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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All of the following are reasons investors should consider constructing global portfolios EXCEPT:

A) reduced foreign exchange risk. Spreading assets over multiple currencies dampens portfolio volatility.

B) additional choice. Markets outside the U.S. represent more than 50 percent of available investment choices.

C) non-U.S. securities often outperform U.S. securities.

D) foreign securities exhibit low correlations with U.S. securities and offer greater diversification benefits.

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Answer and Explanation

Increased foreign exchange risk is the cost of going global. In terms of the home currency (which could be the USD or other currency) including assets denominated in foreign currencies can increase portfolio volatility. This is a particular concern when the foreign currencies depreciate against the home currency.

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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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While in the managerial training program for a large multinational financial services corporation, Galaxi, Inc. (Galaxi), Daniel Waite is assigned to a one-year rotation in the Mediterranean division. Upon arriving at his assignment, Waite purchases a local (foreign currency) bond with an annual coupon of 8.5 percent for 96.5.

One of Waites clients asks him to create a concentrated, two asset portfolio consisting of one European stock and one U.S. stock. Pertinent information on the two stocks and the portfolio is given below:

• Expected return of the U.S. stock = 10 percent with a standard deviation of 23 percent
• Expected return of the European stock = 12 percent with a standard deviation of 37 percent
• Correlation between the two stocks = 0.60
• Weight of the U.S. stock in the portfolio = 70 percent
• Weight of the European stock in the portfolio = 30 percent

After completing his training program in the Mediterranean division, it is now time to return to the U.S. Waite sells the bond he purchased when he arrived (a one year holding period) for 98.0. Waite is pleased with his return, which he calculates at 10.4 percent.

On the plane ride home, Waite sits next to his co-worker, Penny King. Waite and King naturally begin to chat about their experience abroad. King brings up the depressed economic conditions in the Mediterranean and the negative returns she experienced on her local bond investments. She states that her total dollar return on an 8.0 percent annual coupon bond purchased at the same time as Waite's for 95.0 and sold for 98.0 (at the same time as Waite's) was a disappointing negative 10.74 percent.

Waite and King turn their discussion to international investing in general. They agree that, despite the increased integration of world markets, investors can benefit from global investing.

Equity market correlations continue to be low due to a number of factors, comments King. There are so many differences in cultural mores, technology, government regulations, and monetary policy that most national economies still move independently of one another. International diversification works.

I dont think thats entirely true responds Waite. If you look at countries like the G-7, with similar government regulations, fiscal philosophies, and monetary policies, then there really isnt much diversification effect. The correlations arent low enough. You have to be quite selective about which foreign markets you get into. Then diversification can really pay off.

At their layover stop in London, Waite and King unexpectedly meet another colleague from work, Miko Katori. Katori just completed a two year term in Galaxis Tokyo office and has been assigned to London. At lunch Katori tells King and Waite about some of the assignments she worked on during the past two years. She is particularly excited about her personal research. I did a fascinating study using twenty years of bond data and discovered that the correlations between international bond markets can be lower than the correlation between international stock markets.  From this I concluded that adding international bonds to a portfolio will reduce risk but not increase return due to the lower returns on bonds compared to equities

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Assume that Kings calculation is correct and that Waite made a calculation error. Which of the following is closest to Waites actual total dollar return?

A) -32.4%.

B) -10.4%.

C) -18.8%.

D) -11.7%.

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Answer and Explanation

Waite forgot to take into account the impact of the percentage change in the dollar value of the foreign currency. Using the information provided by King, we can determine the percentage change in the value of the foreign currency and then calculate Waite's total dollar return. Use the formula for total dollar return:

This may be calculated as:

R_$ = R_LC + S + R_LCS

where:
R_$ = Return on foreign asset in U.S. dollar terms
R_LC = Return on foreign asset in local currency terms
S = Percentage change in foreign currency

Return on Kings bond = (8.0 + 98.0 95.0) / 95.0 = 0.115789

Solving for S we get:

R_{$ King} = 0.115789 + S + 0.115789S
-0.1074 = 0.115789 + 1.115789S
-0.22319 = 1.115789S

S = -0.20 or 20.0% depreciation of the foreign currency.

Now, Waites total dollar return can be computed.

Return on Waites bond in the local currency = (8.5 + 98.0 - 96.5) / 96.5 = 0.103627

R_{$ Waite} = 0.103627 0.20 + (.1036)(-0.20)

= 0.103627 - 0.20 - 0.02072 = -0.117 or -11.7%

Waite forgot to take into account the impact of the percentage change in the dollar value of the foreign currency. Using the information provided by King, we can determine the percentage change in the value of the foreign currency and then calculate Waite's total dollar return. Use the formula for total dollar return:

This may be calculated as:

R_$ = R_LC + S + R_LCS

where:
R_$ = Return on foreign asset in U.S. dollar terms
R_LC = Return on foreign asset in local currency terms
S = Percentage change in foreign currency

Return on Kings bond = (8.0 + 98.0 95.0) / 95.0 = 0.115789

Solving for S we get:

R_{$ King} = 0.115789 + S + 0.115789S
-0.1074 = 0.115789 + 1.115789S
-0.22319 = 1.115789S

S = -0.20 or 20.0% depreciation of the foreign currency.

Now, Waites total dollar return can be computed.

Return on Waites bond in the local currency = (8.5 + 98.0 - 96.5) / 96.5 = 0.103627

R_{$ Waite} = 0.103627 0.20 + (.1036)(-0.20)

= 0.103627 - 0.20 - 0.02072 = -0.117 or -11.7%

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Regarding the statements by Waite and King on the topic of international investing:

A) Waite is correct; King is correct.

B) Waite is incorrect; King is incorrect.

C) Waite is correct; King is incorrect.

D) Waite is incorrect; King is correct.

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Answer and Explanation

Even among countries with similar government regulations, fiscal policies, and monetary policies, such as the G-7 countries, the correlations can be sufficiently low to offer diversification opportunities.

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With respect to Katoris research, critique her statements regarding her conclusions regarding international bonds in a portfolio context.

Lower Correlation of Bonds

Lower Return of Adding Bonds

A) Incorrect Incorrect

B) Incorrect Correct

C) Correct Correct

D) Correct Incorrect

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Answer and Explanation

International bond market correlations can be lower than international equity markets due to differing government fiscal and monetary policies. Thus adding international bonds to a global portfolio offers opportunities for lower risk and higher return.

International bond market correlations can be lower than international equity markets due to differing government fiscal and monetary policies. Thus adding international bonds to a global portfolio offers opportunities for lower risk and higher return.

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Which of the following is NOT a common method used to limit the extent of foreign influence in an emerging market?

A) Limiting ownership to private investors.

B) Discriminatory taxes being applied to foreign investors.

C) Restricting or limiting foreign ownership of stocks in sensitive industries such as banking or defense.

D) Placing restrictions on the removal of capital or profits.

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Answer and Explanation

In an attempt to keep capital in their countries, many governments of developing economies place restrictions on the repatriation of capital and profits. Other methods that a developing country may use to maintain control of its market include:

1. Blocking or limiting foreign ownership of stock in sensitive industries such as banking and defense.
2. Discriminatory taxes are sometimes applied to foreign investors.
3. Limiting foreign investment to authorized investors which are usually institutional investors.
4. Restricting foreign ownership in a corporation to a minority of outstanding shares.

In an attempt to keep capital in their countries, many governments of developing economies place restrictions on the repatriation of capital and profits. Other methods that a developing country may use to maintain control of its market include:

1. Blocking or limiting foreign ownership of stock in sensitive industries such as banking and defense.
2. Discriminatory taxes are sometimes applied to foreign investors.
3. Limiting foreign investment to authorized investors which are usually institutional investors.
4. Restricting foreign ownership in a corporation to a minority of outstanding shares.

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What is the standard deviation and expected return of the two-stock portfolio?

Standard Deviation

Expected Return

A) 5.960% 10.6%

B) 24.431% 10.6%

C) 0.059% 11.4%

D) 0.244% 11.4%

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Answer and Explanation

σ²_port = w²_u.s.σ²_u.s. + w²_eσ²_e + 2w_u.s.w_eσ_u.s.σ_e ρ_u.s.,e

σ²_port = (.7)²(.23)² + (.3)²(.37)² + (2)(.7)(.3)(.23)(.37)(.6)

σ²_port = 0.0596872

σ= √σ²_port = √.0596872 = .2443096 = 24.431%

Expect return = w_u.s.E(R_u.s.) + w_eE(R_e)

= (.7)(.10) + (.3)(.12) = 10.6%

σ²_port = w²_u.s.σ²_u.s. + w²_eσ²_e + 2w_u.s.w_eσ_u.s.σ_e ρ_u.s.,e

σ²_port = (.7)²(.23)² + (.3)²(.37)² + (2)(.7)(.3)(.23)(.37)(.6)

σ²_port = 0.0596872

σ= √σ²_port = √.0596872 = .2443096 = 24.431%

Expect return = w_u.s.E(R_u.s.) + w_eE(R_e)

= (.7)(.10) + (.3)(.12) = 10.6%

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Which of the following statements about the benefits and risks of international diversification is TRUE?

A) The benefits of international diversification as demonstrated by mean-variance analysis could be overstated if return distributions are leptokurtic.

B) One of the primary arguments in favor of international diversification is that global markets are becoming integrated and the mobility of capital has increased.

C) Increased correlations calculated during periods of rising volatility are indicative that the true correlation of returns between markets is changing.

D) The contribution of currency risk is high, usually about 55% to 75% of the foreign asset risk in local currency terms.

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Answer and Explanation

Having a leptokurtic distribution means that the probability of large positive and large negative returns is greater than under a normal distribution. If large negative events occur more frequently than assumed by mean-variance analysis, the case for global diversification is weakened. One of the primary arguments against international diversification is that global markets are becoming integrated and the mobility of capital has increased. The problem with estimating correlation during periods of rising volatility is that the correlation will be biased upwards when in fact it has not changed. Therefore, an argument against international diversification may not be valid if it relies on correlations calculated during volatile periods. The contribution of currency risk only slightly magnifies the volatility of foreign investments. Studies show that currency risk is about 50% of the foreign stock risk in local currency terms. Moreover, asset and currency risk are not additive, and in many instances currency risk can be hedged or diversified away in an international portfolio.

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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 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%

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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) 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%

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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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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%