Reading 45: The Case for International Diversification－LO currency, position, security

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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 c: Evaluate the contribution of currency risk to the volatility of an international security position.

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Which of the following statements regarding foreign currency risk is FALSE? Foreign currency risk:

A) is about twice that of foreign bond risk.

B) can be hedged with futures and options.

C) is about twice that of foreign stock risk.

D) is often diversified away in a portfolio of foreign assets.

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Answer and Explanation

Foreign currency risk is only about half that of foreign stock risk on average. It is about twice that of foreign bond risk however. Much of it can be diversified away in a portfolio of currencies and can be hedged with derivative instruments.

tycoon

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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Which of the following statements concerning currency risk is most accurate? Currency risk:

A) greatly magnifies the risk of foreign investments.

B) slightly reduces the risk of foreign investments through diversification of the asset risk.

C) greatly reduces the risk of foreign investments through diversification of the asset risk.

D) slightly magnifies the risk of foreign investments.

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Answer and Explanation

Currency risk only slightly magnifies the risk of foreign investments because it is only about half that of foreign stock risk on average and much of it can be diversified away in a portfolio of currencies. Also foreign currency risk and foreign asset risk are not additive due to correlations between them of less than one.

tycoon

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 contribution of currency risk?

A) 11.00%.

B) 37.72%.

C) 14.23%.

D) 2.72%.

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Answer and Explanation

The contribution of currency risk measures the risk incremental to foreign asset risk from currency risk and is the difference between the asset risk in domestic currency terms and the risk of the foreign asset in foreign currency terms. To obtain the contribution of currency risk, we must first calculate the risk of the asset in domestic currency terms. To obtain the risk of the asset in domestic currency terms, we 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 = 0.35² + 0.11² + 2(0.35)(0.11)(0.1) = 0.1423

σ_$ = √0.1423 = 0.3772 = 37.72%

Contribution of Currency = 37.72% - 35.00% = 2.72%

The contribution of currency risk measures the risk incremental to foreign asset risk from currency risk and is the difference between the asset risk in domestic currency terms and the risk of the foreign asset in foreign currency terms. To obtain the contribution of currency risk, we must first calculate the risk of the asset in domestic currency terms. To obtain the risk of the asset in domestic currency terms, we 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 = 0.35² + 0.11² + 2(0.35)(0.11)(0.1) = 0.1423

σ_$ = √0.1423 = 0.3772 = 37.72%

Contribution of Currency = 37.72% - 35.00% = 2.72%

tycoon

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 contribution of currency risk?

A) 46.93%.

B) 24.00%.

C) 8.93%.

D) 22.02%.

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Answer and Explanation

The contribution of currency risk measures the risk incremental to foreign asset risk from currency risk and is the difference between the asset risk in domestic currency terms and the risk of the foreign asset in foreign currency terms. To obtain the contribution of currency risk, we must first calculate the risk of the asset in domestic currency terms. To obtain the risk of the asset in domestic currency terms, we 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 = 0.38² + 0.24² + 2(0.38)(0.24)(0.1) = 0.2202

σ_$ = √0.2202 = 0.4693 = 46.93%

Contribution of Currency = 46.93% - 38.00% = 8.93%

The contribution of currency risk measures the risk incremental to foreign asset risk from currency risk and is the difference between the asset risk in domestic currency terms and the risk of the foreign asset in foreign currency terms. To obtain the contribution of currency risk, we must first calculate the risk of the asset in domestic currency terms. To obtain the risk of the asset in domestic currency terms, we 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 = 0.38² + 0.24² + 2(0.38)(0.24)(0.1) = 0.2202

σ_$ = √0.2202 = 0.4693 = 46.93%

Contribution of Currency = 46.93% - 38.00% = 8.93%

tycoon

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%

tycoon

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) 24.20%.

D) 5.80%.

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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%

tycoon

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%

tycoon

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 expected return of the portfolio?

A) -18.00%.

B) -17.28%.

C) -18.72%.

D) 17.28%.

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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:

-.12 - .06 + (-.12 * -.06) = -.1728 or -17.28%