7．e annual interest rates in England and New Zealand are 6.54 percent and 7.03 percent, 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) 1,043.61 GBP. B) No arbitrage opportunities exist. C) 1,124.88 GBP. D) 1,093.20 GBP. The correct answer was D) Borrow 10,000 GBP at 6.54% = 654 GBP interest due at the end of the year.
Convert to NZD: (10,000 GBP) x (1 NZD/0.41 GBP) = 24,390 NZD.
Lend out NZD at 7.03 % interest: (24,390 NZD) x (1.0703) = 26,104.88 NZD.
Convert back to GBP: (26,104.88 NZD) x (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. 8．e annual interest rate is 8.02 percent in Mexico and 7.45 percent 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) 1,304,207 pesos. B) 1,284,230 pesos. C) 1,292,410 pesos. D) No arbitrage opportunity exists. The correct answer was A) 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) x (CAD/569.87 MXN) = 26,321.79 CAD. 26,321.79 CAD x 0.0745 = 1,960.97 CAD interest due at the end of the year. Lend out pesos 15,000,000 pesos x 1.0802 = 16,203,000 pesos received at the end of the year. Convert to Canadian dollars (16,203,000 MXN) x (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) x (526.78 MXN/CAD) = 1,304,207.19 peso profit. 9．e interest rates in the U.S. and Great Britain are 7.23 percent and 6.94 percent respectively. The forward rate is 1.70$/₤ and the spot rate is 1.73$/₤. Which currency would an investor borrow, if any, to make an arbitrage profit? A) Borrow pounds. B) Borrow dollars. C) No arbitrage profit exits. D) Lending pounds. The correct answer was A) Use the following formula to determine if an arbitrage opportunity exists and which currency to borrow. if 1 + rD > [(1 + rF)(Forward rate)]/Spot rate then borrow foreign. 1.0723 > [(1.0694)(1.70)]/1.73 1.0723 > 1.81798/1.73 1.0723 > 1.0509, therefore borrow foreign (pounds). Alternatively, the dollar is appreciating. [(1.73 - 1.70)/1.70] = 1.76%and the $U.S. interest rate is higher. Clearly, investing in $U.S. (and borrowing pounds) is the way to go. 10.sume an investor living in Hong Kong can borrow in Hong Kong dollars (HKD) or in U.S. dollars (USD). Given the following information, determine whether an arbitrage opportunity exists. If so, how much would the investor profit by borrowing USD 1,000,000 or the equivalent in HKD? (Assume a period of one year.) Spot rate (HKD/$) | 7.77001 | Forward rate (HKD/$) | 7.81983 | Domestic (Hong Kong) interest rate (%) | 6.00000 | Foreign (US) interest rate (%) | 5.00000 |
A) An arbitrage opportunity results in a profit of HKD 25,389. B) An arbitrage opportunity results in a profit of HKD 130,509. C) No arbitrage opportunity. D) An arbitrage opportunity results in a profit of HKD 197,274. The correct answer was A) Step 1: Determine whether an arbitrage opportunity exists. We can arrange the formula for covered interest rate parity (CIP) to look like: (1 + rdomestic) - [((1 + rforeign) * ForwardDC/FC) / SpotDC/FC] = 0 If this condition holds with the financial data above, there are no arbitrage opportunities. (1 + 0.06000) - [((1 + 0.05000) * 7.81983) / 7.77001] = 1.06000 - 1.05673 = 0.00327 Since the no arbitrage condition does not hold, we move on to: Step 2: Borrow Domestic or Foreign? The sign on the result of step 1 is positive, so borrow foreign. (rd - rf) | . | (Forward - Spot) / Spot
| (0.06000 - 0.05000) | . | (7.81983 - 7.77001)/7.77001 | 0.01000 | > | 0.00641 |
Step 3: Arbitrage Process
| Description | Rate | Calculation | Result |
| Borrow Foreign (amt. given in question) | . | . | USD 1,000,000 |
| Convert Borrowed Funds to Domestic | Spot | 1,000,000USD x 7.77001HKD/USD | HKD 7,770,010 |
| Invest Domestic at Domestic interest rate* | . | 7,770,010 HDK x (1 + 0.06000) | HKD 8,236,211 |
| *This is the amount you will have available to repay the loan. | . | . | . |
| Calculate loan payoff (foreign currency) | . | 1,000,000USD x (1+0.05000) | USD (1,050,000) |
| Calculate payoff in Domestic currency** | Fwd | 1,050,000USD x 7.81983HKD/$ | HKD (8,210,822) |
| **This is the amount you need to repay | . | . | . |
| Calculate Arbitrage Profit | . | HKD 8,236,211 - HKD 8,210,822 | HKD 25,389 |
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发表于 2008-5-12 14:19
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