1. 1 Chapter 2 – Problem 1 1.On August 8, 2000, Zimbabwe changed the value of the Zim dollar from Z$38/UD$ to Z$50/USD. a.What was the original U.S. dollar value of the Zim dollar? What is the new U.S. dollar value of the Zim dollar? Prior to devaluation was $0.0263 (1/38). Subsequent to devaluation, the Zim dollar was worth $0.02 (1/50).

2. 2 Chapter 2 – Problem 1 b.By what percent has the Zim dollar devalued (revalued) relative to the U.S. dollar? The U.S. dollar value of the Zim dollar has changed by: (0.02 - 0.0263)/0.0263 = -24%. Thus, the Zim dollar has devalued by 24% against the U.S. dollar.

3. 3 Chapter 2 – Problem 5 5.At the time Argentina launched its new exchange rate scheme, the euro was trading at $0.85. Exporters and importers would be able to convert between dollars and pesos at an exchange rate that was an average of the dollar and the euro exchange rates, that is, P1 = $0.50 + €0.50. a.How many pesos would an exporter receive for one dollar under the new system? P1 = $0.50 + €0.50 = $0.50 + $0.85/2 = $0.925. The peso value of a dollar is thus 1/0.925, or $1 = P1.081. This exchange rate is equivalent to dollar appreciation of 8.1% against the peso.

4. 4 Chapter 2 – Problem 5 b.How many dollars would an importer receive for one peso under the new system? As shown in the answer to Part a, P1 = $0.925. This exchange rate is equivalent to peso devaluation against the dollar of 7.5%.

5. 5 Chapter 3 – Problem 1 1.As mentioned in the chapter, during the currency crisis of September 1992, the Bank of England borrowed DM 33 billion from the Bundesbank when a pound was worth DM 2.78 or $1.912. It sold these DM in the foreign exchange market for pounds in a futile attempt to prevent a devaluation of the pound. It repaid these DM at the post-crisis rate of DM 2.50/£1. By then, the dollar/pound exchange rate was $1.782/£1. a.How much had the pound sterling devalued in the interim against the Deutsche mark? Against the dollar? During this period, the pound depreciated by 10.1% against the mark and by 6.8% against the dollar

6. 6 Chapter 3 – Problem 1 b.What was the cost of intervention to the Bank of England in pounds? In dollars? The Bank of England borrowed DM 33 billion and must repay DM 33 billion. When it borrowed these DM, the DM was worth £0.3597, valuing the loan at £11.87 billion (DM 33 billion x 0.3597). After devaluation, the DM was worth £0.4000. The Bank of England's cost of repaying the DM loan was £13.20 billion (DM 33 billion x 0.4). Thus, the cost of intervention was £1.33 billion. In dollar terms, intervention cost $825 million. DM's initial value of $0.6878 (1.912/2.78) - ending value of $0.7128 (1/2.50) = $0.025 $0.025 x 33,000,000,000 = $825 million.

7. 7 Chapter 4 – Problem 4 4.In early 1996, the short-term interest rate in France was 3.7%, and forecast French inflation was 1.8%. At the same time, the short-term German interest rate was 2.6% and forecast German inflation was 1.6%. a.Based on these figures, what were the real interest rates in France and Germany? The French real interest rate was: 1.037/1.018 - 1 = 1.87%. The corresponding real rate in Germany was 1.026/1.016 - 1 = 0.98%.

8. 8 Chapter 4 – Problem 4 b.To what would you attribute any discrepancy in real rates between France and Germany? Inclusion of a higher inflation risk component in the French real interest rate than in the German real rate. Other possibilities are the perceived effects of currency risk or transactions costs that could offset this arbitrage opportunity.

9. 9 Chapter 4 – Problem 5 5.In July, the one ‑ year interest rate is 12% on British pounds and 9% on U.S. dollars. a.If the current exchange rate is $1.63/£1, what is the expected future exchange rate in one year? According to the international Fisher effect, the spot exchange rate expected in one year equals 1.63 x 1.09/1.12 = $1.5863.

10. 10 Chapter 4 – Problem 5 b.Suppose a change in expectations regarding future U.S. inflation causes the expected future spot rate to decline to $1.52/£1. What should happen to the U.S. interest rate? Assuming that the British interest rate stayed at 12% (because there has been no change in expectations of British inflation), then according to the IFE, 1.52/1.63 = (1+r)/1.12 or r = 4.44%.

11. 11 Chapter 4 – Problem 13 13.Suppose that three-month interest rates (annualized) in Japan and the United States are 7% and 9%, respectively. If the spot rate is ¥142/$1 and the 90-day forward rate is ¥139/$1: a.Where would you invest? Dollar return from an investment in Japan: convert dollars to yen at the spot rate, invest the yen at 1.75% (7% x 3/12), and then sell the proceeds forward for dollars. This yields a dollar return: 142 x 1.0175/139 = 1.0395 or 3.95%. It exceeds the 2.25% (9% x 3/12) return from the United States.

12. 12 Chapter 4 – Problem 13 b.Where would you borrow? The flip side of a lower return in the United States is a lower borrowing cost. Borrow in the United States at 2.25%. Borrow in Japan: 1 JPY / 142 – (1 + 0.07 x 3/12) / 139 = 0.0002779 Cost of debt = 0.0002779 x 142 / 1 = 3.95%

13. 13 Chapter 4 – Problem 13 c.What arbitrage opportunity do these figures present? It makes sense to borrow dollars in New York at 2.25% and invest them in Tokyo at 3.95% (but transaction costs could wipe out the yield differential). d.Assuming no transaction costs, what would be your arbitrage profit per dollar or dollar-equivalent borrowed? The profit would be a 1.7% (3.95% - 2.25%) return per dollar.

14. 14 Chapter 4 – Problem 14 14.Here are some prices in the international money markets: Spot rate = $0.95 /€ Forward rate (one year) = $0.97 /€ Interest rate (€) = 7% per year Interest rate ($) = 9% per year a.Assuming no transaction costs or taxes exist, do covered arbitrage profits exist in the above situation? Describe the flows. Arbitrage profits can be earned by borrowing dollars, buying euros in the spot market, investing the euros at 7%, and selling the euro interest and principal forward for one year for dollars. The annual dollar return on dollars invested in Germany is (1.07 x 0.97)/0.95 - 1 = 9.25%. This return exceeds the 9% return on dollars invested in the United States by 0.25% per annum.

15. 15 Chapter 4 – Problem 14 b.Suppose now that transaction costs in the foreign exchange market equal 0.25% per transaction. Do unexploited covered arbitrage profit opportunities still exist? In this case, the return on arbitraging dollars falls to: 1/0.95 x (1-0.0025) x 1.07 x 0.97 (1-0.0025) – 1.09 = - 0.293% Thus, arbitraging from dollars to euros has now become unprofitable and no capital flows will occur.

16. 16 Chapter 4 – Problem 14 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 50%. In this situation, do covered arbitrage profits exist? How large are they? Describe the transactions required to exploit these profits. In this case, the after ‑ tax interest differential in favor of the U.S. is (1 + 0.09 x 0.50 – 1 + 0.07 x 0.50)/(1 + 0.07 x.50) = 0.97%, while the after ‑ tax forward premium on the euro is 0.75x(0.97 ‑ 0.95)/0.95 = 1.58%. Since the after ‑ tax forward premium exceeds the after ‑ tax interest differential, dollars will continue to flow to Germany as before.

17. 17 Chapter 4 – Problem 15 15.Suppose today's exchange rate is $0.90/€. The 6- month interest rates on dollars and euros are 6% and 3%, respectively. The 6-month forward rate is $0.8978. A foreign exchange advisory service has predicted that the euro will appreciate to $0.9290 within six months. a.How would you use forward contracts to profit in the above situation? Buying euro forward for six months and selling it in the spot market, you expect a profit of $0.0312 (0.9290 - 0.8978) per euro bought forward. This is a semiannual return of 3.48% (0.0312/0.8978). Whether this profit materializes depends on the accuracy of the advisory service's forecast.

18. 18 Chapter 4 – Problem 15 b.How would you use money market instruments (borrowing and lending) to profit? By borrowing dollars at 6% (3% semiannually), converting them to euros in the spot market, investing the euros at 3% (1.5% semiannually), selling the euro proceeds at an expected price of $0.9290/ Є, and repaying the dollar loan, you will earn an expected semiannual return of 1.77%: Return per dollar borrowed = (1/0.90) x 1.015 x 0.9290 - 1.03 = 1.77% c.Which alternatives (forward contracts or money market instruments) would you prefer? Why? The return per dollar in the forward market is substantially higher than the return using the money market speculation. Other things being equal, therefore, the forward market speculation would be preferred.

19. 19 Chapter 7 – Problem 4 4.An investor wishes to buy euros spot (at $0.9080) and sell euros forward for 180 days (at $0.9146). a.What is the swap rate on euros? A premium of 66 points. b.What is the premium on 180 ‑ day euros? The 180 ‑ day premium is (0.9146 ‑ 0.9080)/0.9080 x 2 = 1.45%.

20. 20 Chapter 7 – Problem 5 5.Suppose Credit Suisse quotes spot and 90-day forward rates of $0.7957-60, 8-13. a.What are the outright 90-day forward rates that Credit Suisse is quoting? The outright forwards are: bid rate = $0.7965 = (0.7957 + 0.0008) and ask rate = $0.7973 = (0.7960 + 0.0013). b.What is the forward discount or premium associated with buying 90-day Swiss francs? The forward premium = [(0.7973 - 0.7960)/0.7960]x 4 =0.65%

21. 21 Chapter 7 – Problem 5 c.Compute the percentage bid-ask spreads on spot and forward Swiss francs. The spot bid-ask spread is: (0.7960 - 0.7957)/0.7960 = 0.04%. The corresponding forward bid-ask spread is (0.7973 - 0.7965)/0.7973 = 0.10%.

22. 22 Chapter 7 – Problem 7 7.Suppose the euro is quoted at 0.6064 ‑ 80 in London, and the pound sterling is quoted at 1.6244-59 in Frankfurt. a.Is there a profitable arbitrage situation? Describe it. Buy euros for £0.6080. Use the euros to buy pounds for €1.6259. This is equivalent to selling euros for £0.6150. There is a net profit of £0.0070 per euro bought and sold–a percentage yield of 1.16% (0.0070/0.6080).

23. 23 Chapter 7 – Problem 7 b.Compute the percentage bid ‑ ask spreads on the pound and euro. The percentage bid-ask spreads on the pound and euro are calculated as follows: £ bid-ask spread = (1.6259 - 1.6244)/1.6259 = 0.09% euro bid-ask spread = (0.6080 - 0.6064)/0.6080 = 0.26%

24. 24 Chapter 7 – Problem 8 8. As a foreign exchange trader at Sumitomo Bank, one of your customers would like a yen quote on Australian dollars. Current market rates are: Spot30-day30-day outright forward rates ¥101.37-85/U.S.$115-13¥101.22-72/U.S.$1 A$1.2924-44/U.S.$120-26A$1.2944-70/U.S.$1 a.What bid and ask yen cross rates would you quote on spot Australian dollars? By means of triangular arbitrage, we can calculate the market quotes for the Australian dollar in terms of yen as ¥78.31-81/A$1 As a foreign exchange trader, you would try to buy Australian dollars at slightly less than ¥78.31 and sell them at slightly more than ¥78.81.

25. 25 Chapter 7 – Problem 8 b.What outright yen cross rates would you quote on 30-day forward Australian dollars? By means of triangular arbitrage, we can then calculate the market quotes for the 30-day forward Australian dollar in terms of yen as ¥78.04-58/A$1 For the yen bid price for the forward Australian dollar, we need to first sell Australian dollars forward for U.S. dollars and then sell the U.S. dollars forward for yen. It costs A$1.2970 to buy U.S.$1 forward. With U.S.$1 we can buy ¥101.22. Hence, A$1.2970 = ¥101.22, or A$1 = ¥78.04. This is the yen bid price for the forward Australian dollar. The yen ask price for the Australian dollar can be found by first selling yen forward for U.S. dollars and then using the U.S. dollars to buy forward Australian dollars. Given the quotes above, it costs ¥101.72 to buy U.S.$1, which can be sold for A$1.2944. Hence, A$1.2944 = ¥101.71, or A$1 = ¥78.58. This is the yen ask price for the forward A$.

26. 26 Chapter 7 – Problem 8 c.What is the forward premium or discount on buying 30-day Australian dollars against yen delivery? The ask rate for 30-day forward Australian dollars is ¥78.58 and the spot ask rate is ¥78.81. Thus, the Australian dollar is selling at a forward discount to the yen. The annualized discount equals - 3.43%, computed as follows:

27. 27 Chapter 7 – Problem 10 10.On checking the Telerate screen, you see the following exchange rate and interest rate quotes: Currency90-day interest rates annualSpot rates 90-day forward rates Dollar4.99% - 5.03% Swiss franc3.14% - 3.19%$0.711 - 22$0.726 - 32 a.Can you find an arbitrage opportunity? Two possibilities: Borrow dollars and lend in Swiss francs or borrow Swiss francs and lend in dollars. The profitable arbitrage opportunity is: Lend Swiss francs financed by borrowing U.S. dollars. b.What steps must you take to capitalize on it? Borrow dollars at 1.2575% for 90 days (5.03%/4), convert these dollars into francs at the ask rate of $0.722, lend the francs at 0.785% for 90 days (3.14%/4), and sell the francs forward for dollars at the buy rate of $0.726. c.What is the profit per $1,000,000 arbitraged? The profit is $1,000,000 x [(1.00785/0.722) x 0.726 - 1.012575] = $858.66.