Q1. Kathy Smith, CFA, is an analyst with the Borderless Fund and is doing research on the country of Kenya for her colleague, John Dolan. Smith wants to calculate the inflation rate implied in the forward rates that she obtains from her bank, Global Bank. The current spot exchange rate is 90.772 Kenyan Shillings (KS) for one euro (EUR). The one-year forward rate for the Kenyan Shilling is 95.7686 KS/EUR. The current rate of inflation the European Economic Community is 9%. Smith does not know the current inflation rate for Kenya. Assuming relative purchasing power parity (PPP) applies, the calculated expected inflation rate implied in the forward rate is:

A)   10%.

B)   17%.

C)   15%.

Q2. Brian Kenny, CFA, is an economist for Borderless Fund and was instructed by his colleague, John Dolan to create a forecasted exchange rate at the end of two years, Kenny’s investment horizon for the country of Kenya. The current spot exchange rate is 90.772 Kenyan Shillings (KS) for one euro (EUR). Kenny calculates annual inflation rates of 13% for the next two years for Kenya and 11% for the Economic European Community. Assuming relative purchasing power parity (PPP) holds, the expected forward exchange rate at the end of two years is:

A)   92.4075 KS/EUR.

B)   89.1654 KS/EUR.

C)   94.0725 KS/EUR.

Q3. John Dolan, CFA, is an international fund manager with the Borderless Fund. Dolan is considering an investment in the country of Kenya. He is concerned with the inflationary environment in Kenya, but he feels that it is mitigated by the degree of high economic growth over the next year. Based on his research, Dolan found that Kenya is expecting inflation rates of 17% while the European Economic Community is expecting 9%. The current exchange rate is 90.772 Kenyan Shillings (KS) per euro (EUR). Dolan assumes that relative purchasing power parity applies. If Dolan wants to compute an exchange rate at the end of the year so that he can use it for purposes of portfolio valuation, the closest exchange rate (KS/EUR) would be:

A)   97.4342 KS/EUR.

B)   84.5654 KS/EUR.

C)   98.9415 KS/EUR.

Q4. The Worldwide Equity-Income Fund is a U.S. based mutual fund whose objective is to seek current income through participation in the U.S. and global equity and fixed-income markets. According to its bylaws, Worldwide can invest no more than 25% of its funds in the assets of any one country. Currently, it holds a substantial amount of foreign securities, heavily weighted in British stocks and bonds. Mary Larson, CFA, has recently joined Worldwide as a portfolio manager. Larson is a recent graduate of Washington State University with a double major in Economics and Finance, where she studied interest rate parity and purchasing power parity. Larson’s role at Worldwide will encompass many areas, including forecasting and strategy.

Larson has been asked to examine the current portfolio holdings, and project how the current position will perform over the next year under various interest rate scenarios. U.S. interest rates are currently 7% and the real rate of interest has been about 2% over the past 20 years. Today's spot rate is $1.7921 per British pound.

Due to a weakening in world oil prices, as well as the results from the recent U.S. presidential election, Larson determines it is necessary to calculate her own forecast of the expected inflation rate in the U.S. The international Fisher relation predicts that the interest rate differential between two countries should be equal to the expected inflation differential. Therefore, countries with higher expected inflation rates will have higher nominal interest rates, and vice versa. A change in domestic rates could lead Larson to suggest substantial changes to the current portfolio corporation.

Larson is asked to recall the correct representation of purchasing power parity. S_t is the exchange rate at time t, expressed in units of foreign currency per domestic currency. I_D and I_F are the expected rates of inflation in the domestic and foreign countries, and E( ) denotes an expected value. Which of the following is the most accurate representation of purchasing power parity (PPP)?

A)   E(S₁) / S₀ = [1 + E(i_FC)] / [1 + E(i_DC)].

B)   E(S₁) / S₀ = [1 + E(i_DC)] / 1 + E(i_FC)].

C)   E(S₀) / S₁ = [1 + E(i_FC)] / 1 + E(i_DC)].

答案和详解如下：

Q1. Kathy Smith, CFA, is an analyst with the Borderless Fund and is doing research on the country of Kenya for her colleague, John Dolan. Smith wants to calculate the inflation rate implied in the forward rates that she obtains from her bank, Global Bank. The current spot exchange rate is 90.772 Kenyan Shillings (KS) for one euro (EUR). The one-year forward rate for the Kenyan Shilling is 95.7686 KS/EUR. The current rate of inflation the European Economic Community is 9%. Smith does not know the current inflation rate for Kenya. Assuming relative purchasing power parity (PPP) applies, the calculated expected inflation rate implied in the forward rate is:

A)   10%.

B)   17%.

C)   15%.

Correct answer is C)

Solve for the expected inflation rate for Kenya implied in the forward rate (i_K) by using the same formula for relative PPP:

S₁ = S₀ × [(1 + i_FC) / (1 + i_DC)]
S₁ = KS95.7686 = KS90.772 × [(1 + i_K) / (1 + 0.09)]
i_K = 15%

Q2. Brian Kenny, CFA, is an economist for Borderless Fund and was instructed by his colleague, John Dolan to create a forecasted exchange rate at the end of two years, Kenny’s investment horizon for the country of Kenya. The current spot exchange rate is 90.772 Kenyan Shillings (KS) for one euro (EUR). Kenny calculates annual inflation rates of 13% for the next two years for Kenya and 11% for the Economic European Community. Assuming relative purchasing power parity (PPP) holds, the expected forward exchange rate at the end of two years is:

A)   92.4075 KS/EUR.

B)   89.1654 KS/EUR.

C)   94.0725 KS/EUR.

Correct answer is C)         

The KS is the foreign currency and the EUR is the domestic currency because the spot quote is KS/EUR:

S₁ = S₀ × [(1 + i_FC)² / (1 + i_DC )²]
S₁ = 90.772 × [(1 + 0.13)² / (1 + 0.11)²] = 94.0725 KS/EUR

The KS is expected to depreciate against the EUR over the next two years.

Q3. John Dolan, CFA, is an international fund manager with the Borderless Fund. Dolan is considering an investment in the country of Kenya. He is concerned with the inflationary environment in Kenya, but he feels that it is mitigated by the degree of high economic growth over the next year. Based on his research, Dolan found that Kenya is expecting inflation rates of 17% while the European Economic Community is expecting 9%. The current exchange rate is 90.772 Kenyan Shillings (KS) per euro (EUR). Dolan assumes that relative purchasing power parity applies. If Dolan wants to compute an exchange rate at the end of the year so that he can use it for purposes of portfolio valuation, the closest exchange rate (KS/EUR) would be:

A)   97.4342 KS/EUR.

B)   84.5654 KS/EUR.

C)   98.9415 KS/EUR.

Correct answer is A)

The KS is the foreign currency and the EUR is the domestic currency because the spot quote is KS/EUR:

S₁ = S₀ × [(1 + i_FC) / (1 + i_DC)]
S₁ = KS90.772 × [(1 + 0.17) / (1 + 0.09)] = 97.4342 KS/EUR

The Kenyan Shilling is expected to depreciate against the euro over the next year.

Q4. The Worldwide Equity-Income Fund is a U.S. based mutual fund whose objective is to seek current income through participation in the U.S. and global equity and fixed-income markets. According to its bylaws, Worldwide can invest no more than 25% of its funds in the assets of any one country. Currently, it holds a substantial amount of foreign securities, heavily weighted in British stocks and bonds. Mary Larson, CFA, has recently joined Worldwide as a portfolio manager. Larson is a recent graduate of Washington State University with a double major in Economics and Finance, where she studied interest rate parity and purchasing power parity. Larson’s role at Worldwide will encompass many areas, including forecasting and strategy.

Larson has been asked to examine the current portfolio holdings, and project how the current position will perform over the next year under various interest rate scenarios. U.S. interest rates are currently 7% and the real rate of interest has been about 2% over the past 20 years. Today's spot rate is $1.7921 per British pound.

Due to a weakening in world oil prices, as well as the results from the recent U.S. presidential election, Larson determines it is necessary to calculate her own forecast of the expected inflation rate in the U.S. The international Fisher relation predicts that the interest rate differential between two countries should be equal to the expected inflation differential. Therefore, countries with higher expected inflation rates will have higher nominal interest rates, and vice versa. A change in domestic rates could lead Larson to suggest substantial changes to the current portfolio corporation.

Larson is asked to recall the correct representation of purchasing power parity. S_t is the exchange rate at time t, expressed in units of foreign currency per domestic currency. I_D and I_F are the expected rates of inflation in the domestic and foreign countries, and E( ) denotes an expected value. Which of the following is the most accurate representation of purchasing power parity (PPP)?

A)   E(S₁) / S₀ = [1 + E(i_FC)] / [1 + E(i_DC)].

B)   E(S₁) / S₀ = [1 + E(i_DC)] / 1 + E(i_FC)].

C)   E(S₀) / S₁ = [1 + E(i_FC)] / 1 + E(i_DC)].

Correct answer is A)

The correct representation of purchasing power parity is:  E(S₁) / S₀ = [1 + E(i_FC)] / [1 + E(i_DC)].