1 FINM 7406 Extra Practice Questions - Solutions Q1. Comment on the proposition that the Bretton Woods system was programmed to an eventual demise. Answer: The answer to this question is related to the Triffin paradox. Under the gold- exchange system, the reserve-currency country should run BOP deficits to supply reserves to the world economy, but if the deficits are large and persistent, they can lead to a crisis of confidence in the reserve currency itself, eventually causing the downfall of the system. Q2. Doug Bernard specializes in cross-rate arbitrage. He notices the following quotes: Swiss franc/dollar = SFr1.5971/$ Australian dollar/U.S. dollar = A$1.8215/$ Australian dollar/Swiss franc = A$1.1440/SFr a) Ignoring transaction costs, does Doug Bernard have an arbitrage opportunity based on these quotes? b) If there is an arbitrage opportunity, what steps would he take to make an arbitrage profit, and how would he profit if he has $1,000,000 available for this purpose. Solution: A. The implicit cross-rate between Australian dollars and Swiss franc is A$/SFr = A$/$ x $/SFr = (A$/$)/(SFr/$) = 1.8215/1.5971 = 1.1405. However, the quoted cross-rate is higher at A$1.1440/SFr. So, triangular arbitrage is possible. B. In the quoted cross-rate of A$1.1440/SFr, one Swiss franc is worth A$1.1440, whereas the cross-rate based on the direct rates implies that one Swiss franc is worth A$1.1405. Thus, the Swiss franc is overvalued relative to the A$ in the quoted cross-rate, and Doug Bernard’s strategy for triangular arbitrage should be based on selling Swiss francs to buy A$ as per the quoted cross-rate. Accordingly, the steps Doug Bernard would take for an arbitrage profit is as follows: i. Sell dollars to get Swiss francs: Sell $1,000,000 to get $1,000,000 x SFr1.5971/$ = SFr1,597,100. ii. Sell Swiss francs to buy Australian dollars: Sell SFr1,597,100 to buy SFr1,597,100 x A$1.1440/SFr = A$1,827,082.40. iii. Sell Australian dollars for dollars: Sell A$1,827,082.40 for A$1,827,082.40/A$1.8215/$ = $1,003,064.73. Thus, your arbitrage profit is $1,003,064.73 - $1,000,000 = $3,064.73. 2 Q3. James Clark is a foreign exchange trader with Citibank. He notices the following quotes. Spot exchange rate SFr1.2051/$ Six-month forward exchange rate SFr1.1922/$ Six-month $ interest rate 2.5% per year Six-month SFr interest rate 2.0% per year a. Is the interest rate parity holding? You may ignore transaction costs. b. Is there an arbitrage opportunity? If yes, show what steps need to be taken to make arbitrage profit. Assuming that James Clark is authorized to work with $1,000,000, compute the arbitrage profit in dollars. Solution: a. For six months, iSFr = 1.0% and i$ = 1.25%. the spot exchange rate is $0.8298/SFr and the forward rate is $0.8388/SFr. Thus, (1+ i$ ) = 1.0125 and (F/s) (1 + iSFr) = (0.8388/0.8298) (1.01) = 1.02095 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 1.0125 < 1.02095, we can say that the SFr interest rate quote is more 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 less than what it should be as per the quotes for the other three variables. Therefore, the arbitrage strategy should be based on borrowing in the $ market and lending in the SFr market. The steps would be as follows: Borrow $1,000,000 for six months at 1.25%. Need to pay back $1,000,000 × (1 + 0.0125) = $1,012,500 six months later. Convert $1,000,000 to SFr at the spot rate to get SFr 1,205,100. Lend SFr 1,205,100 for six months at 1.0%. Will get back SFr 1,205,100 × (1 + 0.01) = SFr 1,217,151 six months later. Sell SFr 1,217,151 six months forward. The transaction will be contracted as of the current date but delivery and settlement will only take place six months later. So, six months later, exchange SFr 1,217,151 for SFr 1,217,151/SFr 1.1922/$ = $1,020,929. The arbitrage profit six months later is $1,020,929 – $1,012,500 = $8,429. 3 Q4. Comment on the following statement: “Since the United States imports more than it exports, it is necessary for the United States to import capital from foreign countries to finance its current account deficits.” Solution: The statement presupposes that the U.S. current account deficit causes its capital account surplus. In reality, the causality may be running in the opposite direction: U.S. capital account surplus may cause the country’s current account deficit. Suppose foreigners find the U.S. a great place to invest and send their capital to the U.S., resulting in U.S. capital account surplus. This capital inflow will strengthen the dollar, hurting the U.S. export and encouraging imports from foreign countries, causing current account deficits. Q5. Alpha and Beta Companies can borrow for a five-year term at the following rates: Alpha Beta Moody’s credit rating Aa Baa Fixed-rate borrowing cost 10.5% 12.0% Floating-rate borrowing cost LIBOR LIBOR + 1% a. Calculate the quality spread differential (QSD). b. Develop an interest rate swap in which both Alpha and Beta have an equal cost savings in their borrowing costs. Assume Alpha desires floating-rate debt and Beta desires fixed- rate debt. No swap bank is involved in this transaction. Assume the party, who pays floating-rate to his counterparty, needs to pay LIBOR. Solution: a. The QSD = (12.0% - 10.5%) minus (LIBOR + 1% - LIBOR) = .5%. b. Alpha needs to issue fixed-rate debt at 10.5% and Beta needs to issue floating rate-debt at LIBOR + 1%. Alpha needs to pay LIBOR1 to Beta. Beta needs to pay 10.75% to Alpha. If this is done, Alpha’s floating-rate all-in-cost is: 10.5% + LIBOR - 10.75% = LIBOR - .25%, a .25% savings over issuing floating-rate debt on its own. Beta’s fixed-rate all-in-cost is: LIBOR+ 1% + 10.75% - LIBOR = 11.75%, a .25% savings over issuing fixed-rate debt. 1 FAQ: Alpha needs to pay Floating Rate to Beta, and we assume this floating rate to be LIBOR. It does not matter whether we use LIBOR or LIBOR + X%, the net effect is the same. For example, if we assume Alpha needs to pay LIBOR + 1% to Beta, then Beta would need to pay 10.75% +1% to Alpha. 4 Q6. Suppose that you are a U.S.-based importer of goods from the United Kingdom. You expect the value of the pound to increase against the U.S. dollar over the next 30 days. You will be making payment on a shipment of imported goods in 30 days and want to hedge your currency exposure. The U.S. risk-free rate is 5.5 percent, and the U.K. risk-free rate is 4.5 percent. These rates are expected to remain unchanged over the next month. The current spot rate is $1.50. a. Indicate whether you should use a long or short forward contract to hedge currency risk. b. Calculate the no-arbitrage price at which you could enter into a forward contract that expires in 30 days. c. Move forward 30 days. The spot rate is $1.53. Calculate the value of your forward position at the end of 30 days. Solution: a. The risk to you is that the value of the British pound will rise over the next 30 days and it will require more U.S. dollars to buy the necessary pounds to make payment. To hedge this risk, you should enter a forward contract to buy British pounds. b. S0 = $1.50 T = 30/365 r = 0.055 rf = 0.045 5012.1$ )365/30(*)045.0(1 )365/30(*)055.0(1*50.1$),0( = + + =TF using simple interest rate (Kelvin Tan updated): Frequently asked question: If the time period is more than one year, please use compounding interest rate: 5012.1$ )045.1( )055.1(*50.1$),0( 365/30 365/30 = =TF c. St = $1.53 Long forward payoff= St - F 0288.0$5012.1$53.1$),0( =−=TVt Because you are long, this is a gain of $0.0288 per British pound. 5 Q7. Evaluate the following statement: “A firm can reduce its currency exposure by diversifying across different business lines.” Answer: Conglomerate expansion may be too costly as a means of hedging exchange risk exposure. Investment in a different line of business must be made based on its own merit. Q8. Suppose you are a euro-based investor who just sold Microsoft shares that you had bought six months ago. You had invested 10,000 euros to buy Microsoft shares for $120 per share; the exchange rate was $1.15 per euro. You sold the stock for $135 per share and converted the dollar proceeds into euro at the exchange rate of $1.06 per euro. First, determine the profit from this investment in euro terms using an approximation formula. Second, compute the rate of return on your investment in euro terms. How much of the return is due to the exchange rate movement? Solution: It is useful first to compute the rate of return in euro terms: )(210.0 085.0125.0 15.1 1 15.1 1 06.1 1 120 120135 err $ elyapproximat= += − + −= +≅ This indicates that this euro-based investor benefited from an appreciation of dollar against the euro, as well as from an appreciation of the dollar value of Microsoft shares. The profit in euro terms is about €2,100, and the rate of return is about 21.0% in euro terms, of which 8.5% is due to the exchange rate movement. Q9. Discuss how the cost of capital is determined in segmented vs. integrated capital markets. Answer: In segmented capital markets, the cost of capital will be determined essentially by the securities’ domestic systematic risks. In integrated capital markets, on the other hand, the cost of capital will be determined by the securities’ world systematic risk, regardless of nationality. € 6 Q10. Delta Company, a U.S. MNC, is contemplating making a foreign capital expenditure in South Africa. The initial cost of the project is ZAR10,000. The annual cash flows over the five year economic life of the project in ZAR are estimated to be 3,000, 4,000, 5,000, 6000, and 7,000. The parent firm’s cost of capital in dollars is 9.5 percent. Long-run inflation is forecasted to be 3 percent per annum in the U.S. and 7 percent in South Africa. The current spot foreign exchange rate is ZAR/USD = 3.75. Determine the NPV for the project in USD by: a) Calculating the NPV in ZAR using the ZAR equivalent cost of capital according to the Fisher Effect and then converting to USD at the current spot rate. Solution: ZAR equivalent cost of capital according to the Fisher Effect = 1.095 x [(1.07)/(1.03)] – 1 = .1375 or 13.75 percent. NPVUSD = [3,000/(1.1375)1 + 4,000/(1.1375)2 + 5,000/(1.1375)3 + 6,000/(1.1375)4 + 7,000/(1.1375)5 – 10,000]/3.75 = USD1,700 b) Converting all cash flows from ZAR to USD at Purchasing Power Parity forecasted exchange rates and then calculating the NPV at the dollar cost of capital. Solution: The PPP forecasted ZAR/USD exchange rates are: ZAR/USD(t) = 3.75 x [(1.07)/(1.03)]t ZAR/USD(1) = 3.90; ZAR/USD(2) = 4.05; ZAR/USD(3) = 4.20; ZAR/USD(4) = 4.37; and, ZAR/USD(5) = 4.54. NPVUSD = [(3,000/3.90)/(1.095)1 + 4,000/(4.05)/(1.095)2 + 5,000/(4.20)/(1.095)3 + 6,000/(4.37)/(1.095)4 + 7,000/(4.54)/(1.095)5 – 10,000/(3.75)] = USD1,700 Are the two dollar NPVs different or the same? Explain. The two dollar NPVs are identical as they always will be under the assumption that both PPP and the Fisher Effect hold. Note, that both parity conditions incorporate relative differences in inflation. 7 c. What is the NPV in dollars if the actual pattern of ZAR/USD exchange rates is: S(0) = 3.75, S(1) = 5.7, S(2) = 6.7, S(3) = 7.2, S(4) = 7.7, and S(5) = 8.2? Solution: NPVUSD = [(3,000/5.7)/(1.095)1 + 4,000/(6.7)/(1.095)2 + 5,000/(7.2)/(1.095)3 + 6,000/(7.7)/(1.095)4 + 7,000/(8.2)/(1.095)5 – 10,000/(3.75)] = –USD75. The NPV is negative because actual exchange rates did not evolve as forecasted by PPP. Consequently, actual NPV and forecasted NPV may be different.
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