Question

Consider the exchange rate between the U.S. $ and the U.K. £. Suppose the exchange rate E ∗ is defined as £/$. (a) Denote the one-year forward exchange rate (at time t) for time t+1 by F ∗ t+1. Suppose the nominal interest rate in the U.S. is 8%, the nominal interest rate in the U.K. is 5%, the current exchange rate E ∗ t is £0.67/$, and the forward exchange rate F ∗ t+1 is £0.625/$. Are the numbers given here consistent with the interest rate parity equation? Clearly show all calculations. Based on this information, would you prefer to invest in the U.S. or in the U.K.? (5 points) (b) What effect will the difference between the effective rate of return in the two countries (if any) from part (a) have on the exchange rate (E ∗ ). Clearly show all calculations, and illustrate your answer using a well-labeled graph. (10 points) (c) Consider the exchange rate determined in part (b). Suppose that the Fed (the U.S. central bank) adopts a policy to lower the inflation rate by 2% in the U.S. Explain the effect of such a monetary policy on the exchange rate (E ∗ ). Clearly explain your answer, and illustrate your answer using a well labeled graph. (10 points)

Answer 1

a. According to the parity of the interest rate, the dollar would depreciate relative to £, as the nominal interest rate in the US is higher than GBP. The forward exchange rate according to IRP is USD 1.4925 x 1.08/1.05— 1.5352 per GBP. Expected forward rate, however, is $1,600 per £. Therefore, $is depreciating more than the interest rate parity estimate. By entering into forward contract to sell GBP, the buyer will borrow in $and invest in £ and lock in £ 51.6 per £.

b. The interest rate difference is likely to trigger a depreciation of $ per interest rate differential in respect of £. 1. Borrower $ 100 and invest in UK £ 67 at 5%
2. Enter into forward contract to sell £70.35 and buy $ at 1.6 per £
3. UK investment would returm 67 x1.05 = £ 70.35
4. Convert £70.35 at forward exchange rate to $112.56
5. Pay off $ loan - 100 x 1.08 - 108
6. Total return 112.56/108 = 4.22%

c. Indirectly, inflation has an impact on currency, while inflation is closely related to the exchange rate. The economies aim for an equilibrium between interest rates and inflation, but the relationship between the two is difficult to manage. Taylor's rule attempts to predict stable, target inflation-based growth and interest rates. Higher interest rates attract foreign investment, and demand for a country's currency is likely to rise. Yet higher interest rates also lead to increased inflation rates, which has a negative impact on the currency of the country. Lower interest rates increase consumption spending and economic growth, and usually have positive currency value effects. The Fed is likely to lower the interest rate in order to stimulate economic growth under a low inflation scenario. Therefore the rate parity is likely to decline below the expected level. Anticipated exchange rate parity of 1.4925 x 1.06/1.05= 1.5067