Answers to End of Chapter 7 Questions

33. Triangular Arbitrage. You are given these quotes by the bank:

You can sell Canadian dollars (C$) to the bank for $.70.

You can buy Canadian dollars from the bank for $.73.

The bank is willing to buy dollars for 0.9 euros per dollar.

The bank is willing to sell dollars for 0.94 euros per dollar. .

The bank is willing to buy Canadian dollars for 0.64 euros per C$.

The bank is willing to sell Canadian dollars for 0.68 euros per C$.

You have $100,000. Estimate your profit or loss if you would attempt triangular arbitrage by converting your dollars to euros, and then convert euros to Canadian dollars and then convert Canadian dollars to U.S. dollars.

ANSWER:
$100,000 x .90 = 90,000 euros

90,000/.68 = C$132,353
C$132,353 x $.70 = $92,647

Profit = $92,647 - $100,000 = -$7,353 [loss]

34. Movement in Cross Exchange Rates. Assume that cross exchange rates are always proper such
that triangular arbitrage is not feasible. While at the Miami airport today, you notice that a U.S. dollar can be exchanged for 125 Japanese yen, or 4 Argentine pesos at the foreign exchange booth. Last year, the Japanese yen was valued at $0.01, and the Argentine peso was valued at $.30. Based on this information, the Argentine peso has changed by what percent against the Japanese yen over the last year?

ANSWER:

Convert peso to direct exchange rate:
Peso = ¼ of $1 = $.25

Convert yen to direct exchange rate.

Yen = 1/125 = $.008

Cross-rate now:

Peso =.$25/$.008 = 31.25 yen

Cross rate last year:

Peso = $.30/$.01 = 30 yen

Change = (31.25 - 30) / 30 = +4.17%

35. Impact of Arbitrage on the Forward Rate. Assume that the annual U.S. interest rate is currently
6 percent and Germany’s annual interest rate is currently 8 percent. The spot rate of the euro is $1.10 and the one-year forward rate of the euro is $1.10. Assume that as covered interest arbitrage occurs, the interest rates are not affected, and the spot rate is not affected. Explain how the one-year forward rate of the euro will change in order to restore interest rate parity, and why it will change Your explanation should specify which type of investor (German or U.S.) would be engaging in covered interest arbitrage, whether they are buying or selling euros forward, and how that affects the forward rate of the euro.

ANSWER:
U.S. investors will engage in covered interest arbitrage, which involves forward sales of euros, and will place downward pressure on the one-year forward rate.