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CHAPTER 15 INTERNATIONAL PORTFOLIO INVESTMENT
ANSWERS & SOLUTIONS TO END-OF-CHAPTER QUESTIONS AND PROBLEMS
QUESTIONS
1. What factors are responsible for the recent surge in international portfolio investment (IPI)?
Answer: The recent surge in international portfolio investments reflects the globalization of
financial markets. Specifically, many countries have liberalized and deregulated their capital and
foreign exchange markets in recent years. In addition, commercial and investment banks have
2. Security returns are found to be less correlated across countries than within a country. Why
can this be?
Answer: Security returns are less correlated probably because countries are different from each
3. Explain the concept of the world beta of a security.
Answer: The world beta measures the sensitivity of returns to a security to returns to the world
4. Explain the concept of the Sharpe performance measure.
Answer: The Sharpe performance measure (SHP) is a risk-adjusted performance measure. It is
5. Explain how exchange rate fluctuations affect the return from a foreign market measured in
dollar terms. Discuss the empirical evidence on the effect of exchange rate uncertainty on the
risk of foreign investment.
Answer: It is useful to refer to Equations 15.4 and 15.5 of the text. Exchange rate fluctuations
mostly contribute to the risk of foreign investment through its own volatility as well as its
6. Would exchange rate changes always increase the risk of foreign investment? Discuss the
condition under which exchange rate changes may actually reduce the risk of foreign
investment.
Answer: Exchange rate changes need not always increase the risk of foreign investment. When
7. Evaluate a home country’s multinational corporations as a tool for international
diversification.
Answer: Despite the fact that MNCs have operations worldwide, their stock prices behave very
8. Discuss the advantages and disadvantages of closed-end country funds (CECFs) relative to
the American Depository Receipts (ADRs) as a means of international diversification.
Answer: CECFs can be used to diversify into exotic markets that are otherwise difficult to
9. Why do you think closed-end country funds often trade at a premium or discount?
Answer: CECFs trade at a premium or discount because capital markets of the home and host
10. Why do investors invest the lion’s share of their funds in domestic securities?
Answer: Investors invest heavily in their domestic securities mainly because there are barriers
11. What are the advantages of investing via international mutual funds?
12. Discuss how the advent of the euro would affect international diversification strategies.
Answer: As the euro-zone has the same monetary and exchange-rate policies, the correlations
PROBLEMS
1. Suppose you are a euro-based investor who just sold Microsoft shares that you had bought
six months ago. You had invested 10,000 euros to buy Microsoft shares for $120 per share; the
exchange rate was $1.15 per euro. You sold the stock for $135 per share and converted the
dollar proceeds into euro at the exchange rate of $1.06 per euro. First, determine the profit from
this investment in euro terms. Second, compute the rate of return on your investment in euro
terms. How much of the return is due to the exchange rate movement?
Solution: It is useful first to compute the rate of return in euro terms:
15.1
115.1
1
06.1
1
120
120135
err $
−
+
−
=
+
2. Mr. James K. Silber, an avid international investor, just sold a share of Nestlé, a Swiss firm,
for SF5,080. The share was bought for SF4,600 a year ago. The exchange rate is SF1.60 per
U.S. dollar now and was SF1.78 per dollar a year ago. Mr. Silber received SF120 as a cash
dividend immediately before the share was sold. Compute the rate of return on this investment
in terms of U.S. dollars.
€
3. In the above problem, suppose that Mr. Silber sold SF4,600, his principal investment
amount, forward at the forward exchange rate of SF1.62 per dollar. How would this affect the
dollar rate of return on this Swiss stock investment? In hindsight, should Mr. Silber have sold the
Swiss franc amount forward or not? Why or why not?
4. Japan Life Insurance Company invested $10,000,000 in pure-discount U.S. bonds in May
1995 when the exchange rate was 80 yen per dollar. The company liquidated the investment
one year later for $10,650,000. The exchange rate turned out to be 110 yen per dollar at the
time of liquidation. What rate of return did Japan Life realize on this investment in yen terms?
5. At the start of 1996, the annual interest rate was 6 percent in the United States and 2.8
percent in Japan. The exchange rate was 95 yen per dollar at the time. Mr. Jorus, who is the
manager of a Bermuda-based hedge fund, thought that the substantial interest advantage
associated with investing in the United States relative to investing in Japan was not likely to be
offset by the decline of the dollar against the yen. He thus concluded that it might be a good
idea to borrow in Japan and invest in the United States. At the start of 1996, in fact, he
borrowed ¥1,000 million for one year and invested in the United States. At the end of 1996, the
exchange rate became 105 yen per dollar. How much profit did Mr. Jorus make in dollar terms?
Copyright © 2018 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent
of McGraw-Hill Education.
(¥1,000,000,000/95)(1.06) = $11,157,895.
The dollar amount necessary to pay off yen loan is:
(¥1,000,000,000)(1.028)/105 = $9,790,476.
The dollar profit = $11,157,895 - $9,790,476 = $1,367,419.
Mr. Jorus was able to realize a large dollar profit because the interest rate was higher in the
U.S. than in Japan and the dollar actually appreciated against yen. This is an example of
uncovered interest arbitrage.
6. Suppose we obtain the following data in dollar terms:
Stock market
Return (mean)
Risk (SD)
United States
1.26% per month
4.43%
United Kingdom
1.23% per month
5.55%
The correlation coefficient between the two markets is 0.58. Suppose that you invest equally,
i.e., 50% each, in the two markets. Determine the expected return and standard deviation risk of
the resulting international portfolio.
Solution: The expected return of the equally weighted portfolio is:
7. Suppose you are interested in investing in the stock markets of 7 countries--i.e., Australia,
Canada, Germany, Japan, Switzerland, the United Kingdom, and the United States--the same 7
countries that appear in Exhibit 15.9. Specifically, you would like to solve for the optimal
(tangency) portfolio comprising the above seven stock markets. In solving the optimal portfolio,
use the input data (i.e. correlation coefficients, means, and standard deviations) provided in
Exhibit 15.4. The risk-free interest rate is assumed to be 0.2% per month and you can take a
short position in any stock market. What are the optimal weights for each of the seven stock
markets? What is the risk and return of the optimal portfolio? This problem can be solved using
MPTSolver.xls spreadsheet.
Solution:
8. The HFS Trustees have solicited input from three consultants concerning the risks and
rewards of an allocation to international equities. Two of them strongly favor such action, while
the third consultant commented as follows: “The risk reduction benefits of international
investing have been significantly overstated. Recent studies relating to the cross-country
correlation structure of equity returns during different market phases cast serious doubt on the
ability of international investing to reduce risk, especially in situations when risk reduction is
needed the most.”
a. Describe the behavior of cross-country equity return correlations to which the consultants is
referring. Explain how that behavior may diminish the ability of international investing to reduce
risk in the short run. Assume that the consultant’s assertion is correct.
b. Explain why it might still be more efficient on a risk/reward basis to invest internationally
rather than only domestically in the long run.
The HFS Trustees have decided to invest in non-U.S. equity markets and have hired Jacob
Hind, a specialist manager, to implement this decision. He has recommended that an unhedged
equities position be taken in Japan, providing the following comments and the table data to
support his view: “Appreciation of a foreign currency increases the returns to a U.S. dollar
investor. Since appreciation of the Yen from ¥100/$U.S. to ¥98/$U.S. is expected, the Japanese
stock position should not be hedged.”
Market Rates and Hind’s Expectations
U.S. Japan
Spot rate (yen per $U.S.) n/a 100
Hind’s 12-month currency forecast (yen per $U.S.) n/a 98
1-year Eurocurrency rate (% per annum) 6.00 0.80
Hind’s 1-year inflation forecast (% per annum) 3.00 0.50
Assume that the investment horizon is one year and that there are no costs associated with
currency hedging.
c. State and justify whether Hind’s recommendation (not to hedge) should be followed. Show
any calculations.
Solution:
9. Rebecca Taylor, an international equity portfolio manager, recognizes that optimal country
allocation strategy combined with an optimal currency strategy should produce optimal portfolio
performance. To develop her strategy, Taylor produced the table below, which provides
expected return data for the three countries and three currencies in which she may invest. The
table contains the information she needs to make market strategy (country allocation) decisions
and currency strategy (currency allocation) decisions.
Expected Returns for a U.S.-Based Investor
Country Local Currency Exchange Rate Local Currency
Equity Returns Returns Eurodeposit
Returns
Japan 7.0% 1.0% 5.0%
United Kingdom 10.5 -3.0 11.0
United States 8.4 0.0 7.5
a. Prepare a ranking of the three countries in terms of expected equity-market return premiums.
Show your calculations.
b. Prepare a ranking of the three countries in terms of expected currency return premiums from
the perspective of a U.S. investor. Show your calculations.
c. Explain one advantage a portfolio manager obtains, in formulating a global investment
strategy, by calculating both expected market premiums and expected currency premiums.
Solution:
10. The Glover Scholastic Aid Foundation has received a €20 million global government bond
portfolio from a Greek donor. This bond portfolio will be held in euros and managed separately
from Glover’s existing U.S. dollar-denominated assets. Although the bond portfolio is currently
unhedged, the portfolio manager, Raine Sofia, is investigating various alternatives to hedge the
currency risk of the portfolio. The bond portfolio’s current allocation and the relevant country
performance data are given in Exhibits 1 and 2. Historical correlations for the currencies being
considered by Sofia are given in Exhibit 3. Sofia expects that future returns and correlations will
be approximately equal to those given in Exhibits 2 and 3.
Exhibit 1. Glover Scholastic Aid Foundation Current Allocation Global Government Bond
Portfolio
Country Allocation (%) Maturity (years)
Greece 25 5
A 40 5
B 10 10
C 10 5
D 15 10
Exhibit 2. Country Performance Data (in local currency)
Country
Cash
Return
(%)
5-year
Excess
Bond
Return
(%)
10-year
Excess
Bond
Return
(%)
Unhedged
Currency
Return
(%)
Liquidity of
90-day
Currency
Forward
Contracts
Greece
2.0
1.5
2.0
---
Good
A
1.0
2.0
3.0
– 4.0
Good
B
4.0
0.5
1.0
2.0
Fair
C
3.0
1.0
2.0
– 2.0
Fair
D
2.6
1.4
2.4
– 3.0
Good
Exhibit 3. Historical Currency Correlation Table (1998-2003, weekly observations)
Currency
€
(Greece)
A
B
C
D
€ (Greece)
1.00
–0.77
0.45
–0.57
0.77
A
---
1.00
–0.61
0.56
–0.70
B
---
---
1.00
–0.79
0.88
C
---
---
---
1.00
–0.59
D
---
---
---
---
1.00
a. Calculate the expected total annual return (euro-based) of the current bond portfolio if Sofia
decides to leave the currency risk unhedged. Show your calculations.
b. Explain, with respect to currency exposure and forward rates, the circumstance in which Sofia
should use a currency forward contract to hedge the current bond portfolio’s exposure to a
given currency.
c. Determine which one of the currencies being considered by Sofia would be the best proxy
hedge for Country B bonds. Justify your response with two reasons.
Sofia has been disappointed with the low returns on the current bond portfolio relative to the
benchmark—a diversified global bond index—and is exploring general strategies to generate
excess returns on the portfolio. She has already researched two such strategies: duration
management and investing in markets outside the benchmark index.
d. Identify three general strategies (other than duration management and investing in markets
outside the benchmark index) that Sofia could use to generate excess returns on the current
bond portfolio. Give, for each of the three strategies, a potential benefit specific to the current
bond portfolio.
Solution:
a. The unhedged expected annual portfolio return in euros is calculated as follows:
b. If Sofia expects the unhedged percentage return from exposure to a currency to be less than
the forward discount or premium, she should use a forward contract to hedge exposure to
that currency. The circumstance can also be expressed as:
c. Country D currency would provide the best proxy hedge for Country B bonds for any of the
following reasons:
d.
1. Bond Market Selection:
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of McGraw-Hill Education.
Because there are bonds from only five countries in the current portfolio, better risk-adjusted
returns could be realized by diversifying into government bonds from other countries in the
index that have low correlations with existing bonds.
2. Sector/Credit/Security Selection:
3. Currency Selection:
MINI CASE: SOLVING FOR THE OPTIMAL INTERNATIONAL PORTFOLIO
Suppose you are a financial advisor and your client, who is currently investing only in the
U.S. stock market, is considering diversifying into the U.K. stock market. At the moment, there
are neither particular barriers nor restrictions on investing in the U.K. stock market. Your client
would like to know what kind of benefits can be expected from doing so. Using the data
provided in the above problem (i.e., problem 12), solve the following problems:
(a) Graphically illustrate various combinations of portfolio risk and return that can be generated
by investing in the U.S. and U.K. stock markets with different proportions. Two extreme
proportions are (I) investing 100% in the U.S. with no position in the U.K. market, and (ii)
investing 100% in the U.K. market with no position in the U.S. market.
(b) Solve for the ‘optimal’ international portfolio comprised of the U.S. and U.K. markets.
Assume that the monthly risk-free interest rate is 0.5% and that investors can take a short
(negative) position in either market.
(c) What is the extra return that U.S. investors can expect to capture at the ‘U.S.-equivalent’
risk level? Also trace out the efficient set. [The Appendix 11.B provides an example.]
Suggested Solution to the Optimal International Portfolio:
The variance of the portfolio is:
