Question

The following are quotes for several U.S. currency dealers.

Dealer	A	B	C	D	E
Japanese yen	109.97 - 110.01	110.01 - 110.05	109.98 - 110.00	109.99 - 110.02	110.02 - 110.06
Euro	1.1774 - 1.1776	1.1778 - 1.1781	1.1776 - 1.1778	1.1773 - 1.1775	1.1776 - 1.1778

Inter-dealer arbitrage

1a. Is there an arbitrage opportunity in Japanese yen? If so, what exchanges should you make to take advantage of it? (Be specific about which dealer you would select, what currency you would buy from or sell to that dealer, and how much of the other currency you would pay or receive.

b. How profitable is a round trip trade? (State the profitability either in percent or basis points.)

2a. Is there an arbitrage opportunity in euros? If so, what exchanges should you make to take advantage of it? (Be specific as indicated in question 1.)

b. How profitable is a round trip trade? (State the profitability either in percent or basis points.)

Triangular arbitrage (Inter-market) - assume that the highest bid and lowest ask for each currency are equal (so that the bid-ask spread is zero)

3. The New York spot exchange rate for Canadian dollar (USD/CAD) is 1.2821 and the spot exchange rate for the Mexican peso (USD/MXN) is 19.7538. What must the spot exchange rate for the peso in Toronto (CAD/MXN) be if no arbitrage opportunity exists?

4a. Using the New York market spot exchange rates from the previous questions, if, in Toronto, the exchange rate for the peso is 15.3915, what trades should you make to take advantage of the arbitrage opportunity? For each transaction, be specific about where the trade takes place, which currency you would purchase (or sell) and which currency you would use to pay (or receive)

b. How profitable is a round trip trade? State the profitability either in percent or basis points.

5a. The San Francisco spot exchange rate for the New Zealand dollar (NZD/USD) is 0.6930 and the spot exchange rate for the Malaysian ringgit (USD/MYR) is 3.9695. What must the spot exchange rate for the ringgit in Wellington (NZD/MYR) be if no arbitrage opportunity exists?

6a. Using the San Francisco market spot exchange rates from the previous questions, if, in Wellington, the exchange rate for the ringgit is 2.7485, what trades should you make to take advantage of the arbitrage opportunity? For each transaction, be specific about where the trade takes place, which currency you would purchase (or sell) and which currency you would use to pay (or receive)

b. How profitable is a round trip trade? State the profitability either in percent or basis points.

7a. The New York spot exchange rate for the British pound (GBP/USD) is 1.3436 and the spot exchange rate for the Australian dollar (AUD/USD) is 0.7576. What must the spot exchange rate for the Australian dollar in London (GBP/AUD) be if no arbitrage opportunity exists?

8a. Using the New York market spot exchange rates from the previous questions, if, in London, the exchange rate for the Australian dollar is 1.7749, what trades should you make to take advantage of the arbitrage opportunity? For each transaction, be specific about where the trade takes place, which currency you would purchase (or sell) and which currency you would use to pay (or receive)

b. How profitable is a round trip trade? State the profitability either in percent or basis points.

Covered interest arbitrage (Inter-temporal) - assume that the highest bid and lowest ask are equal (i.e., that the bid-ask spread is zero)

9. Assume the interest rate of 1-year risk free debt denominated in US dollars is 2.75% and the interest rate on 1-year risk free debt denominated in Russian rubles is 7.25%. If the spot market exchange rate for the Russian ruble (USD/RUB) is 61.24, what is the 1-year forward exchange rate if interest rate parity holds?

10a. If the actual 1-year forward exchange rate for Russian rubles is 63.81 and the spot market exchange rate and interest rates are as indicated in question 9, what trades should you make to take advantage of the arbitrage opportunity? Be specific about both current and future transactions (i.e., be sure to specify what currency/currencies are involved and how, and the amount of each – you can make any assumption you like about the amount of currency to start).

b. How profitable is the trade? (State the profitability, either in dollars or rubles and as a percent of initial amount borrowed.)

11. Assume the interest rate on 6-month risk free debt denominated in US dollars is 2.50%, the interest rate on 6-month risk free debt denominated in Tanzania shillings is 9.00%. If the spot market exchange rate for the Tanzanian shilling (USD/TZS) is 2287.4, what must the 6-month forward rate on the Tanzanian shilling be if interest rate parity holds?

12a. If the 6-month forward exchange rate for the Tanzanian shilling 2365.2 and the spot market exchange rate and interest rates are as indicated in question 11, what trades should you make to take advantage of the arbitrage opportunity? Be specific about both current and future transactions (i.e., be sure to specify what currency/currencies are involved and how, and the amount of each – you can make any assumption you like about the amount of currency to start).

b. How profitable is the trade? (State the profitability, either in dollars or shillings and as a percent of initial amount borrowed.)

Answer 1

1(a) . The bid ask from Dealer C is 109.98 / 110 and Dealer E is 110.02 / 110.06. There is possible arbitrage here as below:

• Purchase yen from dealer E for 1 USD and receive JPY 110.02
• Sell these JPY 110.02 to dealer C for receive USD (110.02/110) = 1.000182

??1(b) The profit from the above arbitrage is going to be 0.000182/1 = 0.018%

2(a): The bid ask from Dealer B is 1.1778 / 1.1781 and Dealer D is 1.1773 / 1.1775 There is possible arbitrage here as below:

• Purchase Euro from dealer D for 1 USD and receive Euro (1/1.1775) = 0.849257
• Sell these Euro 0.849257 to dealer B for receive USD (0.849257 * 1.1778) = 1.000255

?(b) The profit from the above arbitrage is going to be 0.000255/1 = 0.025%

3. We are given 1 USD = 1.2821 CAD and 1USD = 19.7538 MXN. No arbitrage condition will be satisfied when 1.2821 CAD will equal 19.7538 MXN which will give us 1 CAD = 15.40738

4 (a) If the exchange rate in Toronto is 1 CAD = 15.3915, it means that the CAD has more value relative to MXN in New York than in Toronto. Hence we can profit as below:

• ?Sell 1 CAD in New York and receive 15.40738 MXN
• Sell these 15.40738 MXN in Toronto and receive 1.001032 CAD
• Hence we receive more CAD than we started with

?(b) The profit in this trade = (0.001032/1) = 0.103%

5 (a): We have 1 NZD = 0.6930 USD or 1 USD = (1/0.6930) NZD = 1.4430 NZDand 1 USD = 3.9695 MYR. For there to be no arbitrage, 1.4430 NZD should equal 3.9695MYR which will give us 1 NZD = (3.9695/1.4430) MYR = 2.7508MYR

6(a) If in Wellington, the exchange rate is 1NZD = 2.7485 MYR, then this means that NZD is more valuable relative to MYR in San Fransicso. Hence we should sell 1 NZD in San Francisco and receive 2.7508 MYR which we should convert back to NZD in Wellington and receive (2.7508/2.7485) NZD = 1.000837 NZD

(b) The profit on the above arbitrage = (0.000837/1) = 0.083%