Exercise 05-solution

Exercise Five -Solution1. Suppose you saw that the following exchange rates quoted in the foreign exchange market:1 US$1 US$ 1 US$ 1 US$1 € 1 £1 £= = = = = = = 7.7465 Chinese Renminbi0.5143 UK Pound Sterling ( £ )0.7599 Euros (€)11.1697 Mexican Pesos 14.7121 Mexican Pesos22.7166 Mexican pesos 15.0612 Chinese Renminbi a) The hypothetical exchange rates above contain an arbitrage opportunity. Explain how to exploit it, using nomore than three of the currencies listed above.Answer: Assume that you have 1 US$ to begin with. Pick currency pairs and try to exchange one currency foranother. If you end up with more than one then that is your arbitrage profits. Otherwise you could workbackwards.Let’s start with 1 US$, sell it for Chinese Renminbi, then sell Chinese Renminbi for UK Pounds and then sell itfor US dollar again. USD GBP USD CNY GBP USD CNY USDUSD == 00007.15143.010612.1517465.71=××× The difference between 1.00007 and 1 is so small that triangular arbitrage hardly exists here.Now try a different three currencies – US$, Peso, Pound. Sell 1 US$ for Peso, sell Peso for Pound and finallysell Pound for USD. USD GBP USD MXN GBP USD MXN USDUSD == 956052.05143.017166.2211697.111=××× The final amount you get is smaller than original one. So you must reverse your trading sequence for aprofitable arbitrage opportunity: Buy Pound with the USD, buy Pesos with the Pound and then buy USD with Pesos. USD MXNUSD GBP MXN USD GBP USD USD == 046.11697.1117166.225143.01=××× So 4.6% will be your arbitrage profit on each dollar. b) You can remove the arbitrage opportunity by changing just one of the exchange rates given. (“The market”should itself accomplish this, via arbitrage.) Which exchange rate is it, and what would the new correct value be?Answer: If you check other currency pairs in triangular arbitrage trading, you will see that it is the Peso/￡ rate that is out of line, rather than one of the dollar exchange rates. For example, verify the followingarbitrage trading order:9992.0==EURUSD MXN EUR USD MXN GBP USD CNY GBP USD CNY USD USD Apart from the rounding error, all currencies along this order are priced correctly, which leaves only the the Peso/￡ rate to be incorrect. The Pound is overvalued relative to the Peso. This is why buying Peso for Pound earned a profit.The correct Peso/￡ rate is : 7183.225143.011697.11=×==GBP USD USD MXN GBP MXN [notes: If one wants to be precise to 4 decimal points, then 0.7599 should have been 0.7592. But these Calculations are not intended to apply to the fourth decimal point, which is the size of transaction costs And therefore not exploitable by arbitrage.]2. Suppose you are a manager of a book store. You can sell copies of World Trade and Payments by Caves, Frankel & Jones, at $135 per copy. The book’s U.S. publisher will sell it to you for $110 a copy. At the same time the book World Trade and Payments is also wholesaled by two foreign firms: A Chinese firm sells it for CNY 700, and a British firm for £ 50 (exchange rates are given above in Problem 1).a)Explain very briefly how you would maximize your profits from textbook purchases and sales.Answer: Given the following exchange rates,1 US$ = 7.7465 Chinese Renminbi1 US$=0.5143 UK Pound Sterling ( £ )The US$ price of buying from China would be $90.36, and the US$ price from the British firm is$97.22. Here is an apparent opportunity for arbitrage of goods – a mismatch of prices at the differentgeographical locations. The strategy “Buy low, sell high” again governs: buying books from theChinese Firm and selling them in the US will maximize profits. As long as the original price plustransportation is less than 110$, you do better buying from China.b)Your skeptical work-study assistant makes some international phone calls, and learns that the copies from the British publisher are of the previous edition, and the copies from the Chinese publisher are actually Xeroxes (影印版, it is illegal to sell it in USA). Now what will you do?Answer: You cannot sell Xerox copies in the US without proper publisher permission. Even if the store were willing to take chances by violating copyright laws, students will certainly not pay the same $135 for a Xerox one; thus, the Chinese alternative no longer offers a pure arbitrage opportunity. Similarly, the previous edition offered by the British firm is not a perfect substitute for the current edition. Consequently, there is no real arbitrage situation anymore, even if the difference in price exceeds transportation costs.c) Give the main reason(s) why it is harder to take advantage of an apparent arbitrage opportunity in a goods market than in a financial market.Answer: The immediate reason is the transportation cost. Arbitrage will start to operate only if the price in one country exceeds the price in the other by more than the shipping costs. Otherwise it is not worthboth to bear the shipment cost and wait for days or weeks to get the product. In this respect, geographicdistance and border effects play important roles. Tariffs and other trade barriers are the second reasonwhy it is harder to take advantage of an apparent arbitrage opportunity in a goods market. Thirdly, as aresult of imperfect information, consumers/retailers may not aware of the price difference in differentlocations, or of the quality of the product that they are importing. Currencies or securities traded infinancial markets, by contrast, have lower transactions costs than goods, and are often standardized.。