Reading 45: The Case for Inter....Diversification－LOS f currency, investment, why, should

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CFA Institute Area 3-5, 7, 12, 14-18: Portfolio Management
Session 17: Portfolio Management in a Global Context
Reading 45: The Case for International Diversification
LOS f: Explain why currency risk should not be a significant barrier to international investment.

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According to a study on bond returns during the period 1987-1996, the U.S. dollar generally weakened relative to the other countries in the study (specifically, Canada, Euro area, Japan and the U.K.). Which of the following statements regarding the impact of exchange rates on security returns is TRUE?

A) When the home currency is weakening, the investor should invest more in foreign bonds.

B) When the home currency is weakening, the investor should invest less in foreign bonds.

C) Exchange rates have little impact on returns.

D) Because the investor is earning dollars and spending dollars, he should invest solely in U.S. securities.

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Answer and Explanation

When the home currency is weakening, the investor should invest more in foreign bonds. As the dollar weakens, a U.S. investor will earn a higher return on foreign investments because each foreign currency unit buys more dollars.

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The following data applies to a foreign stock investment:

• The gain on the stock in foreign currency terms was 15 percent.

• The foreign currency has depreciated by 8 percent.

• The standard deviation of stock returns was 35 percent and the standard deviation of the foreign currency was 11 percent.

• The correlation between the stock returns and the currency is 0.10.

What is the expected return of the portfolio?

A) 7.00%.

B) 23.00%.

C) 5.80%.

D) 24.20%.

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Answer and Explanation

To obtain the return in domestic currency terms use the following formula that considers the return in local currency terms as well as the exchange rate change:

15% - 8% + (15% * - 8%) = 5.80%

15% - 8% + (15% * - 8%) = 5.80%

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The following data applies to a foreign stock investment:

• The gain on the stock in foreign currency terms was 22 percent.

• The foreign currency has appreciated by 7 percent.

• The standard deviation of stock returns was 38 percent and the standard deviation of the foreign currency was 24 percent.

• The correlation between the stock returns and the currency is 0.10.

What is the expected return of the portfolio?

A) 30.54%.

B) 29.00%.

C) -15.00%.

D) 13.46%.

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Answer and Explanation

To obtain the return in domestic currency terms use the following formula that considers the return in local currency terms as well as the exchange rate change:

22% + 7% + (22% * 7%) = 30.54%

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The following data applies to a foreign stock investment:

• The loss on the stock in foreign currency terms was 12 percent.
• The foreign currency has depreciated by 6 percent.
• The standard deviation of stock returns was 33 percent and the standard deviation of the foreign currency was 14 percent.
• The correlation between the stock returns and the currency is 0.20.

What is the risk of the portfolio in U.S. dollar terms as measured by the standard deviation?

A) 14.70%.

B) 5.34%.

C) 47.00%.

D) 38.34%.

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Answer and Explanation

We will use the formula for portfolio risk that considers the risk of the asset in foreign currency terms, the risk of the foreign currency, and the correlation between the two:

σ_$² = 0.33² + 0.14² + 2(0.33)(0.14)(0.2) = 0.1470

σ_$ = √0.1470 = 0.3834 = 38.34%

We will use the formula for portfolio risk that considers the risk of the asset in foreign currency terms, the risk of the foreign currency, and the correlation between the two:

σ_$² = 0.33² + 0.14² + 2(0.33)(0.14)(0.2) = 0.1470

σ_$ = √0.1470 = 0.3834 = 38.34%

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Which of the following statements regarding international diversification is least accurate?

A) Foreign currency risk and foreign asset risk are not additive.

B) Foreign currency risk will diversify the risk from domestic government monetary and fiscal policies.

C) The correlations between foreign assets and foreign currencies is usually low.

D) A depreciating foreign currency benefits the international investor.

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Answer and Explanation

A depreciating foreign currency harms the international investor by resulting in a lower home currency return. Foreign currency risk and foreign asset risk are not additive because the correlations between them are usually quite low, and sometimes negative. Foreign currency risk also helps diversify domestic fiscal and monetary policies.

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Joe Murad, a U.S. investor, invested in foreign securities. The following data is available:

• The return on stock in foreign currency terms was 14%.

• The foreign currency depreciated by 5%.

• The standard deviation of stock returns was 30%.

• The standard deviation of the foreign currency was 10%.

• The correlation between the stock return and the currency was 0.30.

Murads return on his foreign securities investment is:

A) 9.00%.

B) 8.30%.

C) 19.00%.

D) 9.70%.

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Answer and Explanation

Use the following formula to compute the return in dollars:

R_$ = R_LC + S + (R_LC)(S)

R_$ = return on the foreign asset in U.S. dollar terms
R_LC = return on the foreign asset in local currency terms
S = percentage change in the foreign currency

Return = 0.14 + (-0.05) + (.14) (-0.05) = 8.30%

Use the following formula to compute the return in dollars:

R_$ = R_LC + S + (R_LC)(S)

R_$ = return on the foreign asset in U.S. dollar terms
R_LC = return on the foreign asset in local currency terms
S = percentage change in the foreign currency

Return = 0.14 + (-0.05) + (.14) (-0.05) = 8.30%

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The risk of the portfolio in U.S. dollar terms as measured by its standard deviation is:

A) 34.35%.

B) 11.80%.

C) 36.75%.

D) 41.23%.

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Answer and Explanation

The formula used below considers the risk of the asset in foreign currency terms, the risk of the foreign currency, and the correlation between the two:

σ²_$ = σ²_LC + σ²_S + 2σ_LCσ_Sρ_LC,S

where:
σ²_$ = variance of the returns on the foreign asset in U.S. dollar terms
σ²_LC, σ_LC = variance and standard deviation of the foreign asset in local currency terms
σ²_S, σ_S = variance and standard deviation of foreign currency
ρ_LC,S = correlation between returns for the foreign asset in local currency terms and movements in the foreign currency.

Variance = (0.30)² + (0.10)² + 2(.3)(.1)(.3) = .118

Standard deviation = √(0.118) = 34.35%

The formula used below considers the risk of the asset in foreign currency terms, the risk of the foreign currency, and the correlation between the two:

σ²_$ = σ²_LC + σ²_S + 2σ_LCσ_Sρ_LC,S

where:
σ²_$ = variance of the returns on the foreign asset in U.S. dollar terms
σ²_LC, σ_LC = variance and standard deviation of the foreign asset in local currency terms
σ²_S, σ_S = variance and standard deviation of foreign currency
ρ_LC,S = correlation between returns for the foreign asset in local currency terms and movements in the foreign currency.

Variance = (0.30)² + (0.10)² + 2(.3)(.1)(.3) = .118

Standard deviation = √(0.118) = 34.35%

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The contribution of currency risk to the risk of the portfolio is closest to:

A) 4.35%.

B) 4.00%.

C) 5.00%.

D) 8.30%.

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Answer and Explanation

The contribution of the currency risk is the difference between the asset risk in domestic currency terms less the risk of the foreign asset in foreign currency terms.

Contribution of currency risk = σ_$ - σ_LC
Contribution of currency risk = 34.35% - 30.00% = 4.35%

The contribution of the currency risk is the difference between the asset risk in domestic currency terms less the risk of the foreign asset in foreign currency terms.

Contribution of currency risk = σ_$ - σ_LC
Contribution of currency risk = 34.35% - 30.00% = 4.35%