1、IM-0CHAPTER 6 INTERNATIONAL PARITY RELATIONSHIPSSUGGESTED ANSWERS AND SOLUTIONS TO END-OF-CHAPTERQUESTIONS AND PROBLEMSQUESTIONS1. Give a full definition of arbitrage.Answer: Arbitrage can be defined as the act of simultaneously buying and selling the same or equivalent assets or commodities for the
2、 purpose of making certain, guaranteed profits.2. Discuss the implications of the interest rate parity for the exchange rate determination.Answer: Assuming that the forward exchange rate is roughly an unbiased predictor of the future spot rate, IRP can be written as:S = (1 + I)/(1 + I$)ESt+1It. The
3、exchange rate is thus determined by the relative interest rates, and the expected future spot rate, conditional on all the available information, It, as of the present time. One thus can say that expectation is self-fulfilling. Since the information set will be continuously updated as news hit the m
4、arket, the exchange rate will exhibit a highly dynamic, random behavior.3. Explain the conditions under which the forward exchange rate will be an unbiased predictor of the future spot exchange rate.Answer: The forward exchange rate will be an unbiased predictor of the future spot rate if (I) the ri
5、sk premium is insignificant and (ii) foreign exchange markets are informationally efficient. 4. Explain the purchasing power parity, both the absolute and relative versions. What causes the deviations from the purchasing power parity?IM-1Answer: The absolute version of purchasing power parity (PPP):
6、S = P$/P.The relative version is:e = $ - .PPP can be violated if there are barriers to international trade or if people in different countries have different consumption taste. PPP is the law of one price applied to a standard consumption basket.IM-28. Explain the random walk model for exchange rate
7、 forecasting. Can it be consistent with the technical analysis?Answer: The random walk model predicts that the current exchange rate will be the best predictor of the future exchange rate. An implication of the model is that past history of the exchange rate is of no value in predicting future excha
8、nge rate. The model thus is inconsistent with the technical analysis which tries to utilize past history in predicting the future exchange rate.*9. Derive and explain the monetary approach to exchange rate determination.Answer: The monetary approach is associated with the Chicago School of Economics
9、. It is based on two tenets: purchasing power parity and the quantity theory of money. Combing these two theories allows for stating, say, the $/ spot exchange rate as:S($/) = (M$/M)(V$/V)(y/y$),where M denotes the money supply, V the velocity of money, and y the national aggregate output. The theor
10、y holds that what matters in exchange rate determination are:1. The relative money supply,2. The relative velocities of monies, and3. The relative national outputs.10. CFA question: 1997, Level 3.A. Explain the following three concepts of purchasing power parity (PPP):a. The law of one price. b. Abs
11、olute PPP.c. Relative PPP.B. Evaluate the usefulness of relative PPP in predicting movements in foreign exchange rates on:a. Short-term basis (for example, three months)b. Long-term basis (for example, six years)Answer:A. a. The law of one price (LOP) refers to the international arbitrage condition
12、for the standard consumption basket. LOP requires that the consumption basket should be selling for the same price in a given currency across countries. IM-3A. b. Absolute PPP holds that the price level in a country is equal to the price level in another country times the exchange rate between the t
13、wo countries. A. c. Relative PPP holds that the rate of exchange rate change between a pair of countries is about equal to the difference in inflation rates of the two countries. B. a. PPP is not useful for predicting exchange rates on the short-term basis mainly because international commodity arbi
14、trage is a time-consuming process.B. b. PPP is useful for predicting exchange rates on the long-term basis.IM-4PROBLEMS1. Suppose that the treasurer of IBM has an extra cash reserve of $100,000,000 to invest for six months. The six-month interest rate is 8 percent per annum in the United States and
15、6 percent per annum in Germany. Currently, the spot exchange rate is 1.01 per dollar and the six-month forward exchange rate is 0.99 per dollar. The treasurer of IBM does not wish to bear any exchange risk. Where should he/she invest to maximize the return?The market conditions are summarized as fol
16、lows:I$ = 4%; i = 3.5%; S = 1.01/$; F = 0.99/$.If $100,000,000 is invested in the U.S., the maturity value in six months will be$104,000,000 = $100,000,000 (1 + .04).Alternatively, $100,000,000 can be converted into euros and invested at the German interest rate, with the euro maturity value sold fo
17、rward. In this case the dollar maturity value will be$105,590,909 = ($100,000,000 x 1.01)(1 + .035)(1/0.99)Clearly, it is better to invest $100,000,000 in Germany with exchange risk hedging. 2. While you were visiting London, you purchased a Jaguar for 35,000, payable in three months. You have enoug
18、h cash at your bank in New York City, which pays 0.35% interest per month, compounding monthly, to pay for the car. Currently, the spot exchange rate is $1.45/ and the three-month forward exchange rate is $1.40/. In London, the money market interest rate is 2.0% for a three-month investment. There a
19、re two alternative ways of paying for your Jaguar.(a) Keep the funds at your bank in the U.S. and buy 35,000 forward.(b) Buy a certain pound amount spot today and invest the amount in the U.K. for three months so that the maturity value becomes equal to 35,000. Evaluate each payment method. Which me
20、thod would you prefer? Why? Solution: The problem situation is summarized as follows:A/P = 35,000 payable in three monthsiNY = 0.35%/month, compounding monthlyiLD = 2.0% for three monthsS = $1.45/; F = $1.40/.IM-5Option a:When you buy 35,000 forward, you will need $49,000 in three months to fulfill
21、the forward contract. The present value of $49,000 is computed as follows:$49,000/(1.0035)3 = $48,489.Thus, the cost of Jaguar as of today is $48,489.Option b:The present value of 35,000 is 34,314 = 35,000/(1.02). To buy 34,314 today, it will cost $49,755 = 34,314x1.45. Thus the cost of Jaguar as of
22、 today is $49,755.You should definitely choose to use “option a”, and save $1,266, which is the difference between $49,755 and $48489. 3. Currently, the spot exchange rate is $1.50/ and the three-month forward exchange rate is $1.52/. The three-month interest rate is 8.0% per annum in the U.S. and 5
23、.8% per annum in the U.K. Assume that you can borrow as much as $1,500,000 or 1,000,000. a. Determine whether the interest rate parity is currently holding.b. If the IRP is not holding, how would you carry out covered interest arbitrage? Show all the steps and determine the arbitrage profit.c. Expla
24、in how the IRP will be restored as a result of covered arbitrage activities.Solution: Lets summarize the given data first:S = $1.5/; F = $1.52/; I$ = 2.0%; I = 1.45%Credit = $1,500,000 or 1,000,000.a. (1+I$) = 1.02(1+I)(F/S) = (1.0145)(1.52/1.50) = 1.0280Thus, IRP is not holding exactly.b. (1) Borro
25、w $1,500,000; repayment will be $1,530,000. (2) Buy 1,000,000 spot using $1,500,000.(3) Invest 1,000,000 at the pound interest rate of 1.45%;maturity value will be 1,014,500. (4) Sell 1,014,500 forward for $1,542,040Arbitrage profit will be $12,040 IM-6c. Following the arbitrage transactions describ
26、ed above,The dollar interest rate will rise;The pound interest rate will fall;The spot exchange rate will rise;The forward exchange rate will fall.These adjustments will continue until IRP holds.4. Suppose that the current spot exchange rate is 0.80/$ and the three-month forward exchange rate is 0.7
27、813/$. The three-month interest rate is 5.6 percent per annum in the United States and 5.40 percent per annum in France. Assume that you can borrow up to $1,000,000 or 800,000. a. Show how to realize a certain profit via covered interest arbitrage, assuming that you want to realize profit in terms o
28、f U.S. dollars. Also determine the size of your arbitrage profit.b. Assume that you want to realize profit in terms of euros. Show the covered arbitrage process and determine the arbitrage profit in euros.Solution: a. (1+ i $) = 1.014 (F/S) (1+ i ) = 1.053. Thus, one has to borrow dollars and invest
29、 in euros to make arbitrage profit.1. Borrow $1,000,000 and repay $1,014,000 in three months.2. Sell $1,000,000 spot for 1,060,000.3. Invest 1,060,000 at the euro interest rate of 1.35 % for three months and receive 1,074,310 at maturity.4. Sell 1,074,310 forward for $1,053,245.Arbitrage profit = $1
30、,053,245 - $1,014,000 = $39,245.b. Follow the first three steps above. But the last step, involving exchange risk hedging, will be different. 5. Buy $1,014,000 forward for 1,034,280.Arbitrage profit = 1,074,310 - 1,034,280 = 40,030IM-75. In the issue of October 23, 1999, the Economist reports that t
31、he interest rate per annum is 5.93% in the United States and 70.0% in Turkey. Why do you think the interest rate is so high in Turkey? Based on the reported interest rates, how would you predict the change of the exchange rate between the U.S. dollar and the Turkish lira?Solution: A high Turkish int
32、erest rate must reflect a high expected inflation in Turkey. According to international Fisher effect (IFE), we haveE(e) = i$ - iLira= 5.93% - 70.0% = -64.07%The Turkish lira thus is expected to depreciate against the U.S. dollar by about 64%.6. As of November 1, 1999, the exchange rate between the
33、Brazilian real and U.S. dollar is R$1.95/$. The consensus forecast for the U.S. and Brazil inflation rates for the next 1-year period is 2.6% and 20.0%, respectively. How would you forecast the exchange rate to be at around November 1, 2000?Solution: Since the inflation rate is quite high in Brazil,
34、 we may use the purchasing power parity to forecast the exchange rate.E(e) = E($) - E(R$)= 2.6% - 20.0%= -17.4%E(ST) = So(1 + E(e)= (R$1.95/$) (1 + 0.174)= R$2.29/$IM-87. (CFA question) Omni Advisors, an international pension fund manager, uses the concepts of purchasing power parity (PPP) and the I
35、nternational Fisher Effect (IFE) to forecast spot exchange rates. Omni gathers the financial information as follows:Base price level 100Current U.S. price level 105Current South African price level 111Base rand spot exchange rate $0.175Current rand spot exchange rate $0.158 Expected annual U.S. infl
36、ation 7%Expected annual South African inflation 5%Expected U.S. one-year interest rate 10%Expected South African one-year interest rate 8% Calculate the following exchange rates (ZAR and USD refer to the South African and U.S. dollar, respectively).a. The current ZAR spot rate in USD that would have
37、 been forecast by PPP.b. Using the IFE, the expected ZAR spot rate in USD one year from now.c. Using PPP, the expected ZAR spot rate in USD four years from now.Solution:a. ZAR spot rate under PPP = 1.05/1.11(0.175) = $0.1655/rand.b. Expected ZAR spot rate = 1.10/1.08 (0.158) = $0.1609/rand.c. Expect
38、ed ZAR under PPP = (1.07)4/(1.05)4 (0.158) = $0.1704/rand. 8. Suppose that the current spot exchange rate is 1.50/ and the one-year forward exchange rate is 1.60/. The one-year interest rate is 5.4% in euros and 5.2% in pounds. You can borrow at most 1,000,000 or the equivalent pound amount, i.e., 6
39、66,667, at the current spot exchange rate. a. Show how you can realize a guaranteed profit from covered interest arbitrage. Assume that you are a euro-based investor. Also determine the size of the arbitrage profit.b. Discuss how the interest rate parity may be restored as a result of the above tran
40、sactions. c. Suppose you are a pound-based investor. Show the covered arbitrage process and determine the pound profit amount. IM-9Solution:a. First, note that (1+i ) = 1.054 is less than (F/S)(1+i ) = (1.60/1.50)(1.052) = 1.1221. You should thus borrow in euros and lend in pounds. 1) Borrow 1,000,0
41、00 and promise to repay 1,054,000 in one year.2) Buy 666,667 spot for 1,000,000.3) Invest 666,667 at the pound interest rate of 5.2%; the maturity value will be 701,334.4) To hedge exchange risk, sell the maturity value 701,334 forward in exchange for 1,122,134. The arbitrage profit will be the diff
42、erence between 1,122,134 and 1,054,000, i.e., 68,134.b. As a result of the above arbitrage transactions, the euro interest rate will rise, the pound interest rate will fall. In addition, the spot exchange rate (euros per pound) will rise and the forward rate will fall. These adjustments will continu
43、e until the interest rate parity is restored.c. The pound-based investor will carry out the same transactions 1), 2), and 3) in a. But to hedge, he/she will buy 1,054,000 forward in exchange for 658,750. The arbitrage profit will then be 42,584 = 701,334 - 658,750. 9. Due to the integrated nature of
44、 their capital markets, investors in both the U.S. and U.K. require the same real interest rate, 2.5%, on their lending. There is a consensus in capital markets that the annual inflation rate is likely to be 3.5% in the U.S. and 1.5% in the U.K. for the next three years. The spot exchange rate is cu
45、rrently $1.50/. a. Compute the nominal interest rate per annum in both the U.S. and U.K., assuming that the Fisher effect holds. b. What is your expected future spot dollar-pound exchange rate in three years from now?c. Can you infer the forward dollar-pound exchange rate for one-year maturity?Solution.a. Nominal rate in US = (1+) (1+E($) 1 = (1.025)(1.035) 1 = 0.0609 or 6.09%.Nominal rate in UK= (1+) (1+E() 1 = (1.025)(1.015) 1 = 0.0404 or 4.04%.b. E(ST) = (1.0609)3/(1.0404)3 (1.50) = $1.5904/. c. F = 1.0609/1.0404(1.50) = $1.5296/.
