International Financial Management. Prerequisites

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1 International Financial Management Prerequisites 1. The quoted interest rate is 5% p.a. What is the effective interest rate for 6 months if the quoted interest rate is a) simple, b) annually compounded, c) quarterly compounded or d) continuously compounded? 2. A deposit earns interest of 12% p.a., compounded quarterly. At which continuously compounded interest rate would a bond yield the same effective return as this deposit over a period of a) half a year and b) one year? Spot Exchange Markets 3. You have just graduated from the University of Florida and are leaving on a whirlwind tour of Europe. You wish to spend USD 1,000 each in Switzerland, France, and Great Britian (USD 3,000 in total). Your bank offers you the following bid-ask quotes: USD/ CHF , USD/EUR , and USD/GBP a) If you accept these quotes, how many CHF, EUR, and GBP do you have at departure? b) If you return with CHF 300, EUR 1,00, and GBP 75, and the exchange rates are unchanged, how many USD do you have? c) Suppose that instead of selling your remaining CHF 300 once you return home, you want to sell them in Paris. At the train station, you are offered EUR/CHF , while a bank three blocks from the station offers EUR/CHF At what rate are you willing to sell your CHF 300? How many EUR will you receive? 4. BankAustria quotes USD/EUR , and BankAmerica quotes EUR/USD a) Are these quotes identical? b) If not, is there a possibility for least cost dealing or arbitrage? c) If there is an arbitrage opportunity, how would you profit from it? 5. Please use these quotes to answer the following exercises: 1

2 Bid Ask GBP/USD 0,5276 0,5383 USD/EUR 1,2797 1,3055 a) Suppose that you convert 10 EUR into USD and finally into GBP and then use the proceeds to do the reverse conversion. What is the amount you end up with? b) In your answer to a), verify the "Law of the Worst Rate"! c) Please compute the synthetic cross rate. d) Suppose that a bank quotes as stated above. Would you require additional information in order to check possibilities for least cost dealing or arbitrage? If so, which information? e) Suppose that there is another bank quoting EUR/GBP Is there a triangular arbitrage opportunity? f) Given that there are three currencies involved, how many conditions must be satisfied such that there are no arbitrage opportunities? Forward Contracts in Perfect Markets 6. You are given the following data: the spot exchange rate is CAD/EUR 1.617; the p.a. simple interest rate on a six month deposit is 3% in Canada and 4% in Austria. Compute: a) The forward rate for a three-month forward contract. b) The time-t CAD value of a CAD(t) 1 investment. c) The time-t EUR value of a EUR(T) 1 loan. d) The time-t EUR value of a CAD(T) 1 forward sale, given the forward rate computed in a). e) The time-t EUR value of a CAD(T) 1 spot sale (hint: use the certainty equivalent). 7. A Japanese manufacturer has an accounts receivable of USD 1 million due in 90 days. The spot and forward exchange rates are JPY/USD 110 and 109.8, respectively, and the simple interest rate for a three-month deposit is 2 percent p.a. in Japan and 3 percent p.a. in the US. a) If the manufacturer sells the USD 1 million forward for 90 days, how many JPY will she receive at time T? b) How could she replicate a forward sale in the spot and money markets? c) Is the manufacturer indifferent between (a) and (b)? d) If the manufacturer has a preference, is this an example of least cost dealing or arbitrage? 8. Suppose that the spot exchange rate between the Japanese Yen and the US Dollar is JPY/USD The forward rate for 3 months is JPY/USD and the 90-day interest rates are 7/32% p.a. in Japan and 6 1/8% p.a. in the US. Are there any arbitrage opportunities? If so, how would you make a risk-free profit and what would happen if a very large number of investors try to do likewise? 2

3 9. Suppose that the expected spot rate between the Canadian Dollar and the US Dollar in one year is CAD/USD Moreover, let the current forward rate for 1 year equal this expected future spot rate. Draw a diagram which depicts the payoff from a) a forward sale and b) a forward purchase of 1 million USD for 1 year when the realized spot rate differs from the expected rate. The Value of a Forward Contract and Its Implication 10. Which of the following statements are correct? a) A forward purchase contract can be replicated by borrowing foreign currency, converting it into domestic currency, and investing the domestic currency. b) A forward purchase contract can be replicated by borrowing domestic currency, converting it into foreign currency, and investing the foreign currency. c) A forward sale contract can be replicated by borrowing foreign currency, converting it into domestic currency, and investing the domestic currency. d) A forward sale contract can be replicated by borrowing domestic currency, converting it into foreign currency, and investing the foreign currency. 11. After completion of your studies, you work as a trader at a bank's foreign exchange trading room. One day, you enter into a one-year forward purchase of EUR 10 m at USD/EUR An hour later, you see that the rate is now at USD/EUR a) How could you "lock in" your gain? b) At which price would you be willing to enter into the contract needed to set up this hedge? (Suppose that another trader offers to act as the counterparty to this contract conditional on the two of you "splitting the gain". What would be your reaction?) c) At which price would you sell your contract from one hour ago if the US interest rate is 2.25 % p.a.? 12. Please solve the following exercises: a) Given the following data, compute the value today of an outstanding forward purchase contract initiated at t 0 for units of foreign currency (where the exchange rate is HC/FC). Does the new value represent a gain or a loss to the holder of the old contract? (Hint: First compute the new forward rate.) Spot Rate Old Forward Rate r t,t r* t,t (1) USD/GBP 1,96 1,99 6,35% 5,10% (2) JPY/USD 107,62 109,05 3,20% 6,35% b) Repeat the previous question using the same data, but with an outstanding forward sale contract. 3

4 13. A US company expects to receive EUR 1m in one year. The treasurer of this company wants to value this A/R. So, she looks up a consensus forecast which states an average of some experts' opinions about the spot rate in one year's time. This consensus forecast is USD/EUR Moreover, she looks up the interest rate on USD CDs for one year which turns out to be 5.92% p.a. Finally, she does some calculations and reports the value of the A/R as USD a) How did she come up with this number? Did she make a mistake? At lunch, the treasurer talks to a friend and tells him about the interesting consensus forecast she found in a newspaper this morning. In response, her friend wants to show off his own knowledge of international finance: he replies that nobody should really care about some experts' forecasts since the forward rate, as the "consensus" of the market, is the best forecast one may ask for. According to her friend, the treasurer should therefore redo her calculations and replace the consensus forecast of the future spot rate by the forward rate. b) Is the friend a real expert in international finance? c) Suppose that the treasurer follows her friend's suggestions. Would she make a mistake? (Suppose that the forward rate is USD/EUR ) d) Can you think about an alternative way to determine the value of the A/R? 14. Suppose that you sold forward (360 days) GBP 2m at the forward rate CAD/GBP 2.05 to hedge a payment from a British customer. Ten months later the GBP trades at CAD/GBP 2.20 and compounded interest rates for 60 days are 5% p.a. for the CAD and 7% p.a. for the GBP. Unexpectedly, the customer pays 2 months earlier than schedule. Consider the following alternatives. You may: (1) Invest the GBP 2m for 2 months and deliver them to the bank with which you signed the forward contract. (2) Sell the GBP 2m spot and negotiate an early termination of the outstanding forward sale. (3) Sell the GBP 2m spot and buy them forward 60 days so that you can deliver the required amount to your bank. a) Analyze each alternative. Which alternative is the best one? b) Comment on your answers from part a. Is this what you would expect? Why (not)? Forward Contracts and Market Imperfections 15. An American company plans to send an employee to Vienna to learn German. The employee will need EUR 5,000 in 3 months time when the classes begin, and an additional EUR 2,000 in 6 months to cover his living expenses. Today, the American company wants to lock in the costs of training his employee. Given the following information, what amount of USD will the American company have to pay in 3 and in 6 months time? Bid Ask USD/EUR 1,15 1,27 R 6,1% p.a. 6,7% p.a. r* 3,8% p.a. 4,3% p.a. 4

5 16. After completion of your studies, you work as the foreign exchange risk manager of a big company. One day, you enter into a one-year forward purchase of EUR 10 m at USD/EUR An hour later, you see that your bank quotes that the rate is now at USD/EUR a) How could you "lock in" your gain? b) At which price could you sell your contract from one hour ago to your bank if the US interest rate is % p.a.? c) Instead of selling to the bank, you talk to a friend who is the foreign exchange risk manager of the company across the street. It turns out that this company is about to enter into a one-year forward purchase contract of EURO 10 m at the current forward rate. However, after talking to you, your friend considers whether to buy your old forward purchase contract. What is the maximum amount that you could receive from your friend? What are the implications for the value of your old forward purchase contract? 17. Suppose you are a Canadian and are presented with the following information: Investing Borrowing Interest rate in Canada 6% p.a. 7% p.a. Interest rate in USA 4,5% p.a. 6,5% p.a. CAD/USD bid CAD/USD ask Spot rate 1,185 1,191 a) Where should you borrow? b) Where should you invest? c) If interest income is taxed at 50%, but foreign exchange earnings are untaxed, would this affect your answer to part b? Currency Futures Markets 18. An Englishman wishes to hedge an accounts receivable of USD which will become due in 3 weeks time. He contacts his broker and sells 50 futures contracts, each of which is for the sale of USD 125,000 at GBP/USD The contracts expire in 3 weeks. Assume that today is Monday, and that the settlement prices at the end of each day during the first week are as follows: Settlement GBP/USD Mon 0,5263 Tue 0,5245 Wed 0,5266 Thu 0,5311 Fri 0,5327 The initial margin is set at GBP 5,000 per contract and the maintenance margin at GBP 4,000 per contract. No interest is paid on the margin account. Assume that the man withdraws money from 5

6 his margin account whenever he may do so, but that the first time he must make a margin-call, he fails to do so. (i.e. he does pay the initial margin as required). a) Show the value of any withdrawals which the man made, and the value of all margin-calls. b) If the man fails to pay the first margin-call, what does the broker do? What is the final settlement? 19. A German firm wants to hedge the EUR value of a CAD 1m inflow using futures contracts. On Germany's exchange, there is a futures contract for USD 100,000 at EUR/USD a) Your assistant runs a bunch of regressions: (1) S [ EUR / CAD] = α 1 + β1 f [ USD / EUR] (2) S [ EUR / CAD] = α 2 + β 2 f [ EUR / USD] (3) S [ CAD / EUR] = α 3 + β 3 f [ EUR / USD] (4) S [ CAD / EUR] = α 4 + β 4 f [ USD / EUR] Which regression is relevant to you? b) If the relevant β is 0.85, how many contracts do you buy? Sell? 20. A German exporter wants to hedge an outflow of NZD 1m. She decides to hedge the risk with a EUR/USD contract and a EUR/AUD contract. The regression output is, with the t-statistics shown in parentheses, and R2 = 0.59: [ EUR / NZD] = f [ EUR / USD] f [ EUR AUD] S α / (1.57) (17.2) a) How will you hedge if you use both contracts, and if the face value of a USD contract is for USD 50,000 and AUD contract for AUD 75,000? b) Should you use the USD contract, in view of the low t-statistic? Or should you only use the AUD contract? 21. On September 30 th 2004 a US importer learns that she will pay EUR 1,250,000 on January 30th The US importer decided to hedge this position, using EUR futures contracts with an expiration date on the third Wednesday in March On September 30 th the following exchange rates were quoted: Spot rate USD/EUR= 1,2700, futures rate for the expiration month of March 2005 is USD/EUR 1,3020. On January 30 th the CFO of the US importer reports that the total gain/loss on the hedged position (spot position plus futures position) was US$ 10,000. a) Explain what the CFO must have done to implement this hedge. b) What must the basis have been on January 30 th? c) What would the basis on January 30 th need to be in order to make gain/loss of the hedged position zero? 22. When does a currency futures contract have a higher price than does a forward contract with the same time to maturity? Why? 6

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