1. Suppose that a treasurer of Apple has an extra cash reserve of USD 100.000.000 to invest for six months. The six-month interest rate is 8 % per annum in the U.S. and 7 % per annum in Germany. Currently, the spot exchange rate is USD/EUR = 1.01 and the sixmonth forward exchange rate is USD/EUR = 0.99. The treasurer of Apple does not wish to bear any exchange risk. Where should he/she invest to maximize the return?
Investing in the US| Amount in USD| US| Amount in USD| | | 100.000.000,00| 1,0399| 103.992.032,00| |
Investing in Germany| Amount in EUR| GER| Amount in EUR| Amount in USD| | 101.000.000,00| 1,0349| 104.528.834,96| 105.584.681,78|
How we computed the results:
Investing in the US| Amount in USD| US| Amount in USD| | | 100.000.000| = (1,08)^(1/2)| = E4*D4| |
Investing in Germany| Amount in EUR| GER| Amount in EUR| Amount in USD| | =100.000.000*1,01| = (1,07)^(1/2)| = E6*D6| = F6*(1/0,99)|
The treasurer of Apple should invest in Germany to maximize Apple’s return. Despite the fact that the interest rate is higher in the USA, the appreciation of the Euro over the Dollar gives the investor a bigger gain when investing in Germany. To protect himself from the exchange risk, he must make sure that he has signed a contract in which he will exchange his money in Euros back to Dollars by today’s valid forward rate.
2. As of November 1, 1999, the exchange rate between the Brazilian real (BRL) and the USD was USD/BRL = 1.95. The consensus forecast for the U.S. and Brazil inflation rates for the next one-year period is 2.6 % and 20 %, respectively. What would you forecast the exchange rate to be around November 1, 2000?
In order to compute the exchange rate we will use the formula expressing the “Relative Purchasing Power Parity” in mathematical terms:
et = e0 1+iht1+ift = 1.95* 1.21.026 = 2,28
USD/BRL Today (e0)| BR Inflation (ih)| US Inflation (if)| 1,95| 20%| 2,60%|
USD/BRL Forecast (et)| | |
2,280701754| | |
The expected high inflation in Brazil will cause the BRL to depreciate. Therefore the exchange rate between USD/BRL is going to increase. Our forecast for the exchange rate on November 1st of 2000 is USD/BRL=2,28.
3. Santander PP, an international pension fund manager, uses the concepts of purchasing power parity (PPP) and the international fisher effect (IFE) to forecast spot exchange rates. Santander gathers the financial information as follows: Base price level 100
Current U.S. price level 105
Current South African price level 111
Base rand spot exchange rate 0.175 USD
Current rand spot exchange rate 0.158 USD
Expected annual U.S. inflation 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:
a-The current ZAR/USD spot rate that would have been forecast by PPP. b- Using the IFE, the expected ZAR/USD spot rate one year from now. c-Using PPP, the expected ZAR/USD spot rate four years from now.
A – Calculating the ZAR/USD spot rate, adjusting it by its inflation by the PPP formula: et = e0 1+iht1+ift
| ZAR/USD Today (e0)| US Inflation| SA Inflation|
| 0,158| 7%| 5%|
| ZAR/USD Forecast (e1)| | |
| 0,161009524| | |
The ZAR/USD spot rate is: 0,161 ZAR/USD
B – Using the IFE, we find the expected ZAR/USD spot rate one year from now. The IFE states that countries with higher inflation rates have higher interest rates and so that the Spot rate adjust to this interties differentials between the countries. The formula is: ete0=1+rht1+rft
ZAR/USD Today (e0)| US int. rate (rh)| SA int. rate (rf)| 0,158| 10%| 8%|
USD/BRL Forecast (et)| | |
0,160925926| | |
The expected ZAR/USD spot rate for one year is: 0.1609 ZAR/USD
C – Now the years to forecast change (t moves from t=1 to t=4), we calculate the expected ZAR/USD...