Suppose you are an investor who is considering buying a one-year British government bond that has a 4 percent interest rate or a one-year French government bond with a 7 percent interest rate. The exchange rate today is 2.00 euros per pound and you expect the exchange rate to be 2.10 euros per pound one year from now.
a.Which bond would you purchase? Why? Show your calculations. b.Suppose you expect the exchange rate to be 2.05 euros per pound in one year, instead of 2.10 euros per pound. Would you change your decision about which bond to buy? Explain and show your calculations.
What will be an ideal response?
The problem can be solved using either country as the domestic country. Because the interest rate is quoted as euros per pound and, when we compare iD to iF? %?Xe, the exchange rate must be quoted as units of the foreign currency per unit of the domestic currency, it is most natural to choose Britain as the domestic country and France as the foreign country.
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| a. | The answer can be found in one of two ways: look at the difference in interest rates or calculate an example. |
Looking at differences in interest rates: The investment in France pays 3 percentage points more than the investment in Britain. Logically, you would invest in France unless the pound appreciates by 3 percent or more relative to the euro; otherwise, invest in Britain. Because the pound is expected to appreciate by %?Xe =  = .05 = 5% you should invest in Britain. | |
| Use an example, starting with either pounds or euros: | |
| Start with pounds: | |
| If you invest in Britain, you will get back 1,000 £ × 1.04 = 1040 £ | |
| If you invest in France, you will have to trade pounds for euro which will give you 1,000 £ × 2 €/£ = 2000 €; | |
| By investing the euro, you will get 2,000 € × 1.07 = 2,140 €; The amount you get back has to be exchanged for pounds in 1 year. So your expected dollar earning is: 2,140 € ÷ 2.1 €/£ = 1,019.05£. | |
| Thus the investment in Britain yields more pounds after one year. | |
| Alternatively, start with euro: | |
| If you invest in Britain, you have to trade euro for pounds: 1,000 € ÷ 2 €/£ = 500 £; | |
| By investing the pounds, you will earn 500 £ × 1.04 = 520 £; This earning in euro has to be exchanged for euro in 1 year. So your expected earning in euro is 520 £ × 2.1 €/£ = 1,092 €. | |
| If you invest in France, you will earn 1,000 € × 1.07 = 1,070 €. | |
| Thus the investment in Britain yields more euros after one year. | |
| b. | This can also be answered with either method: |
Looking at differences in interest rates: Now %?Xe =  = .025 = 2.5%, thus the expected appreciation in the exchange rate is not enough to make up for the difference in interest rates. So you would switch to investing in France. | |
| In the example starting with pounds, the only change is the last step for investing in France. In this case, you have to trade euro for pounds in 1 year which will give you 2,140 € ÷ 2.05 €/£ = 1,043.90 £, which is more than you get from investing in Britain. | |
| In the example starting with euros, the only change is the last step for investing in Britain. In this case, you have to trade pounds for euro in 1 year which will give you 520 £ × 2.05 €/£ = 1,066 €, which is less than you get from investing in France. |
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