# CHAPTER 5 THE MARKET FOR FOREIGN EXCHANGE SUGGESTED ANSWERS AND SOLUTIONS TO END-OF-CHAPTER QUESTIONS AND PROBLEMS

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5 PROBLEMS 1. Using Exhibit 5.4, calculate a cross-rate matrix for the euro, Swiss franc, Japanese yen, and the British pound. Use the most current American term quotes to calculate the cross-rates so that the triangular matrix resulting is similar to the portion above the diagonal in Exhibit 5.6. Solution: The cross-rate formula we want to use is: S(j/k) = S(\$/k)/S(\$/j). The triangular matrix will contain 4 x (4 + 1)/2 = 10 elements. SF \$ Euro Japan (100) Switzerland U.K Using Exhibit 5.4, calculate the one-, three-, and six-month forward cross-exchange rates between the Canadian dollar and the Swiss franc using the most current quotations. State the forward cross-rates in Canadian terms. Solution: The formulas we want to use are: F N (CD/SF) = F N (\$/SF)/F N (\$/CD) or F N (CD/SF) = F N (CD/\$)/F N (SF/\$). We will use the top formula that uses American term forward exchange rates. F 1 (CD/SF) =.9052/.9986 =.9065 F 3 (CD/SF) =.9077/.9988 =.9088 F 6 (CD/SF) =.9104/.9979 =.9123

6 3. A foreign exchange trader with a U.S. bank took a short position of 5,000,000 when the \$/ exchange rate was Subsequently, the exchange rate has changed to Is this movement in the exchange rate good from the point of view of the position taken by the trader? By how much has the bank s liability changed because of the change in the exchange rate? UPDATE TO CURRENT EX-RATES? CFA Guideline Answer: The increase in the \$/ exchange rate implies that the pound has appreciated with respect to the dollar. This is unfavorable to the trader since the trader has a short position in pounds. Bank s liability in dollars initially was 5,000,000 x 1.55 = \$7,750,000 Bank s liability in dollars now is 5,000,000 x 1.61 = \$8,050, Restate the following one-, three-, and six-month outright forward European term bid-ask quotes in forward points. Spot One-Month Three-Month Six-Month Solution: One-Month Three-Month Six-Month Using the spot and outright forward quotes in problem 3, determine the corresponding bid-ask spreads in points. Solution: Spot 5 One-Month 10 Three-Month 15 Six-Month 20

9 9. Given the following information, what are the NZD/SGD currency against currency bid-ask quotations? American Terms European Terms Bank Quotations Bid Ask Bid Ask New Zealand dollar Singapore dollar Solution: Equation 5.12 from the text implies S b (NZD/SGD) = S b (\$/SGD) x S b (NZD/\$) =.6135 x = The reciprocal, 1/S b (NZD/SGD) = S a (SGD/NZD) = Analogously, it is implied that S a (NZD/SGD) = S a (\$/SGD) x S a (NZD/\$) =.6140 x = The reciprocal, 1/S a (NZD/SGD) = S b (SGD/NZD) = Thus, the NZD/SGD bid-ask spread is NZD NZD and the SGD/NZD spread is SGD SGD 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 Ignoring transaction costs, does Doug Bernard have an arbitrage opportunity based on these quotes? 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. CFA Guideline Answer: A. The implicit cross-rate between Australian dollars and Swiss franc is A\$/SFr = A\$/\$ x \$/SFr = (A\$/\$)/(SFr/\$) = / = However, the quoted cross-rate is higher at A\$ /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\$ 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:

11 The S( /SF) cross exchange rate should be.7627/ = This is an equilibrium rate at which a triangular arbitrage profit will not exist. (The student can determine this for himself.) A profit results from the triangular arbitrage when dollars are first sold for euros because Swiss francs are purchased for euros at too low a rate in comparison to the equilibrium cross-rate, i.e., Swiss francs are purchased for only /SF1.00 instead of the no-arbitrage rate of /SF1.00. Similarly, when dollars are first sold for Swiss francs, an arbitrage loss results because Swiss francs are sold for euros at too low a rate, resulting in too few euros. That is, each Swiss franc is sold for /SF1.00 instead of the higher no-arbitrage rate of /SF The current spot exchange rate is \$1.95/ and the three-month forward rate is \$1.90/. Based on your analysis of the exchange rate, you are pretty confident that the spot exchange rate will be \$1.92/ in three months. Assume that you would like to buy or sell 1,000,000. a. What actions do you need to take to speculate in the forward market? What is the expected dollar profit from speculation? b. What would be your speculative profit in dollar terms if the spot exchange rate actually turns out to be \$1.86/. Solution: a. If you believe the spot exchange rate will be \$1.92/ in three months, you should buy 1,000,000 forward for \$1.90/. Your expected profit will be: \$20,000 = 1,000,000 x (\$1.92 -\$1.90). b. If the spot exchange rate actually turns out to be \$1.86/ in three months, your loss from the long position will be: -\$40,000 = 1,000,000 x (\$1.86 -\$1.90).

12 13. Omni Advisors, an international pension fund manager, plans to sell equities denominated in Swiss Francs (CHF) and purchase an equivalent amount of equities denominated in South African Rands (ZAR). Omni will realize net proceeds of 3 million CHF at the end of 30 days and wants to eliminate the risk that the ZAR will appreciate relative to the CHF during this 30-day period. The following exhibit shows current exchange rates between the ZAR, CHF, and the U.S. dollar (USD). Currency Exchange Rates ZAR/USD ZAR/USD CHF/USD CHF/USD Maturity Bid Ask Bid Ask Spot day day a. Describe the currency transaction that Omni should undertake to eliminate currency risk over the 30-day period. b. Calculate the following: The CHF/ZAR cross-currency rate Omni would use in valuing the Swiss equity portfolio. The current value of Omni s Swiss equity portfolio in ZAR. The annualized forward premium or discount at which the ZAR is trading versus the CHF. CFA Guideline Answer: a. To eliminate the currency risk arising from the possibility that ZAR will appreciate against the CHF over the next 30-day period, Omni should sell 30-day forward CHF against 30-day forward ZAR delivery (sell 30-day forward CHF against USD and buy 30-day forward ZAR against USD). b. The calculations are as follows:

13 Using the currency cross rates of two forward foreign currencies and three currencies (CHF, ZAR, USD), the exchange would be as follows: --30 day forward CHF are sold for USD. Dollars are bought at the forward selling price of CHF = \$1 (done at ask side because going from currency into dollars) --30 day forward ZAR are purchased for USD. Dollars are simultaneously sold to purchase ZAR at the rate of = \$1 (done at the bid side because going from dollars into currency) --For every CHF held, ZAR are received; thus the cross currency rate is CHF/ ZAR = At the time of execution of the forward contracts, the value of the 3 million CHF equity portfolio would be 3,000,000 CHF/ = 12,274, ZAR. To calculate the annualized premium or discount of the ZAR against the CHF requires comparison of the spot selling exchange rate to the forward selling price of CHF for ZAR. Spot rate = CHF/ ZAR = day forward ask rate CHF/ ZAR = The premium/discount formula is: [(forward rate spot rate) / spot rate] x (360 / # day contract) = [( ) / ] x (360 / 30) = % = -1.80% discount ZAR to CHF

14 MINI CASE: SHREWSBURY HERBAL PRODUCTS, LTD. Shrewsbury Herbal Products, located in central England close to the Welsh border, is an old-line producer of herbal teas, seasonings, and medicines. Its products are marketed all over the United Kingdom and in many parts of continental Europe as well. Shrewsbury Herbal generally invoices in British pound sterling when it sells to foreign customers in order to guard against adverse exchange rate changes. Nevertheless, it has just received an order from a large wholesaler in central France for 320,000 of its products, conditional upon delivery being made in three months time and the order invoiced in euros. Shrewsbury s controller, Elton Peters, is concerned with whether the pound will appreciate versus the euro over the next three months, thus eliminating all or most of the profit when the euro receivable is paid. He thinks this is an unlikely possibility, but he decides to contact the firm s banker for suggestions about hedging the exchange rate exposure. Mr. Peters learns from the banker that the current spot exchange rate is / is , thus the invoice amount should be 465,184. Mr. Peters also learns that the three-month forward rates for the pound and the euro versus the U.S. dollar are \$1.8990/ 1.00 and \$1.3154/ 1.00, respectively. The banker offers to set up a forward hedge for selling the euro receivable for pound sterling based on the / forward cross-exchange rate implicit in the forward rates against the dollar. What would you do if you were Mr. Peters?

15 Suggested Solution to Shrewsbury Herbal Products, Ltd. Note to Instructor: This elementary case provides an intuitive look at hedging exchange rate exposure. Students should not have difficulty with it even though hedging will not be formally discussed until Chapter 8. The case is consistent with the discussion that accompanies Exhibit 5.9 of the text. Professor of Finance, Banikanta Mishra, of Xavier Institute of Management Bhubaneswar, India contributed to this solution. Suppose Shrewsbury sells at a twenty percent markup. Thus the cost to the firm of the 320,000 order is 256,000. Thus, the pound could appreciate to 465,184/ 256,000 = /1.00 before all profit was eliminated. This seems rather unlikely. Nevertheless, a ten percent appreciation of the pound ( x 1.10) to / 1.00 would only yield a profit of 34,904 (= 465,184/ ,000). Shrewsbury can hedge the exposure by selling the euros forward for British pounds at F3( / ) = F3(\$/ ) F3(\$/ ) = = At this forward exchange rate, Shrewsbury can lock-in a price of 322,217 (= 465,184/1.4437) for the sale. The forward exchange rate indicates that the euro is trading at a premium to the British pound in the forward market. Thus, the forward hedge allows Shrewsbury to lock-in a greater amount ( 2,217) than if the euro receivable was converted into pounds at the current spot If the euro was trading at a forward discount, Shrewsbury would end up locking-in an amount less than 320,000. Whether that would lead to a loss for the company would depend upon the extent of the discount and the amount of profit built into the price of 320,000. Only if the forward exchange rate is even with the spot rate will Shrewsbury receive exactly 320,000. Obviously, Shrewsbury could ensure that it receives exactly 320,000 at the end of three-month accounts receivable period if it could invoice in. That, however, is not acceptable to the French wholesaler. When invoicing in euros, Shrewsbury could establish the euro invoice amount by use of the forward exchange rate instead of the current spot rate. The invoice amount in that case would be 461,984 = 320,000 x Shrewsbury can now lock-in a receipt of 320,000 if it simultaneously hedges its euro exposure by selling 461,984 at the forward rate of That is, 320,000 = 461,984/

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