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last update: December 2008



Between 1988 and 1991, the price of a room at the Milan Hilton rose from Lit 346,400 to Lit 475,000. At the same time, the exchange rate went from Lit 1,302 = Sl in 1988 to Lit 1,075 = $1 in 1991.

a. By how much has the dollar cost of a room at the Milan Hilton changed over this three-year period?

ANSWER. The dollar price of a room at the Milan Hilton in 1988 was 346,400/1,302 = $266. By 1991, that same room cost 475,000/1,075 = $442. Thus, the dollar price of a room rose durina this three-year period by

(442 - 266) = 66.2%

This involved a combination of a 21.2% appreciation in the dollar value of the lira and a 37.1% increase in the lira price of a hotel room (1.211 x 1.371 = 1.66 1).

b.What has happened to the lira's dollar value during this period?

ANSWER. According to Equation 2. 1, the lira's dollar value has appreciated by

(1/1075) - (1/1302) * 1302 - 1075 = 21.1%
      (1/1302)           1075


During the currency crisis of September 1992, the Bank of England borrowed DM 33 billion from the Bundesbank when a pound was worth DM 2.78 or $1.912. It sold these DM in the foreign exchange market for pounds in a futile attempt to prevent a devaluation of the pound. It repaid these DM at the post-crisis rate of DM 2.50/£1. By then, the dollar/pound exchange rate was $1.782/fl.

a. How much had the pound sterling devalued in the interim against the Deutsche mark? Against the dollar?

ANSWER. During this period, the pound depreciated by 10.1% against the DM

2.50 - 2.78 = 10.1%

and by 6.8% against the dollar

1.792 - 1.912 = 6.8%

b.What was the cost of intervention to the Bank of England in pounds? In dollars?

ANSWER. The Bank of England borrowed DM 33 billion and must repay DM 33 billion. When it borrowed these DM, the DM was worth EO.3597, valuing the loan at 111.87 billion (DM 33 billion x 0.3597). After devaluation, the DM was worth £ O.4000. Hence, the Bank of England's cost of repaying the DM loan was £ 13.20 billion (DM 33 billion x 0.4), a rise of £ 1.33 billion. Thus, the cost to the Bank of England of this DM borrowing and intervention was £ 1.33 billion.

In dollar terms, intervention cost the Bank of England $ 825 million. This estimate is based on the difference of $ 0.025 between the DM's initial value of $0.6878 (1.912/2.78) and its ending value of $0.7128 (1/2.50) times the DM 33 billion borrowed and spent defending the pound. Specifically, the cost calculation is $ 0.025 x 33,000,000,000 = $ 825 million.


On Friday, September 13, 1992, the lira was worth DM 0.0013065. Over the weekend, the lira devalued against the DM to DM 0.0012613.

a. By how much has the lira devalued against the DM?

ANSWER. Using Equation 2.1, the lira devalued by

(0.0012613 - 0.0013065) = -3.46%.

b. By how much has the DM appreciated against the lira?

ANSWER. Using Equation 2.2, the DM appreciated against the lira by

(1/0.0012613) - (1/0.0013065) = 3.8%

c. Suppose Italy borrowed DM 4 billion, which it sold to prop up the lira. Vvlat were the Bank of Italy's lira losses on this currency intervention?

ANSWER. Prior to devaluation, DM billion was worth Lit (4 billion/O.0013065). Following devaluation, the DM 4 billion borrowing would cost Lit (4 billion/0.0012613) to repay. Hence, the Italian government would lose Lit 4 billion x [(1/0.0012613) - (1/0.0013065)] = Lit 109,716,164344, or DM 138,384,998 at the new exchange rate.

d. Suppose Germany spent DM 24 billion in an attempt to defend the lira. What were the Bundesbank's DM losses on this currency intervention?

ANSWER. The Bundesbank would have bought Lit 24 billion/0.0013065. Following lira devaluation, these lira would
be worth DM (24 biflion/0.0013065) x 0.0012613, or DM 23,169,690,012. The result is a foreign exchange loss for the Bundesbank of DM 830,309,988 on this currency intervention.


Panama adopted the U.S. dollar as its official paper money in 1904. There is currently about $400 million to $500 million in U.S. dollars circulating in Panama. If interest rates on U.S. Treasury securities are 7%, what is the value of the seigniorage that Panama is forgoing by using the U.S. dollar instead of its ovm-issue money?

ANSWER. Instead of using U.S. dollars as its currency in circulation, the Panamanian government could substitute its own currency and invest the $400 million to $500 million in U.S. Treasury securities. This policy would earn the Panamanian government $28 million to $35 million annually at the current 7% interest rate. Thus, the Panamanian government is foregoing seignorage worth $28 million to $35 million annually. The present value of this seignorage equals the amount of U.S. dollars in circulation, or $400 million ($28 million/.07) to $500 million ($35 million/.07).


Assuming no transaction costs, suppose f I= $2.4110 in New York, $1 = FF 3.997 in Paris, and FF 1 = £ O.1088
in London. How could you take profitable advantage of these rates?

ANSWER. Sell pounds in New York for $2.4110 apiece. Sell the dollars in Paris for FF 3.997, and sell the francs in London for £ 0.1088. This sequence of actions yields 2.4110 x 3.997 x .1088 pounds or £ 1.0485 per pound initially traded.


As a foreign exchange trader at Sumitomo Bank, one of your customers would like a yen quote on Australian dollars. Current market rates are:

Y 101.37-85 / U.S.$ l

A $1.2924-44 / U.S.$ l

What bid and ask rates would you quote?

ANWSER. By means of triangular arbitrage, we can calculate the market quotes for the Australian dollar in terms of yen as

Y 78.31 ­ 81 / A $ l

These prices can be found as follows. For the yen bid price for the Australian dollar, we need to first sell Australian dollars for U.S. dollars and then sell the U.S. douars for yen. It costs A $1.2944 to buy U.S.$ 1. With U.S. $ l we can buy Y 1O1.37. Hence, A $ 1.2944 = Y 101.37, or A $ l = Y 78.81. This is the yen bid price for the Australian dollar.

The yen ask price for the Australian dollar can be found by first selling yen for U.S. dollars and then using the U.S. dollars to buy Australian dollars. Given the quotes above, it costs Y 1O1.85 to buy U.S. $ I, which can be sold for A $ 1.2924. Hence, A $ 1.2924 = Y 1O1.85, or A $ 1 = Y 78.81. This is the yen ask price for the Australian dollar.

As a foreign exchange trader, you would try to buy Australian dollars at slightly less than Y 78.31 and sell them at slightly more than Y 78.81. Buying and selling Australian dollars at the market price will leave you with no profit. How much better than the market prices you can do depends on the degree of competition you face from other traders and the extent to which your customers are willing to shop around to get better quotes.


On Monday morning, an investor takes a short position in a DM futures contract that matures on Wednesday afternoon. The agreed-upon price is $0.6370 for DM 125,000. At the close of trading on Monday, the futures price has fallen to $ 0.6315. At Tuesday close, the price falls ftirther to $0.6291. At Wednesday close, the price rises to $ 0.6420, and the contract matures. The investor delivers the Deutsche marks at the prevailing price of $0.6420. Detail the daily settlement process. What will be the investor's profit (loss)?

Monday morning
Investor sells DM futures contract that matures in two days. Price is $ 0.6370

Monday close
Futures price falls to $ 0.6315.
Contract is marked to market
Investor receives
125,000*(0.6370-0.6315) = $ 687.50

Tuesday close
Futures price falls to $0.6291. Contract is marked to market
Investor receives 125,000 x (.6315 -.6291) = $300

Wednesday close
Wednesday Futures price rises to $0.6420.
Contract is marked to market
Investor takes delivery of DM 125,000
Investor receives 125,000*-(0.6420-0.6291) = $ 1,612,50
Investor pays 125,000*0,6420 = $ 80,250

Net loss is $1,612.50 - $987.50 = $625.


Suppose that the forward ask price for March 20 on DM is $0.7127 at the same time that the price of IMM mark futures for delivery on March 20 is $0.7145. How could an arbitageur profit from this situation? What will be the arbitrageur's profit per futures contract (size is DM 125,000)?

ANSWER. Since the futures price exceeds the forward rate, the arbitrageur should sell futures contracts at $0.7145 and buy DM forward in the same amount at $0.7127. The arbitrageur will earn 125,000 (.7145 - .7127) = $225 per DM futures contract arbitraged.



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