problem set 1_ans - ECO 365 Fall 2013 University of Toronto...

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ECO 365 Fall 2013 University of Toronto Problem Set 1 Due: Oct. 11 1) One British pound is worth $1.05 and one yen is worth $0.01. If there are no arbitrage opportunities, how many yen are needed to purchase one pound? [5 marks] Solution: If E U / $ = 0 . 01 then $1 is worth U 100. E U / £ = 100 U $1 × $1 . 05 £ 1 = 100 × 1 . 05 = 105 . 2) The exchange rate between the Canadian dollar and the US dollar offered in Toronto is 1 CAD for 0.97 USD. The exchange rate offered in London is 1 pound for 1.12 USD. The exchange rate offered in New York is such that 1 CAD is worth 0.87 pounds. If you have 250,000 CAD, is it possible to make triangular arbitrage profit? If so, then show how and the profit that you make. If not, explain why not. [10 marks] Solution: Consider the 2 possible transactions that can be made: 1. Convert CAD to USD in TO, then convert the USD to pounds in London, and finally convert the pounds back to CAD in New York. If you do so, then the 250,000 CAD are converted to 250,000 × 0.97 = 242,500 USD. These USD are then converted to 242,500/1.12 = £ 216,517.857. Lastly, convert the £ back to CAD in NY, which yields 248,871.10 CAD. Going this route yields a loss. 2. Alternative is to convert the CAD to £ in NY, convert the £ to USD in London, and then convert the USD back to CAD in Toronto. The first transaction yields 250,000 × 0.87 = £ 217,500. The second transactions yields 217,500 × 1.12 = 243,600 USD. The 3rd 1
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transaction yields 243,600/0.97 = 251,134 CAD. The profit earned is 251,134 - 250,000 = 1,134 CAD. 3) The interest rate on a U deposit is 0 and the interest rate on an Australian dollar (AUD) deposit is 4.75%. One AUD is worth U 92.81 at the current spot rate. The exchange rate a year from now is uncertain. With 95% probability, one AUD will be worth U 94.50 a year from now. With a 5% probability one AUD will be worth U 80.53 a year from now. a) Calculate the expected rate of depreciation of the U against the AUD. [Hint: see pp. 344-346 in the textbook]. [4 marks] Solution: 0 . 95 94 . 50 - 92 . 81 92 . 81 + 0 . 05 80 . 53 - 92 . 81 92 . 81 = 0 . 017 - 0 . 007 = 0 . 010 = 1% . The U is expected to depreciate against the AUD by 1%. b) If you could borrow U to engage in carry trade, would you? Show all calculations. [3 marks] Solution: The return on a U deposit is 0. The expected return from borrowing U converting 2
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to AUD and investing in AUD, and then converting the proceeds back to U is R $ + 0 . 01 = 0 . 0475 + 0 . 01 = 0 . 0575 = 5 . 75% > R U = 0 . Therefore, you would engage in carry trade. c) Would your answer change if the expected exchange rate a year from now was 94.50 U per AUD with 90% probability and 65.00 U per AUD with 10% probability? Show all calculations. [3 marks] Solution: Expected depreciation of the U against the AUD is 0 . 90 94 . 5 - 92 . 81 92 . 81 + 0 . 10 65 - 92 . 81 92 . 81 = 0 . 016 - 0 . 030 = - 0 . 014 = - 1 . 4% . The expected depreciation is negative which means that the U is expected to appreciate against the AUD. The expected return in U from investing in an AUD deposit is R $ - 0 . 014 = 0 . 0475 - 0 . 014 = 0 . 0335 = 3 . 35% > 0 . Therefore, you would still engage in the carry trade. 4) Let S p denote private savings, FA denote the financial account, KA the capital account, and SD the statistical discrepancy. Fill in the missing values. [6 marks] 3
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S p I G T CA FA KA SD 20 89 100 -150 -11 44 48 4 170 153 -306 23 18 280 210 210 -13 -27 Solution We use 2 formulas: (i) CA = S p + I - ( G - T ) , and (ii) CA + FA + KA + SD = 0 .
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  • Spring '08
  • JORDIMONDRIA
  • Economics, Foreign exchange market, United States dollar, intertemporal budget constraint

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