dollar Return on Foreign Investments -

(A) Over the past year, the dollar has depreciated by about 10 percent against the euro. A year ago you took out a home equity loan in the U.S. at an interest rate of 8 percent and you invested the money in a German mutual fund that paid a 5 percent euro return. What net return did you earn on all of these transactions over the year? (PLEASE INCLUDE FORMULAS USED TO SOLVE PROBLEM).

(B) You can borrow or invest in the U.S. at an annual rate of 6 percent. Suppose you logon to your favorite financial website and see that you could borrow or invest in Japan at a 5 percent annual rate. The current exchange rate between the dollar and the yen is $0.01/yen. You can use the futures market to lock it in at an exchange rate for one year from now at $0.0095/yen. Is there a profit opportunity here? Prove it by borrowing (either $1 million or $100 yen) in one country and investing in the other? (PLEASE INCLUDE FORMULAS USED TO SOLVE PROBLEM).

Inflation and Exchange Rates -

(C) Suppose gold sells for $1,000 per ounce in the U.S. and it sells for 1,000 Canadian dollars per ounce in Canada. Suppose further, the exchange rate is $1 per Canadian dollar. If U.S. inflation is 6 percent next year, Canadian inflation is 2 percent, and exchange rates do not change, how could you make an arbitrage profit in the gold market? (PLEASE INCLUDE FORMULAS USED TO SOLVE PROBLEM).

(D) Suppose U.S. interest rates on a risk-free, one-year bond are 4 percent and European interest rates on a risk-free, one-year bond are 6 percent. Suppose further than inflation is 2 percent in the U.S. and 4 percent in Europe. Assume it takes one year for the exchange rate to adjust to inflation differences. What is the predicted change in the $/euro exchange rate for the next year? Given that, what would the dollar return on a European bond be for this year? (PLEASE INCLUDE FORMULAS USED TO SOLVE PROBLEM).

Answer 1

(A) EUR to USD Exchange Rate 1 year ago = 1.119 EUR / $ or 0.894 $ / EUR (Data sourced from "bloomberg.com")

As the dollar has depreciated by 10 % against the euro in a year, it implies that 10 % more $ is purchasable today as compared to this time last year for one unit of euro.

Current Exchange Rate = 0.894 x 1.1 $ / EUR = 0.9834 $ / EUR or 1.0168 EUR / $

Let the home equity loan be of value $ 100000

Loan Liabiliy due after 1 year = 100000 x 1.08 = $ 108000

Euro Value of Loan = 100000 x 1.119 = $ 111900

Euro Value of Loan is invested at the German Mutual Fund return rate of 5 % to yield at present, an amount = 111900 x 1.05 = 117495 EUR

$ Value of Investment Yield = 117495 / 1.0168 = $ 115553.698

Net Profit = 11553.698 - 108000 = $ 7553.698

Net Return = (7553.698 / 100000) x 100 = 7.55 % approximately.

NOTE: Please raise separate queries for solutions to the remaining unrelated questions.