978-0077861605 Chapter 15 Solution Manual Part 2

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 = 12 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%