Finance Exercise
Homework
Problem 1 (2 points)
Between 1980 and 1995, the ¥/$ exchange rate moved from ¥226.63/$ to ¥93.96/$. During the same 15-year period, the consumer price index (CPI) in Japan rose from 91.0 to 119.2 and the U.S. CPI rose from 82.4 to 152.4.
- If PPP has held over this period, what would the ¥/$ exchange rate have been in 1995? (1 point)
- What happened to the real value of the yen in term of dollars during this period? Explain your answer. (1 point)
Problem 2 (2 points)
Suppose that the current spot exchange rate is €1.50/₤ and the one-year forward exchange rate is ₤0.625/€. The one-year interest rate is 5.4% in euros and 5.2% in pounds. You can borrow at most €1,000,000 or the equivalent pound amount, i.e., ₤666,667, at the current spot exchange rate.
- Show how you can realize a guaranteed profit from covered interest arbitrage. Assume that you are a euro-based investor. Also determine the size of the arbitrage profit. (1 point)
- Assume that you want to realize profit in terms of ₤. Show the covered arbitrage process and determine the pound profit amount. (1 point)
Problem 3 (4 points)
- The euro is quoted as $/€ = 1.1420–1.1425, and the Canadian dollar is quoted as C$/US$ = 1.3540–1.3545. What is the direct quotation for the euro in Canada? Explain the rationale behind the formula used. (2 points)
- How large would transactions costs (in percentage) have to be to make triangular arbitrage between the exchange rates S^{$/£} = $1.5422/£, S^{$/€} = $0.9251/€, and S^{€/£} = €6650/£ profitable? (1 point)
- The U.S. and the country of Rueland have the same real interest rate of 3%. The expected inflation over the next year is 6 percent in the U.S. versus 21% in Rueland. Interest rate parity exists. The one-year currency futures contract on Rueland’s currency (called the ru) is priced at $.40 per ru. What is the spot rate of the ru? (1 point)
Problem 4 (3 points)
- As an employee of the foreign exchange department for a large company, you have been given the following information.
Beginning of Year
Spot rate of £ = $1.596
Spot rate of Australian dollar (A$) = $.70
Cross exchange rate: £1 = A$2.28
One-year forward rate of A$ = $.71
One-year forward rate of £ = $1.58004
One-year U.S. interest rate = 8.00%
One-year British interest rate = 9.09%
One-year Australian interest rate = 7.00%
Determine whether triangular arbitrage is feasible, and if so, how it should be conducted to make a profit. (0.5 point)
- Using the information in question 1, determine whether covered interest arbitrage is feasible and, if so, how it should be conducted to make a profit. (1 point)
- Based on the information in question 1 for the beginning of the year, use the international Fisher effect (IFE) theory to forecast the annual percentage change in the British pound’s value over the year. (0.5 point)
- Assume that at the beginning of the year, the pound’s value is in equilibrium. Assume that over the year the British inflation rate is 6 percent while the U.S. inflation rate is 4 percent. Assume that any change in the pound’s value due to the inflation differential has occurred by the end of the year. Using this information and the information provided in question 1, determine how the pound’s value changed over the year. (0.5 point)
- Assume that the pound’s depreciation over the year was attributed directly to central bank intervention. Explain the type of direct intervention that would place downward pressure on the value of the pound. (0.5 point)
Problem 5: Blades, Inc. Case (Madura 11^{th} edition, Chapter 7, p. 238-239) (4 points)
- The first arbitrage opportunity relates to locational arbitrage. Holt has obtained spot rate quotations from two banks in Thailand, Minzu Bank and Sobat Bank, both located in Bangkok. The bid and ask prices of Thai baht for each bank are displayed in the table below:
Minzu Bank | Sobat Bank | |
Bid | $0.0224 | $0.0228 |
Ask | $0.0227 | $0.0229 |
Determine whether the foreign exchange quotations are appropriate. If they are not appropriate, determine the profit you could generate by withdrawing $100,000 from Blades’ checking account and engaging in arbitrage before the rates are adjusted. (1 point)
- Besides the bid and ask quotes for the Thai baht provided in the previous question, Minzu Bank has provided the following quotations for the U.S. dollar and the Japanese yen:
Quoted Bid Price | Quoted Ask Price | |
Value of a Japanese yen in U.S. dollars | $0.0085 | $0.0086 |
Value of a Thai baht in Japanese yen | ¥2.69 | ¥2.70 |
Determine whether the cross exchange rate between the Thai baht and Japanese yen is appropriate. If it is not appropriate, determine the profit you could generate for Blades Inc, by withdrawing $100,000 from Blades’ checking account and engaging in triangular arbitrage before the rates are adjusted. (1 point)
- Ben Holt has obtained several forward contract quotations for the Thai baht to determine whether covered interest arbitrage may be possible. He was quoted a forward rate of $0.0225 per Thai baht for a 90-day forward contract. The current spot rate is $0.0227. Ninety-day interest rates available to Blades in the S. are 2 percent, while 90-day interest rates in Thailand are 3.75 percent (these rates are not annualized). Holt is aware that covered interest arbitrage, unlike locational and triangular arbitrage, requires an investment of funds. Thus, he would like to be able to estimate the dollar profit resulting from arbitrage over and above the dollar amount available on a 90-day U.S. deposit.
Determine whether the forward rate is priced appropriately. If it is not priced appropriately, determine the profit you could generate for Blades by withdrawing $100,000 from Blades’ checking account and engaging in covered interest arbitrage. Measure the profit as the excess amount above what you could generate by investing in the U.S. money market. (1 point)
- Why are arbitrage opportunities likely to disappear soon after they have been discovered? To illustrate your answer, assume that covered interest arbitrage involving the immediate purchase and forward sale of baht is possible. Discuss how the baht’s spot and forward rates would adjust until covered interest arbitrage is no longer possible. What is the resulting equilibrium state called? (1 point)