Solutions Chapter 15 Internationsl Investments

INSTRUCTORS MANUAL: MULTINATIONAL FINANCIAL MANAGEMENT, 9TH ED.

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CHAPTER 15

SUGGESTED ANSWERS TO CHAPTER 15 QUESTIONS 1. As seen in Exhibit 15.2, Hong Kong stocks are over twice as volatile as U.S. stocks. Does that mean that

risk-averse American investors should avoid Hong Kong equities? Explain. ANSWER. No. Although Hong Stock stocks are much more volatile /than U.S. stocks, their systematic component of risk is relatively low because of the low correlation with the U.S. market. The net result is that the systematic risk (beta) of the average Hong Kong stock from a U.S. perspective is only 0.85, compared with a beta of 1.0 for the average U.S. stock. In other words, diversifying into Hong Kong stocks will reduce the riskiness of a portfolio currently concentrated in U.S. stocks. 2. What characteristics of foreign securities lead to diversification benefits for American investors? ANSWER. The two basic characteristics are: a) Many foreign securities are issued by companies that produce goods and services not available from U.S.

companies. b) All U.S. companies are more or less subject to the same cyclical economic fluctuations. Foreign securities by

contrast involve claims on economies whose cycles are not perfectly in phase with the U.S. economic cycle. Thus, just as movements in different stocks partially offset one another in an all-U.S. portfolio, so also movements in U.S. and non-U.S. stocks cancel out each other somewhat.

3. Will increasing integration of national capital markets reduce the benefits of international diversifications? ANSWER. Despite increasing integration of national capital markets, they still don't march in lock step. Some economies and, hence, their markets will do better than others at any given time, so having stakes in several countries still spreads risks. Nonetheless, increasing integration could lead to more comovement in common risk factors (e.g., real interest rate changes). If so, this will increase the correlation of national markets and decrease the risk-reducing benefits of diversifying internationally. Ultimately, it's an empirical issue, and one that should be addressed, as to whether the benefits of international investing are declining. My sense is that international investing can still reduce portfolio risk but the degree of risk reduction is less today than in the past. 4. Studies show that the correlations between domestic stocks are greater than the correlations between domestic and

foreign stocks. Explain why this is likely to be the case. What implications does this fact have for international investing?

ANSWER. Domestic stocks are more highly correlated because they are all subject in one way or another to the state of the domestic economy. The lower correlations between domestic and foreign stocks reflect the lower correlations between the domestic and foreign economies. These lower correlations also imply that international investing is likely to lead to greater diversification than just investing across industries within a country. As the text shows, these lower correlations appear to be persisting despite the greater integration of the global economy. 5. Who is likely to gain more from investing overseas, a resident of the United States or of Mexico? Explain. ANSWER. Mexican investors will gain much more from international investing. The size of the U.S. economy is such that the U.S. and world stock markets are highly correlated whereas the Mexican stock market, being much smaller, shows a much lower correlation with the world stock market. The result is greater diversification (and, hence, risk reduction) benefits for the Mexican investor than for the U.S. investor. In addition, the U.S. has a much greater range of industries than does Mexico, giving much more scope for industry diversification outside Mexico than would be true for a U.S. investor who has access to such a broad range of industries already.

CHAPTER 15: INTERNATIONAL PORTFOLIO INVESTMENT

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6. Suppose that Mexican bonds are yielding more than 100 percent annually. Does this high yield make them suitable for American investors looking to raise the return on their portfolios? Explain.

ANSWER. These returns are denominated in nominal peso terms, subjecting them to currency risk. Nonetheless, holding a small percentage of your portfolio in Mexican bonds will reduce its risk, without sacrificing expected return. This is because arbitrage will equilibrate expected returns across countries at the same time that the actual returns from the Mexican peso bonds are relatively uncorrelated with returns on the U.S. stock market. Hence, the primary reason for holding Mexican bonds is to reduce risk, not raise expected return. 7. According to one investment advisor, "I feel more comfortable investing in Western Europe or Canada. I would

not invest in South America or other regions with a record of debt defaults and restructuring. The underwriters of large new issues of ADRs of companies from these areas assure us that things are different now. Maybe, but who can say that a government that has defaulted on debt won't change the rules again?" Comment on this statement.

ANSWER. It's true. A nation that has already defaulted on its debt is less trustworthy than one that never has. However, this possibility has already been factored into the prices of that nation's bonds and stocks in the form of a large discount to what they would sell for absent that past experience. The real--and important--question is whether the discount is high enough to provide an expected return high enough to compensate for those risks. If so, then Latin American stocks and bonds would be a reasonable investment since they would provide additional diversification benefits. 8. Investors should avoid Hong Kong, given its problematic outlook now that Britain has surrendered the colony to

China. Comment. ANSWER. The problematic outlook for Hong Kong now that it is a special province of China is already reflected in the price of Hong Kong assets (in the form of discounted prices). Thus, the expected risk-adjusted return on Hong Kong assets is the same as that on assets elsewhere. It is precisely these different risks, which are uncoordinated with risks elsewhere, that give rise to the benefits of international diversification. 9. As noted in the chapter, from 1949 to 1990, the Japanese market rose 25,000 percent. a. Given these returns, does it make sense for Japanese investors to diversify internationally? ANSWER. Note that the same argument could be made as to why nonJapanese investors should also invest all their money in Japan. Implicit in this argument is the expectation that historically high returns will persist into the future. Such an expectation is an unreasonable one in efficient markets. Thus, unless one unrealistically expects these superior returns to persist into the future, diversification would make sense for both Japanese and nonJapanese investors. The benefits of this diversification were pointed out in 1990, when the Tokyo Stock Exchange fell 35% in dollar terms (39% in yen), while the Morgan Stanley Capital International World Index fell by "just" 18.6% in dollar terms. b. What arguments would you use to persuade a Japanese investor to invest overseas? ANSWER. Here are two arguments. First, you can't expect stock markets to keep going up in a straight line. All markets entail risk, and one way to counter that risk is through diversification. This argument should by now be bolstered by the crash of the Japanese stock market in 1990. Second, to the extent that the Japanese investor consumes foreign goods and services, international investing can reduce the risk associated with the investor's consumption stream by matching foreign currency inflows with foreign currency outflows. For example, if the yen depreciates, the higher yen cost of buying foreign goods and services will be offset by the higher yen value of foreign assets. c. Why might Japanese (and other) investors still prefer to invest in domestic securities despite the potential gains

from international diversification? ANSWER. If investors buy mostly domestic goods and services (or at least goods and services priced in a domestic context), investing overseas will expose them to currency risk that is not offset by gains on the consumption side. For


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example, if the yen appreciates, the yen value of dollar assets will decline. If the Japanese investor is not consuming much in the way of U.S. goods and services, the reduction in consumption costs will not offset the investment losses. 10. Because ADRs are denominated in dollars and are traded in the United States, they present less foreign exchange

risk to U.S. investors than do the underlying foreign shares of stock. Comment. ANSWER. The answer to this question depends on the distinction between the currency of denomination and the currency of determination. Although the ADR currency of denomination is the dollar, the currency of determination is the local currency (or whatever currency determines the cash flows of the stock). More specifically, the price of an ADR is the price of the share of stock in its foreign currency multiplied by the spot dollar value of the foreign currency. As the spot exchange rate changes, the dollar price of the ADR will also change (unless the foreign currency value of the stock changes in inverse proportion to the change in the spot price, an unlikely scenario). Hence, ADRs are as subject to exchange risk as the underlying shares of foreign stock.

ADDITIONAL CHAPTER 15 QUESTIONS AND ANSWERS 1. An alternative to investing in foreign stocks is to invest in the shares of domestic multinationals. Are

multinationals likely to provide a reasonable substitute for international portfolio investment? ANSWER. No. The empirical evidence clearly shows that multinationals cannot provide a substitute for international portfolio investment. The economic rationale for this is simple. Multinationals already comprise part of the domestic stock index. A subset of an index cannot provide diversification benefits that the full index cannot. If domestic multinationals could provide a reasonable substitute for foreign stocks, then international investing should provide minimal incremental diversification benefits. In fact, the evidence is that international diversification provides substantial risk reduction benefits. 2. Why did Latin American stocks perform so well in recent years? Is this performance likely to continue? Explain. ANSWER. Until recently, Latin American countries followed statist economic policies that shackled their economies, discouraged private initiative, and imposed high risks on private enterprise. Local stock prices discounted these high risks and the lack of profitable private sector growth opportunities. In recent years, Latin American governments have begun to dismantle many of their statist policies. Investors have responded to the resulting more favorable investment opportunities by reducing the discounts they had imposed on local stocks. The result was a jump in stock prices across Latin America. In an efficient market, stocks that are expected to earn excess returns in the future will see their prices jump immediately, thereby eliminating the expectation of future excess returns. The same holds true for stock markets. Current Latin American stock prices already reflect expectations of a more profitable future. Thus, in order for these stock prices to continue to grow as fast as they have in recent years, the future will have to turn out to be much more profitable than it is already expected to be. Since one cannot expect the future to be better than it is already expected to be, Latin American stocks can be expected to earn future returns that are just equal to their risk-adjusted cost of capital. Of course, if one believes that the Latin American future will turn out to be more bountiful than the expectations already embodied in Latin stock prices, then one can expect Latin American stocks to continue their superior performance. Then, however, the issue becomes whether one is privy to inside information or has better insight into economic trends than current investors do. 3. Would you expect emerging markets on average to outperform developed country markets in the future? Explain. ANSWER. As in the answer to question 7, in an efficient market, the performance of emerging markets should be about in line with expectations. This means that the expected risk-adjusted return on emerging markets should be just about equal to that on developed country markets. Emerging markets can be expected to outperform developed country markets only if investors perceive the former markets to be riskier and thereby demand a risk premium (relative to developed country markets) for investing in them. This situation may well be the case, leading to a higher


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expected return on emerging markets than on developed country markets. At the same time, the lower systematic risk of emerging markets may lead to a lower risk premium and lower future expected returns. 4. The Brazilian stock market rose by 165% during 1988. Are American investors likely to be pleased with that

performance? Explain. ANSWER. These returns are stated in nominal cruzeiro terms. American investors are interested in dollar returns. Thus American pleasure with the Brazilian market's performance depends on how much the cruzeiro devalued during the year. In fact, the cruzeiro (actually the cruzado then) devalued by about 90% during the year. Hence, the dollar return on the Brazilian market was approximately -74%. Not good enough to keep investors happy. 5. Comment on the following statement: "On October 19, 1987, the U.S. stock market crashed. As the globe turned

the following day, the devastation spread from New York to Tokyo, Hong Kong, Sydney, and Singapore, and on to Frankfurt, Paris, and London, then back to New York. The domino-style spread of the crash from one market to the next accelerated as international investors attempted to outrun the wave of panic selling from Tokyo to London and back to New York. It is difficult to imagine that some investors thought they had been able to diversify their investment risks by spreading their money across different stock markets around the world, when in fact their downside risks were actually multiplying as one market followed another into decline."

ANSWER. The fact that markets move in sync with each other does not mean that there are no benefits to international diversification. As long as market movements are not perfectly correlated, international portfolio diversification can deliver a higher level of expected return for the same degree of risk or a lower level of risk for the same expected return. Thus, the real issue is an empirical one: Are market movements perfectly correlated? The answer is a resounding no. Here is an important piece of evidence: the performance of the various stock markets around the world during the year 1987. Despite the claim put forth in the statement, there was wide variation in returns among the different markets. This is precisely why international diversification works. 1987 WORLD STOCK MARKET PERFORMANCE Change from 12/31/96 to 12/31/87 (%): in U.S.$ Japan Spain U.K. EAFE* The World Canada Denmark Australia Belgium Norway Netherlands

42.4 32.6 31.5 23.2 14.3 11.6 11.3

6.7 4.3 3.6 3.5

Mexico Singapore/Malaysia United States Austria Sweden Hong Kong Switzerland France Italy West Germany

3.2 0.8 0.6 0.4 0.4

-7.2 -10.7 -15.0 -22.5 -26.0

Source: Morgan Stanley Capital International Perspective (Geneva) * Europe, Australia, Far East Index 6. Persian Gulf countries receive virtually all their income from oil revenues denominated in dollars. At the same

time, they buy substantial amounts of goods and services from Japan and Western Europe. Their investment portfolios are heavily weighted towards short-term U.S. Treasury bills and other dollar-denominated money market instruments. Comment on their asset allocation.

ANSWER. Persian Gulf countries face exchange risk because of the currency mismatch between the dollar revenues they generate through oil sales and the nondollar costs they incur in buying goods and services from Japan and Western Europe. If the U.S. dollar devalues, for example, Persian Gulf oil revenues will buy fewer nonAmerican goods and services. One way to hedge this risk is to hold a substantial fraction of the investment portfolio in nondollar-denominated assets. In this way, the very same event that reduced the purchasing power of their revenues


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would increase the purchasing power of their investment returns. But this is not the strategy they have been following. One possible reason for the divergence is that these countries prefer highly liquid--meaning dollar--assets. 7. In deciding where to invest your money, you read that Germany looks like it's well-positioned to capitalize on

the opening of Eastern Europe. But Britain is troubled by weak growth and high inflation and interest rates. Which of these countries would it make sense to invest in? Explain.

ANSWER. As noted in the answer to the previous question, investors have already factored these expectations into the prices of assets in these countries. As events diverge from the expected, stock prices will adjust to reflect these new expectations so that at any point in time the expected risk-adjusted return from investing in different countries and assets will be the same. And the fact that the risks noted in the question are likely to be uncorrelated with each other should raise the diversification benefits from investing in both nations simultaneously. 8. Does the high volatility of emerging markets lead to high expected returns for investors? ANSWER. Not necessarily. To the extent that emerging markets are open to foreign investors, then these investors are likely to be the marginal investors in these markets. In that case, what matters is the systematic component of that volatility (systematic in the context of the globally-diversified portfolios of the foreign investors). 9. As more U.S. investors shift funds into emerging markets, what factors will drive expected returns? ANSWER. Historically, most foreign investors have stayed out of emerging markets because of local government regulations, various restrictions on foreign investors' ability to own local stocks, high transaction costs, and the significant political and economic risks associated with these markets. The net result is that these markets have been largely segmented and their expected returns driven by the specific risks of those markets (because the marginal investor has not been well diversified). As U.S. and other foreign investors become more important investors, the expected returns in emerging markets will be based more on the contribution of those markets to the systematic risk of a globally-diversified portfolio. The initial reaction of these markets will be a price jump as expected future cash flows get capitalized at a lower rate. In the future, however, this will mean lower expected returns from investing in emerging markets. 10. During 1995, the Morgan Stanley Capital International world index of developed country stock markets rose by

18.7% in dollar terms. In contrast, the IFC emerging markets index fell by just over 17% in dollar terms. Many investment advisors point to this sorry performance of emerging markets as an expensive lesson to investors not to venture too far from home. Do the diverging performances of mature and emerging markets argue against investing in emerging markets?

ANSWER. The experience of 1995 illustrates the riskiness of emerging markets. Paradoxically, however, the poor performance of emerging markets in a year when practically all developed country stock markets jumped is reassuring. By providing more evidence that emerging and mature markets move independently of each other, the diverging performances of these markets in 1995 bolster the case for diversifying across these different sets of markets. Indeed, the fact that practically all mature markets moved together in 1995 argues against putting all of one's money in these markets. It makes sense for investors to hedge against risk by putting some of their money in markets that tend to move independently of their main investment markets, thereby making their overall portfolio less risky than it was fully invested in highly correlated markets. One who had followed this advice would have benefited in 1993, when emerging markets significantly outperformed mature ones.

SUGGESTED SOLUTIONS TO CHAPTER 15 PROBLEMS 1. During the year the price of British gilts (government bonds) went from 102 to 106, while paying a coupon of

9. At the same time, the exchange rate went from 1:$1.76 to 1:$1.62. What was the total dollar return, in percent, on gilts for the year?


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ANSWER. Rewriting Equation 15.4, the one-period total dollar return on a foreign bond investment r$ can be calculated as follows:

where B(t) = local currency bond price at time t C = local currency coupon income

G = percent change in dollar value of LC With an initial bond price of 102, coupon income of 9, end-of-period bond price of 106, and pound depreciation of (1.62 - 1.76)/1.76 = -7.95%, the total dollar return is 3.79%:

r$ = [1 + (106 - 102 + 9)/102](1 - .0795) - 1= (1.1275)(0.9205) - 1= 3.79% 2. During a recent six-month period, Swiss government bonds yielded a local-currency return of -1.6 percent.

However, the Swiss franc rose by 8 percent against the dollar over this six-month period. Corresponding figures for France were 1.8 percent and 2.6 percent. Which bond earned the higher U.S. dollar return? What was the return?

ANSWER. The dollar return on Swiss bonds equaled (1 - .016)(1 + 0.08) - 1 = 6.27%. The return on French bonds was lower at (1.018)(1.026) - 1 = 4.45%. In this case, Swiss franc appreciation more than offset the lower local currency return on Swiss bonds. 3. During the year Toyota Motor Company shares went from 9,000 to 11,200, while paying a dividend of 60. At

the same time, the exchange rate went from $1 = 145 to $1 = 120. What was the total dollar return, in percent, on Toyota stock for the year?

ANSWER. Rewriting Equation 15.5, the one-period total dollar return on a foreign stock investment R$ can be calculated as follows:

where P(t) = local currency stock price at time t

DIV = local currency dividend income Substituting in the numbers yields a total dollar return on Toyota stock for the year of 51.17%:

R$ = [1 + (11,200 - 9,000 + 60)/9,000](1+.2083) - 1 = (1.2511)(1.2083) - 1 = 51.17% Note that yen appreciation during the year was (145 - 120)/120 = 20.83%.

g) + (1 B(0)

C + B(0) B(1) + 1 = r + 1

(loss) gain

Currency x

returncurrency Local

= returnDollar

$

g) + (1 P(0)

DIV + P(0) P(1) + 1 = R + 1

gain(lossCurrency x

returncurrency Local

= returnDollar

$


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4. During 1989, the Mexican stock market climbed 112 percent in peso terms while the peso depreciated by 28.6

percent against the U.S. dollar. What was the dollar return on the Mexican stock market during the year? ANSWER. According to these data, the dollar return on the Mexican stock market during 1989 was 51.37%: R$ = (1 + 1.12)(1 - 0.286) - 1 = 51.37% 5a. In 1992, the Brazilian market rose by 1,117 percent in cruzeiro terms, while the cruzeiro fell by 91.4 percent in

dollar terms. Meanwhile, the U.S. market rose by 8.5 percent. Which market did better? ANSWER. The dollar return on the Brazilian market can be calculated using Equation 15.5: R$ = (1 + 11.17)(1 - 0.914) - 1 = 4.66% The numbers reflect the fact that a return of 1,127% is equivalent to receiving an additional Cr11.17 for each Cr1 invested. Based on these figures, the U.S. market return of 8.5% bested the dollar return on the Brazilian market by almost 4 percentage points. b. In 1993, the Brazilian market rose by 4,190 percent in cruzeiro terms, while the cruzeiro fell by 95.9 percent in

dollar terms. Did the Brazilian market do better in dollar terms in 1992 or in 1993? ANSWER. Redoing the numbers in the answer to part a, we see that the Brazilian market did far better in 1993 than in 1992: R$ = (1 + 41.90)(1 - 0.959) - 1 = 75.89% In this case, the extraordinarily large local currency return more than offset the dramatic devaluation of the cruzeiro. 6. Suppose that the dollar is now worth 1.1372. If one-year German bunds are yielding 9.8 percent and one-year

U.S. Treasury bonds are yielding 6.5 percent, at what end-of-year exchange rate will the dollar returns on the two bonds be equal? What amount of euro appreciation or depreciation does this equilibrating exchange rate represent?

ANSWER. To begin, given that German bunds are yielding more than U.S. Treasuries, it is clear that for dollar returns on these two securities to equilibrate, the euro must depreciate against the dollar by about the interest differential, which is 3.3%. Using Equation 15.4, the expected dollar return on investing $1 in a bund (after first converting it into 1.1372) for a year can be found as 1.1372(1.098)e1 = 1.2486e1 where e1 is the unknown end-of-year exchange rate ($/). Note that ex ante, one cannot anticipate any capital gains or losses on investing. Setting this figure equal to the $1.065 expected dollar return from investing one dollar in a Treasury bond yields the solution e1 = $0.8529, which converts into a direct quote for the dollar of 1.1724. This exchange rate entails a euro depreciation of (1.1372 - 1.1724)/1.1724 = -3.01% against the dollar. Alternatively, the dollar has appreciated against the euro by (1.1724 - 1.1372)/1.1372 = 3.10%. 7. In 1990, Matsushita bought MCA Inc. for $6.1 billion. At the time of the purchase, the exchange rate was about

145/$. By the time that Matsushita sold an 80% stake in MCA to Seagram for $5.7 billion in 1995, the yen had appreciated to a rate of about 97/$.

a. Ignoring the time value of money, what was Matsushita's dollar gain or loss on its investment in MCA? ANSWER. If an 80% stake in MCA was worth $5.7 billion, then the entire firm was worth $7.125 billion. Based on this valuation, Matsushita actually made $1.025 billion on its purchase of MCA. That is, by buying MCA at a price of $6.1 billion and selling it for a price that valued the business at $7.125 billion, Matsushita made $1.025 billion.


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b. What was Matsushita's yen gain or loss on the sale? ANSWER. Taking into account the differences in exchange rates, Matshushita paid 884,500,000,000 (6,100,000,000 x 145) for MCA in 1990 and sold MCA in 1995 for a price that valued it at 691,125,000,000 (7,125,000,000 x 97). The net result was a loss for Matsushita of 193,375,000,000 on its purchase of MCA. c. What did Matsushita's yen gain or loss translate into in terms of dollars? What accounts for the difference

between this figure and your answer to part a? ANSWER. Matsushita's yen loss converts into a dollar loss of $1,993,556,701 (193,375,000,000/97). This figure differs from the answer in part a because it takes into account the change in exchange rates between 1990 and 1995. In effect, it asks what would have happened if Matsushita had held onto its yen instead of converting them into a dollar asset that didn't appreciate in line with the yen's appreciation. In other words, this computed dollar loss represents an opportunity cost. 8. Suppose that the standard deviations of the British and U.S. stock markets have risen to 38 percent and 22

percent, respectively, while the correlation between the U.S. and British markets has risen to 0.67. What is the new beta of the British market from a U.S. perspective?

ANSWER. Using the following formula to calculate the beta of the British market we can calculate the new British market beta from the perspective of a U.S. investor to be 0.67 x 38/22 = 1.16. 9. A portfolio manager is considering the benefits of increasing his diversification by investing overseas. He can

purchase shares in individual country funds with the following characteristics: U.S. (%) U.K. (%) Spain (%) Expected return Standard deviation of return Correlation with U.S.

15 10 1.0

12 9

0.33

5 4

0.06 a. What is the expected return and standard deviation of return of a portfolio with 25 percent invested in the United

Kingdom and 75 percent in the United States? ANSWER. Use the formulas rp = w1r1 + w2r2 and p2 = w1212 + w2222 + 2w1w2r1212 to calculate the means and standard deviations of the portfolios.

% US

%UK

Expected Return

Standard Deviation

25 50 75

75 50 25

12.75 13.50 14.25

7.93 7.75 8.51

b. What is the expected return and standard deviation of return of a portfolio with 25 percent invested in Spain and

75 percent in the United States? ANSWER. Using the same formulas as in the answer to part a, we can calculate the means and standard deviations of the various portfolios as follows:

market U.S. of deviation Standardmarket British of

deviation Standard

x market U.S.

withnCorrelatio =

betamarket British


9

%US %Spain Expected Return

Standard Deviation

25 50 75

75 50 25

7.50

10.00 12.50

4.02 5.50 7.63

c. Calculate the expected return and standard deviation of return of a portfolio with 50 percent invested in the United States and 50 percent in the United Kingdom. With 50 percent invested in the United States and 50 percent invested in Spain.

d. Calculate the expected return and standard deviation of return of a portfolio with 25 percent invested in the

United States and 75 percent in the United Kingdom. With 25 percent invested in the United States and 75 percent invested in Spain.

ANSWER. The answers to items a and b contain the answers to items c and d. e. Plot these two sets of risk-return combinations (a) through (d) as in Exhibit 15.5. Which leads to a better set of

risk-return choices, Spain or the United Kingdom? ANSWER. As the following diagram shows, Spain offers better diversification opportunities because its fund returns are less correlated with the U.S. market (corr. = 0.06) than U.K. funds (corr. = 0.33). However, it also obvious that investors are sacrificing a significant amount of expected return by choosing to add Spanish stocks to their portfolios.

6%

7%

8%

9%

10%

11%

12%

13%

14%

15%

3% 4% 5% 6% 7% 8% 9%

Expected return

S tandard deviation

Ri sk -R e tur n Combina ti ons for U .S ., Spai n, a nd the U .K .

Po rtfo lio C omb in at i on s o f U .S. an d Sp an ish F un ds

Po rtfo lio C omb in at i on s o f U .S. an d U.K. F un ds

f. How can you achieve an even better risk-return combination? ANSWER. An investor can improve on the risk-return combination selected in the answer to part d by including the U.K. fund in the portfolio. You can never do worse by expanding the set of portfolio assets. The appropriate percent to invest in the U.K. fund depends on the correlation between the U.K. fund and the Spain fund, which we don't know.


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10. Suppose that the standard deviation of the return on Nestl, a Swiss firm, in terms of Swiss francs is 19 percent and the standard deviation of the rate of change in the dollar-franc exchange rate is 15 percent. In addition, the estimated correlation between the Swiss franc return on Nestl and the rate of change in the exchange rate is 0.17. Given these figures, what is the standard deviation of the dollar rate of return on investing in Nestl stock?

ANSWER. According to Equation 15.8 in the text, we can write the standard deviation of the dollar return, $, as $ = [f2 + g2 + 2fgf,g] where f2 = the variance (the standard deviation squared) of the foreign currency return

g2 = the variance of the change in the exchange rate f,g = the correlation between the foreign currency return and the exchange rate change

Applying this equation, the standard deviation of the dollar rate of return on investing in Nestl stock is 27.33%:

ADDITIONAL CHAPTER 15 PROBLEMS AND SOLUTIONS 1. On February 14, 1994, the dollar fell from 106.85 to 102.65. Meanwhile, the Tokyo stock market fell 1.63% as

measured in yen. What was the one-day dollar return on the Tokyo stock market? ANSWER. On that day, the dollar value of the yen rose by (106..85 - 102.65)/102.65 = 4.09%. Using Equation 15.5 (see the answer to problem 3), the one-day return on the Tokyo Stock Exchange was R$ = (1 - 0.0163)(1.0409) - 1 = 2.39% 2. During 1997, the Korean Stock Exchange's composite index fell by 42%, while the won lost half its value against

the dollar. What was the combined effect of these two declines on the dollar return associated with Korean stocks during 1997?

ANSWER. According to these data, the dollar return on the Korean Stock Exchange during 1997 was -71%: R$ = (1 - 0.42)(1 - 0.5) - 1 = -71%

3. Here are data on stock market returns and exchange rate changes during 1988 for 12 stock markets. Determine the dollar return on each of these markets.

0.2733 = .17) x .15 x .19 x 2 + 150. + 19(0. = (Nestle) 221/2

$


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Country

Return in

Local Currency

(%)

LC Units/Dollar

12/31/87 LC Units/Dollars

12/31/88

Australia Belgium Canada France West Germany Holland Italy Japan Spain Sweden Switzerland United Kingdom

14.5 56.3 10.9 56.8 27.9 42.8 26.2 44.8 25.0 60.5 31.9 9.1

1.41 35.1 1.29 5.65 1.68 1.88 1230 129 114 6.03 1.37 0.56

1.17 38.8 1.20 6.31 1.85 2.09 1357 128 116 6.30 1.58 0.57

ANSWER. Using Equation 15.5, here are the total dollar returns on these markets during 1988:

Currency gain

(loss) (%) Total dollar return (%)

Australia Belgium Canada France West Germany Holland Italy Japan Spain Sweden Switzerland United Kingdom

20.5 -9.5 7.5

-10.5 -9.2

-10.1 -9.4 0.8

-1.7 -4.3

-13.3 -1.8

38.0 41.4 19.2 40.4 16.2 28.5 14.4 45.9 22.8 53.6 14.4 7.2

4. Suppose that over a ten-year period the annualized peseta return of a Spanish bond has been 12.1%. If a comparable dollar bond has yielded an annualized return of 8.3%, what cumulative devaluation of the peseta over this period would be necessary for the return on the dollar bond to exceed the dollar return on the Spanish bond? ANSWER. The answer to this question can be found by solving the following equation: (1.121)10(1 - d) = (1.083)10 where d is the cumulative peseta devaluation over the ten-year period. In other words, the dollar return on investing in the Spanish bond just equals the dollar return on investing in the comparable dollar-denominated bond. The solution to this equation is d = 0.2917, or a cumulative peseta devaluation of 29.17%. 5. The standard deviations of U.S. and Mexican returns over the period 1989-1993 were 12.7% and 29.7%, respectively. In addition, the correlation between the U.S. and Mexican markets over this period was 0.34. Assuming that these data reflect the future as well, what is the Mexican market beta relative to the U.S. market? ANSWER. Using the formula presented in the text, and substituting in the numbers in the problem, we have


12

In other words, despite the much greater riskiness of the Mexican market relative to the U.S. market, the low correlation between the two markets led to a Mexican market beta (0.80) which is lower than the U.S. market beta (1.00). 6. In an attempt to diversify your portfolio internationally, you must decide how to invest in Brazil. You can invest in an index fund that replicates the Brazilian stock market, or you can buy shares of the Brazil Fund traded on the New York Stock Exchange. The covariance of dollar returns on the index with the S&P 500 is 0.02; the covariance of dollar returns on the Brazil Fund with the S&P 500 is 0.03; the variance of the S&P 500 index is 0.035; and the beta of the Brazil Fund with respect to the Brazilian index is 0.90. In addition, the Brazil Fund and the Brazilian index are expected to yield annual dollar returns of 21 percent and 19 percent, respectively, in contrast to expected annual returns of 18 percent from investing in the S&P 500. a. Ignoring other considerations, should you buy the Brazil Fund or the Brazilian index fund? ANSWER. To answer this question, we need to determine which investment provides a better risk-return trade-off in the context of the U.S. market, which is represented here by the S&P 500. This means that we must calculate the beta for the Brazilian index with respect to the S&P 500, Brazilian index, and the corresponding beta for the Brazil Fund, Brazil Fund (the Brazil Fund's beta relative to the Brazilian index is irrelevant). By definition, Brazilian index = 0.02/0.035, or 0.57, and Brazil Fund = 0.03/0.035, or 0.86. Given these betas and the 5% Treasury bill rate mentioned in Part b, the CAPM predicts an expected return on the Brazilian index of 5% + 0.57(18% - 5%) = 12.43% and an expected return on the Brazil Fund of 5% + .86(18% - 5%) = 16.14%. Given their actual expected returns 19 percent and 21 percent, respectively, both investments appear to offer excess risk-adjusted returns, but the excess return for the Brazilian index of 6.57% (19% - 12.43%) exceeds the Brazil Fund's excess return of 4.86% (21% - 16.14%). Hence, the Brazilian index fund appears to provide a better risk-return trade-off than the Brazil Fund. b. Suppose the U.S. Treasury bill rate is 5 percent. Assuming the S&P 500 has a beta of 1, plot the capital market

line and show the positions of the Brazil Fund and the Brazilian stock index relative to the capital market line. ANSWER. The following chart shows the position of the Treasury bill, S&P 500, Brazil Fund, and Brazilian index relative to the capital market line. Notice that both the Brazil Fund and Brazilian index are above the capital market line. In other words, for the same degree of systematic risk, their expected return exceeds the return expected in the United States.

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Documents

Solutions Chapter 15 Internationsl Investments