Business Assignment 2 Suggested Answers. 1. Describe how the following transactions are recorded in the balance of payments.

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1 Business 079 Assignment 2 Suggested Answers. Describe how the following transactions are recorded in the balance of payments. (a) A Hong Kong resident, who owns a house valued at C$500,000, migrates to Canada. Answer: Credit Debit Unilateral Transfers In (UT i ) $500,000 Investment in foreign real estate (CA o ) $500,000 (b) The Canadian government donates $ million in cash to Somalia. Answer: Credit Debit Unilateral Transfers Out (UT o ) $,000,000 Capital Account In (CA i ) $,000,000 (c) A Canadian corporation pays $ million in dividends to foreign residents, who choose to hold the dividends in the form of bank deposits in Toronto. Answer: Credit Debit Income Out (D o ) $,000,000 Foreign Liabilities In (OI i ) $,000,000

2 (d) A Mexican company sells $2 million worth of cement to a Canadian company and deposits the check in a bank in Toronto. Answer: Credit Debit Imports of Goods (M g ) $2,000,000 Foreign Liabilities In (OI i ) $2,000, Two countries, the United States and England, produce only one good, wheat. Suppose the price of a bushel of wheat is $3.25 in the United States and.35 in England. (a) According to the law of one price, what should the $/ spot exchange rate be? Answer: Let S denote the $/ spot exchange rate. Then S = $ = $2.07/. (b) Suppose the price of wheat over the next year is expected to rise to $3.50 in the United States and to.60 in England. What should the one-year $/ forward rate be? Answer: Let F denote the forward rate in $/. Then F = $ = $2.875/ Note that the dollar is expected to appreciate against the pound due to a higher expected inflation rate in England than in the U.S.. That is, π e US = = 7.69% π e UK = = 8.52%, where π e US and π e UK denote expected inflation in the U.S. and the U.K., respectively. (c) If the U.S. government imposes a tariff of $0.50 per bushel on wheat imported from England, what is the maximum possible change in the spot exchange rate 2

3 that could occur? Answer: Suppose that the price of wheat remains constant in both countries, due to the nature of the wheat market. That is, suppose $3.25 a bushel is the lowest price a wheat producer can offer and suppose there is free entry of wheat producers in the market. A producer charging more than $3.25 a bushel would have no customer and thus every producer is forced to sell at the same price, i.e. $3.25. Suppose the same reasoning applies to the U.K.. In this case, wheat will be exported from the U.K. to the U.S. only if the exchange rate S is such that 3.25 =.35S S = $2.0370/. Suppose, on the other hand, that the price of wheat increases in the U.S.. Its maximum increase being $0.50, the maximum exchange rate is then =.35S S = $2.7778/. Either way, the maximum exchange rate change is the same, i.e = $0.370/ or = 5.38%. 3. In early 996, the short-term interest rate in France was 3.7%, and forecast French inflation was.8%. At the same time, the short-term German interest rate was 2.6% and forecast German inflation was.6% (a) Based on these figures, what were the real interest rates in France and Germany? Answer: The real interest rate in France was =.9% and the real interest rate in Germany was =.0%. 3

4 (b) To what would you attribute any discrepancy in real rates between France and Germany? Answer: There seems to be an arbitrage opportunity here since short-term loans earn more in real terms in France than in Germany. However, these are expected inflation rates, they won t realize with certainty. If France s inflation rate is more volatile than Germany s, the profit from this arbitrage opportunity may not be enough to compensate for its risk, thus precluding arbitrageurs intervention.. During 995, the Mexican peso exchange rate rose from 5.33peso/$ to 7.6peso/$. At the same time, U.S. inflation was approximately 3% in contrast to Mexican inflation of about 8.7%. (a) By how much did the nominal value of the peso change during 995? Answer: The value of the peso, in dollars, decreased from /5.33 = $0.876 to /7.6 = $0.309, a change of = $0.0567/peso or = 30.22%. (b) By how much did the real value of the peso change during 995? Answer: Let $0.876/peso be the real exchange rate at the beginning of 995. At the end of 995, the real exchange was = $0.890/peso, an increase of = 0.75%. 5. Suppose that three-month interest rates (annualized) in Japan and the United States are 7% and 9%, respectively. If the spot rate is 2/$ and the 90-day forward rate is 39/$, (a) where would you invest? Answer: This will answer the whole problem. Each $ invested (resp. borrowed)

5 in Japan for 90 days returns (resp. costs) ( ) 39/$ = $ with certainty. On the other hand, investing (resp. borrowing) $ in the U.S. for 90 days returns (resp. costs).09 = $ with certainty. It is therefore possible to make a riskless profit of = $0.070 per dollar by borrowing in the U.S. and investing the proceeds in Japan. (b) where would you borrow? (c) What arbitrage opportunity do these figures present? 6. Here are some prices in the international money market: Spot rate = $0.75/DM; forward rate (one year) = $0.77/DM; interest rate in DM is 7% per year; interest rate in $ is 9% per year. (a) Assuming no transaction costs or taxes exist, do covered arbitrage profits exist in the above situation? Describe the flows. Answer: Investing (resp. borrowing) $ in Germany returns (resp. costs) = $ with certainty after one year. On the other hand, investing (resp. borrowing) $ in the U.S. returns (resp. costs) $0.09 per year. It is therefore possible to make a riskless profit of = $ per dollar by borrowing in the U.S. and investing the proceeds in Germany. 5

6 This arbitrage opportunity exists because the percent increase in the value of the DM, is greater than the interest rate differential of = 2.67%, =.87% between Germany and the U.S.. That is, investing in Germany returns more than the cost of borrowing in the U.S. because the deutschmark appreciation outweighs the interest rate differential. (b) Suppose now that transaction costs in the foreign exchange market equal 0.25% per transaction. Do unexploited covered arbitrage profit opportunities still exist? Answer: This cost could arise from bid-ask spreads, for example, on both the spot rate and the forward rate. In this case, investing $ in Germany returns ( ) ( ) = $0.0930, which is still greater than what needs to be repaid if the dollar is borrowed in the U.S.. Thus the arbitrage opportunity remains. (c) Suppose no transaction costs exist. Let the capital gains tax on currency profits equal 25% and the ordinary income tax on interest income equal 30%. In this situation, do covered arbitrage profits exist? How large are they? Describe the transactions required to exploit these profits. Answer: In this case, the after-tax gain from currency appreciation is ( ) 0.77 ( 0.25) 0.75 = 2%, whereas the after-tax interest rate differential is ( ) ( ) = = 0.97%. If interest is tax-exempt, then a riskless profit can still be made by borrowing in the U.S. and investing the proceeds in Germany. 6

7 If the cost of borrowing in the U.S. remains 9%, then the differential between the borrowing rate in the U.S. and the lending rate in Germany is = 5.3%, thus precluding risk-free arbitrage opportunities. The return from investing in Germany is nevertheless greater than the return from investing in the U.S. and thus money will keep flowing to Germany. 7. On checking the Telerate screen, you see the following exchange rate and interest rate quotes: 90-day Interest Rates Currency (annualized) Spot Rates 90-day Forward Rates Dollar.99%- 5.03% Swiss Franc 3.%-3.9% $ $ (a) Can you find an arbitrage opportunity? Answer: The cost of borrowing in the U.S. for 90 days is 5.03 =.2575% and the dollar return from investing in Switzerland for 90 days is ( ) =.33%. Hence borrowing in the U.S. and investing the proceeds in Switzerland yields a riskless profit. On the other hand, the dollar cost of borrowing in Switzerland is ( ) = 3.776% and the return from investing in the U.S. for 90 days is =.275%. 7

8 Clearly, borrowing in Switzerland to invest the proceeds in the U.S. is not a good move. (b) What steps must you take to capitalize on it? Answer: Borrow in the U.S. and invest the proceeds in Switzerland. (c) What is the profit per $,000,000 arbitraged? Answer: With $,000,000, an arbitrageur makes, 000, 000 ( ) = $859. 8

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