Full Test Bank Ch19 International Portfolio Diversification

Chapter 19 International Portfolio Diversification

Notes to instructors:

Answers to non-numeric multiple choice questions are arranged alphabetically, so that answers are randomly assigned to the five outcomes.

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1. In perfect financial markets, rational investors have equal access to information and to market prices.

2. In a portfolio with many securities, the extent to which risk is reduced through portfolio diversification primarily depends on the covariance between individual assets in the portfolio.

3. In a portfolio with many securities, the extent to which risk is reduced through portfolio diversification primarily depends on the expected returns and variances of individual assets in the portfolio.

It primarily depends on the covariances (or correlations).

4. As the number of assets held in a portfolio increases, the variance of return on the portfolio becomes more dependent on the covariances between the individual assets and less dependent on the variances of the individual assets.

5. The risk of an individual asset when held in a portfolio with a large number of assets depends primarily on its return covariance with other assets in the portfolio and not on its return variance.

6. The extent to which risk is reduced by portfolio diversification does not depend on the correlations between assets in the portfolio.

It depends very much on the correlations (and covariances).

7. Return variance on a portfolio with many assets depends more on the variances of the individual assets in the portfolio than on the covariances between the individual assets.

It is more dependent on the return covariances.

8. The Sharpe index is useful for measuring the risk-adjusted performance of a single asset in a well-diversified portfolio.

The Sharpe index is best for measuring the performance of a portfolio.

9. Total risk equals systematic risk plus unsystematic risk plus error.

Unsystematic risk includes any random noise or error.

10. A foreign stock goes up 10 percent in price in the foreign currency as the domestic currency depreciates by 10 percent. The price of the foreign stock in domestic currency stays the same.

It increases in value by (1.10)(1.10) – 1 = 0.21, or 21%.

11. Financial contracts in high-inflation countries are seldom pegged to inflation because their value would be eroded at a rapid rate.

Their value would be eroded if they were not pegged.

12. The variance of foreign stock returns to domestic residents is primarily due to variance in foreign market returns and to a lesser extent to variance in exchange rates.

13. The variance of foreign bond returns to domestic residents is primarily due to return variance in foreign market returns and to a lesser extent to variance in exchange rates.

It is due primarily to exchange rate variability.

14. Solnik [“Why not diversify internationally?” Financial Analysts Journal] estimated that systematic risk comprises approximately 74 percent of individual security variance within a portfolio of U.S. stocks.

Unsystematic risk comprises 74 percent of total risk in a U.S. portfolio (see Exhibit 19.8).

15. American depository receipts pay dividends in dollars and trade on U.S. exchanges just like other domestic U.S. shares.

16. The correlation between returns on companies in the same industry and domiciled in the same country is usually greater than the correlation between returns on companies in the same industry but in different countries.

17. In an economist’s perfect world with no barriers to the free flow of goods and capital, multinational corporations can create value for investors by diversifying internationally.

No value is created because investors are able to diversify their own portfolios.

18. The return-risk efficiency of an internationally diversified portfolio of stocks and bonds can be improved by hedging the currency risk of foreign investments.

19. Empirical evidence suggests that stock return volatility varies predictably over time.

20. The future benefits of risk reduction through international portfolio diversification can be estimated fairly precisely using historical data.

Expected returns, variances, and covariances vary considerably over time.

21. Correlations between national stock markets are fairly stable over time.

They appear to vary considerably over time.

Multiple Choice Select the BEST ANSWER

1. The perfect market assumptions include each of the following EXCEPT ____.

a. equal access to registered brokers

b. equal access to market prices

c. frictionless markets

d. no costs of financial distress

e. rational investors

2. Frictionless financial markets could have which of the following?

a. agency costs

b. bid-ask spreads

c. brokerage fees

d. government intervention

e. irrational investors

3. Which of the following conditions is sufficient to ensure an operationally efficient market?

a. frictionless markets

b. perfect competition

c. rational investors

d. more than one of the above

e. none of the above

4. Suppose E[rA] = 14.8%, A = 17.9%, E[rB] = 17.1%, and B = 31.9%. Assuming a mean-variance framework, which of the following statements is ?

a. A is preferred to B.

b. B is preferred to A.

c. A and B are equally desirable.

d. Whether A or B is preferred depends on the correlation between the two assets.

e. Which asset is preferred depends on individual preferences.

5. The benefits of international diversification are limited by the lack of ____ foreign markets.

a. free convertibility of currencies in

b. information about

c. liquidity in

d. more than one of the above

e. none of the above

6. You live in New York and buy a share of Phillips at a price of 166 euros. At the end of the year, you receive a dividend of 4 euros and the stock price is 160 euros. If the euro appreciates by 8 percent during the year, what was your percentage return in dollars for the year?

a. –10%

b. –1%

c. + 7%

d. + 9%

e. + 11%

7. You live in London and have invested in shares of Societe Gererale de Belgique at a price of €52.00. By the end of the year, you have received dividends of €1.00, share price has risen to €54.50, and the pound has fallen 20 percent against the euro. Which of the following is closest to your pound sterling return for the year?

a. –15%

b. 0%

c. + 7%

d. + 28%

e. + 33%

8. A stock in India rises 20 percent in local terms. The Indian rupee rises 25 percent against the U.K. pound sterling. What is the return in pound sterling?

a. –5%

b. 0%

c. 5%

d. 45%

e. 50%

9. A stock in India rises 20 percent in local terms. Pound sterling rises 25 percent against the Indian rupee. What is the return in pound sterling?

a. –4%

b. 0%

c. 4%

d. 45%

e. 50%

10. Returns on foreign assets can be decomposed into ___.

a. CAPM betas and systematic risks

b. expected returns and momentum effects

c. local market returns and currency returns

d. relative financial distress and value premiums

e. total risks and idiosyncratic risks

11. What is the variance on the Indian (Rp = rupee) stock market to a Canadian investor if Var(r^Rp) = 0.105, Var(s^C£/Rp) = 0.088, and the local Indian stock market is independent of the value of the rupee?

a. –0.017

b. 0.017

c. 0.193

d. cannot be determined from the given information

e. none of the above

12. The standard deviation of return to the Indian stock market is 24.8 percent in local currency. The standard deviation of the Indian rupee against the Canadian dollar is 30.2 percent. Ignoring interactions between the Indian stock market and the value of the Indian rupee, what is the standard deviation of return of the Indian market to a Canadian investor?

a. 0.550

b. 0.153

c. 0.391

d. cannot be determined from the given information

e. none of the above

13. Which of (a) through (c) is ?

a. The risk of an individual asset when held in a portfolio with a large number of assets depends on its covariance with other assets in the portfolio.

b. As the number of assets held in a portfolio increases, the covariance terms begin to dominate the portfolio variance calculation.

c. The extent to which risk is reduced by portfolio diversification depends on how highly the individual assets in the portfolio are correlated.

d. All of the above are

e. All of the above are

14. Which of (a) through (d) is ?

a. The systematic risk of a portfolio is measured by the standard deviation (or variance) of return on the portfolio.

b. If two assets are perfectly correlated, then the standard deviation of a portfolio of these two assets is a simple weighted average of the standard deviations of the assets.

c. The variance of a portfolio with N securities is calculated as a weighted average of the N² cells in the variance-covariance matrix.

d. The expected return of a portfolio of assets is a simple weighted average of the expected returns of the individual assets in the portfolio.

e. Two assets that are perfectly negatively correlated can be combined to create a riskless portfolio.

15. Which of (a) through (c) is ?

a. In the CAPM, that portion of an individual asset’s risk that cannot be diversified away by holding the asset in a large portfolio is called systematic risk.

b. In the CAPM, that portion of an individual asset’s risk that cannot be diversified away by holding the asset in a large portfolio is called market risk.

c. In the CAPM, that portion of an individual asset’s risk that cannot be diversified away by holding a portfolio with many securities is called nondiversifiable risk.

d. All of the above are

e. None of the above is

16. Which of the following could account for investors’ tendency to favor local assets?

A the additional information costs of international diversification

B the ability of a domestic stock portfolio to hedge domestic inflation risk

C the higher returns typically earned on foreign investments

a. A and B

b. B and C

c. A and C

d. A, B, and C

e. A only

17. Which of (a) through (d) is ?

a. If an asset’s returns are distributed as normal, then its return distribution can be completely described by its mean and variance of return.

b. Returns on foreign stocks are leptokurtic.

c. Correlation and covariance measure how closely two assets move together.

d. The correlation coefficient between two assets is the covariance scaled by the standard deviations of the two assets.

e. All of the above are

18. Which of (a) through (c) is ?

a. Both domestic and foreign nominal cash flows are exposed to purchasing power risk.

b. The real value of a future foreign currency cash flow in the domestic currency depends on domestic inflation.

c. Hedging foreign currency risk substitutes exposure to domestic purchasing power risk for exposure to currency risk.

d. All of the above are

e. Two of the above are

19. ____ are not an impediment to the free flow of capital across national borders.

a. Foreign exchange controls

b. Capital inflow and outflow controls

c. Stock exchanges

d. Transactions costs

e. Withholding taxes

20. Quantitative inputs to portfolio analysis include which of (a) through (c)?

a. correlations

b. expected returns

c. variances

d. three of the above

e. two of the above

21. The risk-reduction benefits of hedging the currency risk in an international investment portfolio are greatest for a portfolio of ____.

a. commodity futures

b. domestic bonds

c. domestic stocks

d. foreign bonds

e. foreign stocks

QUESTIONS 22-25 ARE BASED ON EXHIBIT 19.2 IN THE TEXT (repeated here)

Exhibit T19.1 Return statistics

Annual returns Correlations

Mean Mean Std dev SI(W) Beta(W) CA CH GE IN JA UK US

Canada (CA) 11.0% 28.1% 0.340 1.11

China (CH) 18.0% 42.1% 0.390 1.18 0.72

Germany (GE) 9.1% 31.1% 0.240 1.47 0.76 0.65

India (IN) 22.5% 45.6% 0.460 1.29 0.70 0.67 0.64

Japan (JA) 3.5% 20.0% 0.100 0.70 0.60 0.51 0.56 0.56

U.K. (UK) 7.2% 23.5% 0.240 1.00 0.82 0.66 0.87 0.63 0.61

U.S. (US) 6.6% 19.6% 0.260 0.93 0.81 0.63 0.88 0.62 0.57 0.85

U.S. treasuries 1.5% 1.7% 0.000 0.00 0.05 0.14 0.04 0.08 0.00 0.03 -0.05

Source: Annual USD net returns to Morgan Stanley Capital International (msci.com) indices. Sharpe Indices (μ_i – μ_F)/σ_i are based on annual returns and Treasury yields from the U.S. Federal Reserve (federalreserve.gov). Betas and correlations are based on monthly returns.

22. Based on Exhibit T19.1, what is the standard deviation of an equal-weighted portfolio of Canadian and German equities?

a. 4.5%

b. 17.4%

c. 20.7%

d. 24.1%

e. 27.8%

23. Based on Exhibit T19.1, what is the Sharpe index of an equal-weighted portfolio of Canadian and German equities?

a. 0.138

b. 0.209

c. 0.241

d. 0.288

e. 0.308

24. Based on Exhibit T19.1, what is the standard deviation of an equal-weighted portfolio of Indian and Chinese equities?

a. 16.6%

b. 19.3%

c. 26.4%

d. 35.9%

e. 40.1%

25. Based on Exhibit T19.1, what is the Sharpe index of an equal-weighted portfolio of Indian and Chinese equities?

a. 0.138

b. 0.209

c. 0.236

d. 0.341

e. 0.468

26. Based on Exhibit T19.1, what is the standard deviation of an equal-weighted portfolio of U.S. treasuries and U.S. equities?

a. 9.8%

b. 12.4%

c. 16.3%

d. 21.4%

e. 25.9%

Problems (These can be converted into Multiple Choice questions.)

1. Suppose expected dollar returns to U.S. investors in the Germany and Japanese stock markets are 9.1 percent and 3.5 percent, respectively, based on data in Exhibit 19.2. The German standard deviation of return is 31.1 percent and the Japanese standard deviation of return is 20.0 percent.

a. Calculate the expected return of an equally weighted portfolio of these two indices.

b. Calculate the standard deviations of equally weighted portfolios of the two indices under: (i) perfect positive correlation, (ii) perfect negative correlation, and (iii) the observed correlation of 0.56.

c. By changing the portfolio weights, draw a line between the U.S. and German assets in return-risk (i.e., E[r] – σ space) space for each case.

d. Based on a U.S. risk-free rate of 1.5 percent and the graph in part (c), which of the three portfolios identified in (b) provides the highest excess return per unit of standard deviation?

2. A portfolio consists of two assets, A and B, representing weights of 30 percent and 70 percent, respectively. What is the standard deviation of the portfolio if the standard deviation of asset A is 27.6 percent, and the standard deviation of asset B is 17.0 percent, and the correlation coefficient is 0.833?

3. Assets X and Y are perfectly positively correlated. The standard deviations are _X = 0.312 and _Y = 0.426. What is the standard deviation of a portfolio with weights w_X = 40% and w_Y = 60%?

4. Assets X and Y are perfectly negatively correlated. Standard deviations are _X = 0.126 and _Y = 0.079. What is the standard deviation of an equally weighted portfolio of X and Y?

5. Suppose Swiss treasuries yield 1.5 percent. If the Swiss national stock market return has a mean of 11% and a standard deviation was 24.4 percent, what is the ex-post return/risk performance of the market according to the Sharpe index?

6. Canadian stocks have a mean return of 11.0 percent and a standard deviation of 28.1 percent. French stocks have a mean return of 5.6 percent and a standard deviation of 25.4 percent. The correlation between the markets is 0.778. What is the standard deviation of an equal-weighted portfolio of Canadian and French equities?

7. If a shipment of Pilsner Urquell from the Czech Republic costs 345,628 korunas and the spot exchange rate is 33.24 korunas per euro, what should be the price of the shipment in euros?

8. The Mexican stock market goes up 30 percent in pesos, but the peso falls 20 percent against the dollar. What is the dollar return on an investment in Mexican stocks?

9. You live in Brazil, where the currency is the Brazilian real (BRL). You buy shares of GE at a price of $33.50. At year-end you’ve received dividends of $0.72 and share price is $36.00. The spot rate changed from $0.4810/BRL at the start of the year to $0.4660/BRL at year-end. Calculate your total return in BRL.

Problem Solutions

1. a. E[r_P] = ½(9.1%) + ½(3.5%) = 6.3%.

b. (i) σ_P = (w_USσ_US + w_Gσ_G) = (½)(0.311) + (½)(0.200) = 0.256, or 256%

(ii) σ_P = |(w_USσ_US − w_Gσ_G)| = |(½)(0.311) − (½)(0.200)| = 0.056, or 5.6%

(iii) σ_P = (w_US²σ_US² + w_G²σ_G² + 2w_USw_Gσ_USσ_Gρ_US,G)^½

= [(½)²(0.311)² + (½)²(0.200)² + 2(½)(½)(0.311)(0.200)(0.56)]^½ = 0.227, or 22.7%

c. Graphically:

d. A correlation of negative one results in the most efficient set of portfolios.

For  = 1: SI = (6.3 .5%) / 25.6% = 0.188

For  = 1: SI = (6.3% .5%) / 5.6% = 0.865

For  = 0.4: SI = (6.3% %) / 22.7% = 0.211

2. σ_AB = σ_Aσ_Bρ_AB = (0.276)(0.170)(0.833) = 0.039

Var(r_P) = σ_P² = w_A²σ_A² + w_B²σ_B² + 2w_Aw_Bσ_AB

= (0.30)²(0.276)² + (0.70)²(0.170)² + 2(0.30)(0.70)(0.039) = 0.0374

So, σ_P = (σ_P²)^½ = (0.0374)^½ = 0.1935, or 19.35%

3. σ_P = (w_Xσ_X + w_Yσ_Y) = (0.4)(0.312) + (0.6)(0.426) = 0.3804

4. σ_P = √[(w_Xσ_Y − w_Qσ_Q)²] = |(0.5)(0.126) – (0.5)(0.079)| = 0.1025

5. Sharpe index = (r_P − r_rF)/σ_P = (0.11 – 0.015)/0.244 = 0.389

6. σ_P = [ (½)²(0.281)² + (½)²(0.254)² + 2(½)(½)(0.778)(0.281)(0.254) ]^½ = 0.252, or σ_P = 25.2%

7. V_t^d = V_t^fS_t^d/f = K345,628 (€1/K33.24) = €10,397.95

8. (1 + r^$) = (1 + r^MXN)(1 + s^$/MXN) = (1.3)(1 – 0.2) = 1.04, or r^$ = 4%

9. (1 + r^BRL) = (1 + r^$)(1 + s^BRL/$) = (($36.00 + $0.72)/($33.50)) (1/(($0.466/BRL)/($0.481/BRL))) = 1.1314,

or r^BRL ≈ 13.1%