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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 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 $U.S.) n/a 98
1-year Eurocurrency rate (% per annum) 6.00 0.80
Hind’s 1-year inflation forecast (% per annum) 3.00 0.50
Assume that the investment horizon is one year and that there are no costs associated with
currency hedging.
c. State and justify whether Hind’s recommendation (not to hedge) should be followed. Show
any calculations.
Solution:
a. Cross-country correlations tend to increase during the turbulent market phase, reducing the
b. Unless the investor has to liquidate investments during the turbulent phase, he/she can ride
c. The interest rate parity implies that the forward exchange rate would be ¥95.09/$:
which is compared with Hind’s expected future spot rate of ¥98/$. Clearly, the HFS Trustees
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:
c. Computing expected currency premium helps the portfolio manager to decide whether to
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:
WG × (rG + eH,G) + WA × (rA + eH,A) + WB × (rB + eH,B) + WC × (rC + eH,C) + WD × (rD + eH,D)
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:
• The liquidity of 90-day currency forward contracts for country D is good.
d.
1. Bond Market Selection:
Because there are bonds from only five countries in the current portfolio, better risk-adjusted
2. Sector/Credit/Security Selection:
The current portfolio is invested exclusively in government bonds. Other sectors such as
3. Currency Selection:
Active currency management can be used to produce superior risk-adjusted returns. One
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:
Let U.S. be market 1 and U.K. be market 2. The parameter values are: ¯1 = 1.26%, ¯2 = 1.23%,
1 = 4.43%, 2 = 5.55%, Rf = 0.5%.
Accordingly, 12 = 12 ρ12 = (4.43)(5.55)(0.58) = 14.26, 12 = 19.62, 22 = 30.80.
(a) E(Rp) = 1.26w1 + 1.23w2
The variance of the portfolio is:
Var(Rp) = 19.62w12 + 30.80w22 + 2(14.26)w1w2
Some possible portfolios are:
w1w2E(Rp) Var(Rp)
(c) ¯I = Rf + US
Here, = Slope of efficient set = (¯OIP - Rf )/ OIP
¯OIP = (0.79)(1.26) + (0.21)(1.23) = 1.26%
