Q15. The annual interest rate is 8.02% in Mexico and 7.45% in Canada. The spot peso-dollar exchange rate is 569.87 MXN/CAD, and the one-year forward rate is 526.78 MXN/CAD. If an arbitrage opportunity exists, how much would a person living in Mexico make borrowing 15,000,000 pesos or the equivalent in Canadian dollars?

A)      1,292,410 pesos.

B)      1,304,207 pesos.

C)      1,284,230 pesos.

Q16. The annual interest rates in England and New Zealand are 6.54% and 7.03%, respectively. The one-year forward exchange rate between the British pound and the New Zealand dollar is 0.45 GBP/NZD and the spot rate is 0.41 GBP/NZD. If a person living in London can borrow 10,000 pounds or the equivalent amount in New Zealand dollars, how much arbitrage profit, if any, can he make?

A)      1,093.20 GBP.

B)      1,043.61 GBP.

C)      1,124.88 GBP.

Q17. The forward rate between the Mexican peso and the U.S. dollar is 556.75 MXN/USD and the spot rate is 581.23 MXN/USD. The Mexican interest rate is 5.89%, and the U.S. rate is 5.75%. If a person lives in Mexico and can borrow $10,000 or the equivalent in pesos, how much can she make if currency arbitrage opportunities exist?

A)      $479.59.

B)      $459.39.

C)      Arbitrage opportunities do not exist.

Q18. The spot rate between the Canadian dollar and the British pound is 1.265 CAD/₤ and the forward rate is 1.193 CAD/₤. The interest rate in Canada and England are 6.13% and 6.01%, respectively. A person living in Toronto, Canada can borrow either Canadian dollars or pounds. If an arbitrage opportunity exists, which currency would they lend or borrow?

A)      Borrow pounds.

B)      Lend pounds.

C)      Borrow Canadian dollars.

答案和详解如下：

Q15. The annual interest rate is 8.02% in Mexico and 7.45% in Canada. The spot peso-dollar exchange rate is 569.87 MXN/CAD, and the one-year forward rate is 526.78 MXN/CAD. If an arbitrage opportunity exists, how much would a person living in Mexico make borrowing 15,000,000 pesos or the equivalent in Canadian dollars?

A)      1,292,410 pesos.

B)      1,304,207 pesos.

C)      1,284,230 pesos.

Correct answer is B)

Note that peso is at a forward premium (less pesos per CAD in the future) and that peso interest rate is higher. Therefore it is clear there are arbitrage profits from lending in pesos and borrowing CAD.

First convert to Canadian dollars to determine the amount of interest due at the end of the year. (15,000,000 MXN) × (CAD/569.87 MXN) = 26,321.79 CAD.

26,321.79 CAD × 0.0745 = 1,960.97 CAD interest due at the end of the year.

Lend out pesos 15,000,000 pesos × 1.0802 = 16,203,000 pesos received at the end of the year.

Convert to Canadian dollars (16,203,000 MXN) × (CAD/526.78 MXN) = 30,758.57 CAD.

Subtract the original loan amount and interest: 30,758.57 − 26,321.79 (original loan) − 1,960.97 (interest) = 2,475.81 CAD profit.

Convert the remainder back to pesos: (2,475.81 CAD) × (526.78 MXN/CAD) = 1,304,207.19 peso profit.

Q16. The annual interest rates in England and New Zealand are 6.54% and 7.03%, respectively. The one-year forward exchange rate between the British pound and the New Zealand dollar is 0.45 GBP/NZD and the spot rate is 0.41 GBP/NZD. If a person living in London can borrow 10,000 pounds or the equivalent amount in New Zealand dollars, how much arbitrage profit, if any, can he make?

A)      1,093.20 GBP.

B)      1,043.61 GBP.

C)      1,124.88 GBP.

Correct answer is A)

Borrow 10,000 GBP at 6.54% = 654 GBP interest due at the end of the year.
Convert to NZD: (10,000 GBP) × (1 NZD/0.41 GBP) = 24,390 NZD.
Lend out NZD at 7.03% interest: (24,390 NZD) × (1.0703) = 26,104.88 NZD.
Convert back to GBP: (26,104.88 NZD) × (0.45 GBP/NZD) = 11,747.20 GBP.
11,747.20 GBP − 10,000 GBP (original amount borrowed) − 654 GBP interest = 1,093.20 GBP profit.

Q17. The forward rate between the Mexican peso and the U.S. dollar is 556.75 MXN/USD and the spot rate is 581.23 MXN/USD. The Mexican interest rate is 5.89%, and the U.S. rate is 5.75%. If a person lives in Mexico and can borrow $10,000 or the equivalent in pesos, how much can she make if currency arbitrage opportunities exist?

A)      $479.59.

B)      $459.39.

C)      Arbitrage opportunities do not exist.

Correct answer is A)

First determine if arbitrage opportunities exist by using the following equation:

if 1 + r_D > [(1 + r_F)(Forward rate)] / Spot rate, then borrow foreign (dollars).

1.0589 > [(1.0575)(556.75)] / 581.23

1.0589 > 588.763 / 581.23

1.0589 > 1.01296, therefore, borrow foreign (dollars).

Borrow $10,000 at 5.75%, interest = $575 due at the end of the year. Convert to pesos using the spot rate: ($10,000) × (581.23 MXN/USD) = 5,812,300 pesos.

Lend out at 5.89%: (5,812,300 pesos) × (1.0589) = 6,154,644.47 pesos. Convert to dollars: (6,154,644.47 MXN) × (USD/556.75 MXN) = $11,054.59. $11,054.59 − $10,000 (original amount borrowed) − $575 (interest) = $479.59 profit.

Q18. The spot rate between the Canadian dollar and the British pound is 1.265 CAD/₤ and the forward rate is 1.193 CAD/₤. The interest rate in Canada and England are 6.13% and 6.01%, respectively. A person living in Toronto, Canada can borrow either Canadian dollars or pounds. If an arbitrage opportunity exists, which currency would they lend or borrow?

A)      Borrow pounds.

B)      Lend pounds.

C)      Borrow Canadian dollars.

Correct answer is A)

Use the following formula to determine if an arbitrage opportunity exists and which currency to borrow.

if 1 + r_D > [(1 + r_F)(Forward rate)] / Spot rate, then borrow foreign.

1.0613 > [(1.0601)(1.193)] / 1.265

1.0613 > 1.265 / 1.265

1.0613 > 1 therefore borrow foreign (British pound) and lend domestic (Canadian dollar).

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