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Unformatted text preview: PROBLEMS 8. Assume you are a trader with Deutsche Bank. From the quote screen on your computer terminal, you notice that Dresdner Bank is quoting 0.7627/$1.00 and Credit Suisse is offering SF1.1806/$1.00. You learn that UBS is making a direct market between the Swiss franc and the euro, with a current /SF quote of .6395. Show how you can make a triangular arbitrage profit by trading at these prices. (Ignore bidask spreads for this problem.) Assume you have $5,000,000 with which to conduct the arbitrage. What happens if you initially sell dollars for Swiss francs? What /SF price will eliminate triangular arbitrage? 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. 9. The current spot exchange rate is $1.95/ and the threemonth 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?...
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 Spring '08
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