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# Exchange Rate, PPP, Inflation, and Interest Rate

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1. Jones is asked to recall the correct representation of purchasing power parity. St is the exchange rate at time t, expressed in units of foreign currency per domestic currency. ID and IF are the expected rates of inflation in the domestic and foreign countries, and E( ) denotes an expected value. Which of the following is the CORRECT representation of purchasing power parity?

A) E(S0) / S1 = [1 + E(iFC)] / 1 + E(iDC)].
B) E(S1) / S0 = [1 + E(iDC)] / 1 + E(iFC)].
C) S0 / E(S1) = [1 + E(iFC)] / [1 + E(iDC)].
D) S1 / S0 = [1 + E(iFC)] / [1 + E(iDC)].

2. U.S. interest rates are currently 7 percent and the real rate of interest has been about 2 percent over the past 20 years. Today's spot rate is \$1.7921 per British pound. Jones predicts that the spot exchange rate for British pounds will be \$1.8653 per pound in one year. Using the information above and assuming the expected inflation rate in the U.S. is 6 percent, Jones has arrived at her conclusion based upon the assumption that the inflation rate in Great Britain will be:

A) 10.3%.
B) 1.8%.
C) 8.4%.
D) 3.6%.

3. Based upon the interest rate information given above, and using the exact version of the Fisher relationship, Larson calculates that the market-consensus implied expected inflation rate in the U.S. is:

A) -4.7%.
B) 5.0%.
C) 4.9%.
D) 5.1%.

4. Jackson is a portfolio manager looking to take a currency position on the Chinese yuan. The current spot rate is 8.2781 yuan per U.S. dollar, while the two-year forward rate is 9.3336. Wang's expected holding period is one year. Jackson calculates the average expected percentage change in the exchange rate over the next year to be:

A) 6.18%.
B) 12.75%.
C) -6.18%.
D) -12.75%.

5. George Gao, CFA, is a currency portfolio manager who believes that the asset market approach can be applied to make short run forecasts of exchange rates based on the long-term effects of the changes in a country's money supply. Recently, Japan unexpectedly reduced its money supply by 5 percent, increasing interest rates from 1 percent to 1.5 percent. Japan's current spot rate is 108.74 Japanese yen per United States dollar (JY/USD). George believes that it will take two years for the effects of the decrease in the money supply to reduce the inflation rate in Japan. The current interest rate in the U.S. is 2 percent. Based on George's calculations, the decrease in the money supply will translate to an immediate spot exchange rate of:

A) 104.32 JY/USD.
B) 102.29 JY/USD.
C) 103.30 JY/USD.
D) 108.74 JY/USD.

6. A domestic investor from the U.S. invested in securities in Mexico one year ago. At that time, the exchange rate was \$0.07 per peso. The ratio of the price levels of the domestic consumption basket to the foreign consumption basket was also equal to 7. Over the past year the U.S. inflation rate was 2 percent and the inflation rate in Mexico was 6 percent. The current end-of-the year spot exchange rate is \$0.085 per peso.

What was the beginning real exchange rate one year ago?
A) 0.070.
B) 0.010.
C) 0.035.
D) 0.020.

What is the end of year real exchange rate?
A) 0.013.
B) 0.010.
C) 0.021.
D) 0.006.

7. Which of the following statements regarding the real exchange rate is FALSE? Using the data in this example, the:

A) change in the nominal exchange rate does not reflect the inflation differential; therefore, the real exchange rate has changed.
B) changes in rates imply that exchange rate risk was present.
C) constant real rate implies that the changes in the nominal rate are simply a reflection of the inflation differential.
D) changes in the real exchange rates would have a significant impact on realized returns for investors.

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#### Solution Preview

1.  Jones is asked to recall the correct representation of purchasing power parity. St is the exchange rate at time t, expressed in units of foreign currency per domestic currency. ID and IF are the expected rates of inflation in the domestic and foreign countries, and E( ) denotes an expected value. Which of the following is the CORRECT representation of purchasing power parity?

A) E(S0) / S1 = [1 + E(iFC)] / 1 + E(iDC)].
B) E(S1) / S0 = [1 + E(iDC)] / 1 + E(iFC)].
C) S0 / E(S1) = [1 + E(iFC)] / [1 + E(iDC)].
D) S1 / S0 = [1 + E(iFC)] / [1 + E(iDC)].

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Answer: D) S1 / S0 = [1 + E(iFC)] / [1 + E(iDC)].

2.  U.S. interest rates are currently 7 percent and the real rate of interest has been about 2 percent over the past 20 years. Today's spot rate is \$1.7921 per British pound. Jones predicts that the spot exchange rate for British pounds will be \$1.8653 per pound in one year. Using the information above and assuming the expected inflation rate in the U.S. is 6 percent, Jones has arrived at her conclusion based upon the assumption that the inflation rate in Great Britain will be:

A) 10.3%.
B) 1.8%.
C) 8.4%.
D) 3.6%.

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Forward / Spot = ((1+ US inflation) ) / ((1+ British inflation) )

or British inflation = {(1+US inflation) /(Forward /Spot) }-1

Forward= \$1.8653 / GBP
Spot= \$1.7921 / GBP
Annual inflation in US is 6%

Therefore British inflation is = 1.84% ={(1+6.% / ( 1.8653/1.7921) -}1

Check:
USD/GBP spot is \$1.79210 / ...

#### Solution Summary

Different multiple choice questions on purchasing power parity, exchange rates have been answered and discussed in the solution.

\$2.19