Eun & Resnick, “International Financial Management,” 7e
Ch. 05, “The Market for Foreign Exchange”
EndofChapter Problems and Solutions
Exhibit 5.4:
Solution: The crossrate 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 
129.70 
1.2335 
.8499 
1.3092 
Japan (100) 
.9510 
.6552 
1.0094 

Switzerland 
.6890 
1.0614 

U.K 
1.5405 
Solution: The formulas we want to use are:
F_{N}(AD/SF) = F_{N}($/SF)/F_{N}($/AD)
or
F_{N}(AD/SF) = F_{N}(AD/$)/F_{N}(SF/$).
We will use the top formula that uses American term forward exchange rates.
F_{1}(AD/SF) = 1.0617/.9521 = 1.1151
F_{3}(AD/SF) = 1.0624/.9482 = 1.1204
F_{6}(AD/SF) = 1.0636/.9425 = 1.1285
Solution:
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 = $8,050,000
Spot 1.34311.3436
OneMonth 1.34321.3442
ThreeMonth 1.34481.3463
SixMonth 1.34881.3508
Solution:
OneMonth 0106
ThreeMonth 1727
SixMonth 5772
Solution:
Spot 5
OneMonth 10
ThreeMonth 15
SixMonth 20
Solution: The formula we want to use is:
f_{N,CD} = [(F_{N}($/¥)  S($/¥/$)/S($/¥)] x 360/N
f_{1,CD} = [(.010095  .010094)/.010094] x 360/30 = .0012
f_{3,CD} = [(.010099  .010094)/.010094] x 360/90 = .0020
f_{6,CD} = [(.010106  .010094)/.010094] x 360/180 = .0024
The pattern of forward premiums indicates that the Japanese yen is trading at a premium versus the U.S. dollar. That is, it becomes more expensive to buy a Japanese yen forward for U.S. dollars (in absolute and percentage terms) the further into the future one contracts.
Solution: The formula we want to use is:
f_{N,$} = [(F_{N} (£/$)  S(£/$))/S(£/$)] x 360/N
f_{1,$} = [(.6493  .6491)/.6491] x 360/30 = .0037
f_{3,$} = [(.6494  .6491)/.6491] x 360/90 = .0018
f_{6,$} = [(.6498  .6491)/.6491] x 360/180 = .0022
The pattern of forward premiums indicates that the dollar is trading at a premium versus the British pound. The onemonth premium is larger than the either the threemonth or sixmonth premium in percentage but not absolute terms.
SFr/$ = 1.596070
A$/$ = 1.722535
An Australian firm asks the bank for an A$/SFr quote. What crossrate would the bank quote?
Solution:
The SFr/A$ quotation is obtained as follows. In obtaining this quotation, we keep in mind that SFr/A$ = SFr/$/A$/$, and that the price (bid or ask) for each transaction is the one that is more advantageous to the bank.
The SFr/A$ bid price is the number of SFr the bank is willing to pay to buy one A$. This transaction (buy A$—sell SFr) is equivalent to selling SFr to buy dollars (at the bid rate of 1.5960 and the selling those dollars to buy A$ (at an ask rate of 1.7235). Mathematically, the transaction is as follows:
bid SFr/A$ = (bid SFr/$)/(ask A$/$) = 1.5960/1.7235 = 0.9260
The SFr/A$ ask price is the number of SFr the bank is asking for one A$. This transaction (sell A$—buy SFr) is equivalent to buying SFr with dollars (at the ask rate of 1.5970 and then simultaneously purchasing these dollars against A$ (at a bid rate of 1.7225). This may be expressed as follows:
ask SFr/A$ = (ask SFr/$)/(bid A$/$) = 1.5970/1.7225 = 0.9271
The resulting quotation by the bank is
SFr/A$ = 0.9260—0.9271
American Terms European Terms
Bank Quotations Bid Ask Bid Ask
New Zealand dollar .7265 .7272 1.3751 1.3765
Singapore dollar .6135 .6140 1.6287 1.6300
Solution: Equation 5.12 from the text implies S^{b}(NZD/SGD) = S^{b}($/SGD) x S^{b}(NZD/$) = .6135 x 1.3751 = .8436. The reciprocal, 1/S^{b}(NZD/SGD) = S^{a}(SGD/NZD) = 1.1854. Analogously, it is implied that S^{a}(NZD/SGD) = S^{a}($/SGD) x S^{a}(NZD/$) = .6140 x 1.3765 = .8452. The reciprocal, 1/S^{a}(NZD/SGD) = S^{b}(SGD/NZD) = 1.1832. Thus, the NZD/SGD bidask spread is NZD0.8436NZD0.8452 and the SGD/NZD spread is SGD1.1832SGD1.1854.
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.
Solution:
Thus, your arbitrage profit is $1,003,064.73  $1,000,000 = $3,064.73.
Solution: To make a triangular arbitrage profit the Deutsche Bank trader would sell $5,000,000 to Dresdner Bank at €0.7627/$1.00. This trade would yield €3,813,500= $5,000,000 x .7627. The Deutsche Bank trader would then sell the euros for Swiss francs to Union Bank of Switzerland at a price of €0.6395/SF1.00, yielding SF5,963,253 = €3,813,500/.6395. The Deutsche Bank trader will resell the Swiss francs to Credit Suisse for $5,051,036 = SF5,963,253/1.1806, yielding a triangular arbitrage profit of $51,036.
If the Deutsche Bank trader initially sold $5,000,000 for Swiss francs, instead of euros, the trade would yield SF5,903,000 = $5,000,000 x 1.1806. The Swiss francs would in turn be traded for euros to UBS for €3,774,969= SF5,903,000 x .6395. The euros would be resold to Dresdner Bank for $4,949,481 = €3,774,969/.7627, or a loss of $50,519. Thus, it is necessary to conduct the triangular arbitrage in the correct order.
The S(€/SF) cross exchange rate should be .7627/1.1806 = .6460. 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 crossrate, i.e., Swiss francs are purchased for only €0.6395/SF1.00 instead of the noarbitrage rate of €0.6460/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 €0.6395/SF1.00 instead of the higher noarbitrage rate of €0.6460/SF1.00.
Solution:
$20,000 = £1,000,000 x ($1.92 $1.90).
$40,000 = £1,000,000 x ($1.86 $1.90).
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 30day 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 
6.2681 
6.2789 
1.5282 
1.5343 
30day 
6.2538 
6.2641 
1.5226 
1.5285 
90day 
6.2104 
6.2200 
1.5058 
1.5115 
Solution:
30 day forward CHF are sold for USD. Dollars are bought at the forward selling price of CHF1.5285 = $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 6.2538 = $1 (done at the bid side because going from dollars into currency)
For every 1.5285 CHF held, 6.2538 ZAR are received; thus the cross currency rate is 1.5285 CHF/6.2538 ZAR = 0.244411398.
Spot rate = 1.5343 CHF/6.2681 ZAR = 0.244779120
30 day forward ask rate 1.5285 CHF/6.2538 ZAR = 0.244411398
The premium/discount formula is:
[(forward rate – spot rate) / spot rate] x (360 / # day contract) =
[(0.244411398 – 0.24477912) / 0.24477912] x (360 / 30) =
1.8027126 % = 1.80% discount ZAR to CHF
MINI CASE: SHREWSBURY HERBAL PRODUCTS, LTD.
Shrewsbury Herbal Products, located in central England close to the Welsh border, is an oldline 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 €1.4537, thus the invoice amount should be €465,184. Mr. Peters also learns that the threemonth forward rates for the pound and the euro versus the U.S. dollar are $1.8990/£1.00 and $1.3154/€1.00, respectively. The banker offers to set up a forward hedge for selling the euro receivable for pound sterling based on the €/£ forward crossexchange rate implicit in the forward rates against the dollar.
What would you do if you were Mr. Peters?
Suggested Solution to Shrewsbury Herbal Products, Ltd.
Suppose Shrewsbury sells at a twenty percent markup. Thus the cost to the firm of the £320,000 order is £256,000. Thus, the pound could appreciate to €465,184/£256,000 = €1.8171/1.00 before all profit was eliminated. This seems rather unlikely. Nevertheless, a ten percent appreciation of the pound (€1.4537 x 1.10) to €1.5991/£1.00 would only yield a profit of £34,904 (= €465,184/1.5991  £256,000). Shrewsbury can hedge the exposure by selling the euros forward for British pounds at F3(€/£) = F3($/£) ÷ F3($/€) = 1.8990 ÷ 1.3154 = 1.4437. At this forward exchange rate, Shrewsbury can “lockin” 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 lockin 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 lockingin 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 threemonth 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 1.4437. Shrewsbury can now lockin a receipt of £320,000 if it simultaneously hedges its euro exposure by selling €461,984 at the forward rate of 1.4437. That is, £320,000 = €461,984/1.4437.
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