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Cumulative Exam FINC 540 Name: _____________________ Last 4 digit of id#:___________ (30 points) 1. a) A foreign exchange arbitrageur notices that the Japanese yen to U.S. dollar spot exchange rate is 108/$ and the three-month forward exchange rate is 107.30/$. The three-month $ interest rate is 1.20 percent per annum and the three-month interest rate is 5.20 percent per annum. a. Is the interest rate parity holding? Also, you need to indicate amount of mispricing, if any. b. Is there an arbitrage possibility? b). If yes, what steps would be needed to make an arbitrage profit? Assuming that the arbitrageur is authorized to work with $1,000,000 for this purpose, how much would the arbitrage profit be in dollars? 2. (15 points) Suppose the international parity conditions hold. Does that mean that the nominal interest rates would be equal among countries? Why or why not? 3. (25 points) Barclays Sa($/) =1.4655 Credit Lyonnais Sa(/$)=.8175; Credit Agricole Sb(/ )=1.1990. Calculate the triangular arbitrage profit if Credit Agricole is mispricing the cross rate in the market. 4. (30 points) You are the treasurer of a major Japanese construction company. Today is January 15. You expect to receive 10 million at the end of March, as payment from a client on some construction work in France. You know that you will need this sum somewhere else in Europe at the end of June. Meanwhile, you wish to invest these 10 million for three months. The current three-month interest rate in euros is 4%, but you are worried that it will quickly drop. Listed below are Euribor futures quotations on EUREX: Maturity (month-end) Price February 96.02% March 96.08% June 96.20% September 96.25% a. Knowing that Euribor contracts have a size of 1 million, what should you do to freeze a lending rate when you will receive the money? b. At the end of March, when you receive the money, the three-month Euribor is equal to 3%. How much money (number of euros) have you gained by engaging in the above transaction (as opposed to doing nothing on January 15)? Cumulative Exam FINC 540 Name: _____________________ Last 4 digit of id#:___________ (30 points) 1. a) A foreign exchange arbitrageur notices that the Japanese yen to U.S. dollar spot exchange rate is 108/$ and the three-month forward exchange rate is 107.30/$. The three-month $ interest rate is 1.20 percent per annum and the three-month interest rate is 5.20 percent per annum. a. Is the interest rate parity holding? Also, you need to indicate amount of mispricing, if any. b. Is there an arbitrage possibility? a) For three months, i =0.30% and i $ = 1.30 %. the spot exchange rate is $0.009259/ and the forward rate is $0.00931966/. Thus, (1+ i $ ) = 1.013 and (F/s) (1 + i ) = (0.00931966/0.009259) (1.003) = 1.009571 Because the left and right sides of IRP are not equal, IRP is not holding. b) Because IRP is not holding, there is an arbitrage possibility: Because 1.013 >1.009571 , We can say that the interest rate quote is less than what it should be as per the quotes for the other three variables. Equivalently, we can also say that the $ interest rate quote is more than what it should be as per the quotes for the other three variables. Therefore, the arbitrage strategy b). If yes, what steps would be needed to make an arbitrage profit? Assuming that the arbitrageur is authorized to work with $1,000,000 for this purpose, how much would the arbitrage profit be in dollars? The steps would be as follows: 1. Borrow 9259.259 for three months at 0.30%. Need to pay back $9259.259 (1 + 0.003) = 9287.0370 three months later. 2. Convert 9259.259 to $ at the spot rate to get $ 1000000. 3. Lend $1000000 for three months at 1.30%. Will get back 1,000000 (1 + 0.013) = three months later. =1013000 4. Sell $ 1,013000 three months forward. The transaction will be contracted as of the current date but delivery and settlement will only take place three months later. So,three months later, exchange 1,013000 for 1,013000/107.30 = 9440.820. The arbitrage profit three months later is 9440.820- 9287.0370= 153.783 2. (15 points) Suppose the international parity conditions hold. Does that mean that the nominal interest rates would be equal among countries? Why or why not? No, the country which has the higher will have higher nominal interest rate. Therefore, the nominal interest rate will be different among all countries. 3. (25 points) Barclays Sa($/) =1.4655 Credit Lyonnais Sa(/$)=.8175; Credit Agricole Sb(/ )=1.1990. Calculate the triangular arbitrage profit if Credit Agricole is mispricing the cross rate in the market. If you have $100 in hand then you can make the traingular arbitrage profit in the following way. IF you convert from Dollar to Euro then= 1 Dollar=0.8175 Euro So 100 Dollars would be equal to 100*0.8175= 81.75 Euro If We convert Euro to Pound then it will be 1.119 Euro equal to 1 Pound therefore 81.75 Euro will be 81.75/1.119= 73.0563 Pound Now again we convert the Pound to Dollar it will be 1 pound equal to 1.4655 Dolalr So 7.0563 Pound will be equal to 73.0563*1.4655= 107.06 So by doing the triangular arbitrage we can gain $7.06. 4. (30 points) You are the treasurer of a major Japanese construction company. Today is January 15. You expect to receive 10 million at the end of March, as payment from a client on some construction work in France. You know that you will need this sum somewhere else in Europe at the end of June. Meanwhile, you wish to invest these 10 million for three months. The current three-month interest rate in euros is 4%, but you are worried that it will quickly drop. Listed below are Euribor futures quotations on EUREX: Maturity (month-end) Price February 96.02% March 96.08% June 96.20% September 96.25% a. Knowing that Euribor contracts have a size of 1 million, what should you do to freeze a lending rate when you will receive the money? a.) In order to freeze a lending rate when I will receive the money, I will buy 10 futures contracts that expire in March and have a price of 96.08%. I am now freezing a three-month lending rate of 3.92% for the end of March. b. At the end of March, when you receive the money, the three-month Euribor is equal to 3%. How much money (number of euros) have you gained by engaging in the above transaction (as opposed to doing nothing on January 15)? b.) At the end of March, the futures price will converge to 97%, given the 3% interest rate at that time. Hence, I will make a profit on the futures contracts equal to: Profit = 10 million [97% 96.08%]/4 = 23,000. This profit will offset the drop in interest rate from January to March. I can then invest from March to June the 10 million received at a rate of 3%