Certain Selected Problems Chapter 7

1. The $: € exchange rate is €1 = $0 1. The $: € exchange rate is €1 = $0.95, and the €/SFr exchange rate is SFr 1 = €0.71. What is the SFr/$ exchange rate?

Answer. SFr1 = €0.71 x 0.95 = $0.6745.

2. Suppose the direct quote for sterling in New York is 1. 1110‑5 2. Suppose the direct quote for sterling in New York is 1.1110‑5. What is the direct quote for dollars in London?

Answer. The direct quote for the dollar in London is just the reciprocal of the direct quote for the pound in New York or 1/1.1115 ‑ 1/1.1110 = 0.8997‑0.9001.

3. Using the data in Exhibit 7 3. Using the data in Exhibit 7.5, calculate the 30‑day, 90‑day, and 180‑day forward discounts for the Canadian dollar.

The 30‑day forward discount is:[($0. 7536 ‑ $0. 7545)/$0 The 30‑day forward discount is:[($0.7536 ‑ $0.7545)/$0.7545] x 12 = 1.43% The 90‑day forward discount is: [($0.7520 ‑ $0.7545)/$0.7545] x 4 = 1.33% The 180‑day forward discount is:[($0.7501 ‑ $0.7545)/$0.7545] x 2 = 1.17%

4. An investor wishes to buy euros spot (at $0 4. An investor wishes to buy euros spot (at $0.9080) and sell euros forward for 180 days (at $0.9146). a. What is the swap rate on euros? b. What is the premium on 180‑day euros?

Answer. A premium of 66 points. Answer. The 180‑day premium is (0.9146 ‑ 0.9080)/0.9080 x 2 = 1.45%.

7. Suppose the euro is quoted at 0 7. Suppose the euro is quoted at 0.7064‑80 in London, and the pound sterling is quoted at 1.6244-59 in Frankfurt. a. Is there a profitable arbitrage situation? Describe it.

Answer. Sell euros for £0. 7080/€ in London Answer. Sell euros for £0.7080/€ in London. Use the pounds to buy euros for €1.6244/£ in Frankfurt. This is equivalent to buying pounds for £0.6156. There is a net profit of £0.0924 per pound bought and sold–a percentage yield of 13.05% (0.0924/0.7080).

b. Compute the percentage bid‑ask spreads on the pound and euro.

Answer. The percentage bid-ask spreads on the pound and euro are calculated as follows: euro bid-ask spread = (0.7080 - 0.7064)/0.7080 = 0.23%

8. As a foreign exchange trader at Sumitomo Bank, one of your customers would like a yen quote on Australian dollars. Current market rates are:

a. What bid and ask yen cross rates would you quote on spot Australian dollars?

Answer. By means of triangular arbitrage, we can calculate the market quotes for the Australian dollar in terms of yen as ¥78.31-81/A$1

b. What outright yen cross rates would you quote on 30-day forward Australian dollars?

By means of triangular arbitrage, we can then calculate the market quotes for the 30-day forward Australian dollar in terms of yen as ¥78.04-58/A$1

c. What is the forward premium or discount on buying 30-day Australian dollars against yen delivery?

9. Suppose Air France receives the following indirect quotes in New York: €0.92 - 3 and £0.63 - 4. Given these quotes, what range of £/ € bid and ask quotes in Paris will permit arbitrage?

Answer. Triangular arbitrage can take place in either of two ways: (1) Convert from euros to dollars (at the ask rate), then from dollars to pounds (at the bid rate), or (2) convert from pounds to dollars (at the ask rate), then from dollars to euros (at the bid rate). The first quote will give us the bid price for the euro in terms of the pound and the second quote will yield the ask price. Using the given rates, Air France would end up with the following amounts:

The import of the figures in method (1) is that Air France can buy pounds in New York for €1.4762/£, which is the equivalent of selling euros at a rate of £0.6774/ €. So, if Air France can buy euros in Paris for less than £0.6774/ € (which is the equivalent of selling pounds for more than €0.6774/£), it can earn an arbitrage profit.

Similarly, the figures in method (2) tell us that Air France can buy euros in New York at a cost of £0.6957/ €. Given this exchange rate, Air France can earn an arbitrage profit if it can sell these euros for more than £0.6957/FF in Paris. Thus, Air France can profitably arbitrage between New York and Paris if the bid rate for the euro in Paris is greater than £0.6957/ € or the ask rate is less than £0.6774/ €.

10. On checking the Telerate screen, you see the following exchange rate and interest rate quotes:

a. Can you find an arbitrage opportunity?

Answer. Yes. There are two possibilities: Borrow dollars and lend in Swiss francs or borrow Swiss francs and lend in dollars. The profitable arbitrage opportunity lies in the former: Lend Swiss francs financed by borrowing U.S. dollars.

b. What steps must you take to capitalize on it?

Answer. Borrow dollars at 1. 2575% for 90 days (5 Answer. Borrow dollars at 1.2575% for 90 days (5.03%/4), convert these dollars into francs at the ask rate of $0.722, lend the francs at 0.785% for 90 days (3.14%/4), and immediately sell the francs forward for dollars at the buy rate of $0.726.

c. What is the profit per $1,000,000 arbitraged?

Answer. The profit is $1,000,000 x [(1. 00785/0. 722) x 0. 726 - 1