LOS g: Calculate the end-of-period real exchange rate and the domestic-currency expost return on a foreign bond (security), given the end-of-period exchange rate, the beginning-of-period real exchange rate, and the inflation rates during the period.

Q1. A U.S. investor purchased a U.K. bond one year ago. The exchange rate at the time was 1.5 to 1 (dollars to pounds) and the beginning-of-period ratio of the price levels of the consumption baskets was 2 to 1 (dollars to pounds). Beginning of the year interest rates were 7% in the U.S. and 12% in the U.K. Inflation during the year was expected to be 5% in the U.S. and 10% in the U.K. Today the exchange rate is 1.6. What is the ex-post domestic currency return on the U.K. bond to the U.S. investor?

A)   14.67%.

B)   18.67%.

C)   5.33%.

Q2. A U.S. investor purchased a U.K. bond one year ago. The exchange rate at the time was 1.5 to 1 (dollars to pounds) and the beginning-of-period ratio of the price levels of the consumption baskets was 2 ($ to ￡). During the year, inflation in the U.S. was 5% and in the U.K. was 10%. Today the exchange rate is 1.6. What is the end-of-period real exchange rate?

A)   0.84.

B)   1.64.

C)   1.45.

Q3. A U.S. investor purchased a Swiss bond one year ago. At the time of purchase, U.S. inflation and interest rates were 2% and 4%, respectively, while Swiss rates were 5% and 7%, respectively. The beginning-of-period exchange rate was 2 ($/SF; SF is the Swiss Franc). The ratio of the price of the U.S. to Swiss consumption baskets at the beginning of the period was also 2. Inflation was exactly as expected during the year. What was the end-of-period real exchange rate?

A)   2.02.

B)   1.00.

C)   0.92.

LOS g: Calculate the end-of-period real exchange rate and the domestic-currency expost return on a foreign bond (security), given the end-of-period exchange rate, the beginning-of-period real exchange rate, and the inflation rates during the period. fficeffice" />

Q1. A ffice:smarttags" />U.S. investor purchased a U.K. bond one year ago. The exchange rate at the time was 1.5 to 1 (dollars to pounds) and the beginning-of-period ratio of the price levels of the consumption baskets was 2 to 1 (dollars to pounds). Beginning of the year interest rates were 7% in the U.S. and 12% in the U.K. Inflation during the year was expected to be 5% in the U.S. and 10% in the U.K. Today the exchange rate is 1.6. What is the ex-post domestic currency return on the U.K. bond to the U.S. investor?

A)   14.67%.

B)   18.67%.

C)   5.33%.

Correct answer is B)

The dollar was expected to appreciate (lower inflation), but depreciated by 6.67% (= 1.6 / 1.5 = 1.0667 or 6.67%) instead. Hence, the return to U.S. investor is the foreign interest rate plus currency appreciation, or 18.67% (= 12% foreign rate + 6.67% appreciation).

Q2. A U.S. investor purchased a U.K. bond one year ago. The exchange rate at the time was 1.5 to 1 (dollars to pounds) and the beginning-of-period ratio of the price levels of the consumption baskets was 2 ($ to ￡). During the year, inflation in the U.S. was 5% and in the U.K. was 10%. Today the exchange rate is 1.6. What is the end-of-period real exchange rate?

A)   0.84.

B)   1.64.

C)   1.45.

Correct answer is A)

The end-of-period real exchange rate is calculated as: X = S (P_F/P_D). Here, the new price levels are 1.1 for the U.K. (1 × 1.1 = 1.1) and 2.1 for the U.S. (2 × 1.05 = 2.1). Hence, the end-of-period real rate is 0.838 [= X = S (P_F / P_D) = 1.6 (1.1 / 2.1)].

Q3. A U.S. investor purchased a Swiss bond one year ago. At the time of purchase, U.S. inflation and interest rates were 2% and 4%, respectively, while Swiss rates were 5% and 7%, respectively. The beginning-of-period exchange rate was 2 ($/SF; SF is the Swiss Franc). The ratio of the price of the U.S. to Swiss consumption baskets at the beginning of the period was also 2. Inflation was exactly as expected during the year. What was the end-of-period real exchange rate?

A)   2.02.

B)   1.00.

C)   0.92.

Correct answer is B)

First calculate the expected spot rate using purchasing power parity: E(S₁) = 2 × (1.02 / 1.05) = 1.9429. If the end-of-period nominal rate is 1.94, then the end-of-period real rate must be 0.999 = X = S (P_F / P_D) = 1.94(1 × 1.05 / 2 × 1.02).