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country equity
World 0.95 0.86
returns
United Kingdom 0.83 0.49
Canada 0.82 0.72
Germany 0.75 0.33
Sweden 0.73 0.38
Netherlands 0.71 0.56
Australia 0.71 0.47
France 0.70 0.42
Denmark 0.67 0.33
Hong Kong 0.67 0.29
Spain 0.65 0.25
Switzerland 0.65 0.49
Norway 0.63 0.44
Japan 0.58 0.27
Italy 0.55 0.22
Austria 0.46 0.12
Belgium 0.46 0.41

*Source: Datastream.
**Source: Campbell R. Harvey, “The World Price of Covariance Risk,” Journal of Finance, March 1991.




F I G U R E 21.6
100
International
diversification.
Portfolio standard
80
deviation as a percent
of the average
standard deviation of
Percent risk




60
a one-stock portfolio.
Source: B. Solnik, “Why
Not Diversify
40
Internationally Rather Than
U.S. stocks Domestically,” Financial
27
Analysts Journal, July 1976.
20 Reprinted by permission.
Global stocks
11.7

0
1 10 20 30 40 50
Number of stocks



But suppose we replace expected returns with realized average returns from a sample period to
construct an efficient frontier; what is the possible use of this graph?
The ex post efficient frontier (derived from realized returns) describes the portfolio of only
one investor”the clairvoyant who actually expected the precise averages of realized returns
on all assets and estimated a covariance matrix that materialized, precisely, in the actual real-
izations of the sample period returns on all assets. Obviously, we are talking about a slim to
Bodie’Kane’Marcus: VI. Active Investment 21. International Investing © The McGraw’Hill
Essentials of Investments, Management Companies, 2003
Fifth Edition




Dancing in Step
account for a bigger slice of many companies™ overall
Individual stock markets are increasingly being driven
profits”high-tech firms are especially global in their
by global rather than local factors. But why do na-
reach. And finally, the Internet has made it easier for
tional markets not have minds of their own? They did
investors to get information on foreign firms. So firms
have once.
in the same industry, but in different economies, are
Traditionally, one way that investors sought to reduce
valued on a similar basis.
risk was by diversifying overseas: when American shares
By breaking down movements in share prices into
slumped, the loss there would be offset by a gain in, say,
global effects, country-specific effects, and firm-specific
European shares. That, at any rate, was the theory. In
effects, a new study by economists at the IMF tries to
recent years, however, stock markets seem to have
find out what percentage of a stock™s performance is
moved more closely in step with one another. The cor-
due to global rather than country factors. The model
relation between changes in American and European
distinguishes between two kinds of global factors: the
share prices has risen from 0.4 in the mid-1990s to 0.8
global business cycle and global-industry effects, which
last year.
similarly influence firms in the same sector but in differ-
The health of a market™s home economy may mat-
ent countries.
ter less than it used to for a number of reasons. First,
The study finds that there has indeed been a big in-
the scrapping of controls on capital (combined with
crease in the importance of global factors”of both
more efficient trading systems) has increased cross-
kinds”in explaining movements in share prices since
border trading of shares, creating something closer to a
the mid-1990s.
global equity market. Second, it has become increas-
ingly common for big companies to be listed on more SOURCE: Abridged from The Economist, March 22, 2001. Copyright
than one market. Third, as a result of the wave of © 2001 The Economist Newspaper Ltd. All rights reserved. Reprinted
cross-border mergers and acquisitions, overseas profits with permission. Further reproduction prohibited. www.economist.com.




empty set of investors. For all other, less than clairvoyant investors, such a frontier may have
value only for purposes of performance evaluation.
In the world of volatile stocks, some stocks are bound to realize large, unexpected average
returns. This will be reflected in ex post efficient frontiers of enormous “potential.” They will,
however, suggest exaggerated diversification benefits. Such (elusive) potential was enumer-
ated in Chapter 20 on performance evaluation. It has no meaning as a tool to discuss the po-
tential for future investments for real-life investors.


Realistic Benefits from International Diversification
While recent realized returns can be highly misleading estimates of expected future returns,
they are more useful for measuring prospective risk. There are two compelling reasons for
this. First, market efficiency (or even near efficiency) implies that stock prices will be impos-
sible to predict with any accuracy, but no such implication applies to risk measures. Second,
it is a statistical fact that errors in estimates of standard deviation and correlation from realized
data are of a lower order of magnitude than estimates of expected returns. For these reasons,
using risk estimates from realized returns does not exaggerate as much the potential benefits
from diversification.
Figure 21.7 shows the efficient frontier using realized average monthly returns on the stock
indexes of the 25 developed countries, with and without short sales. Even when the (ex post)
efficient frontier is constrained to preclude short sales, it greatly exaggerates the benefits from
diversification. Unfortunately, such misleading efficient frontiers are presented in many arti-
cles and texts on the benefits of diversification.
A more reasonable description of diversification is achievable only when we input reason-
able equilibrium expected returns. Absent superior information, such expected returns are best
based on appropriate risk measures of the assets. The capital asset pricing model (CAPM)
742
Bodie’Kane’Marcus: VI. Active Investment 21. International Investing © The McGraw’Hill
Essentials of Investments, Management Companies, 2003
Fifth Edition




743
21 International Investing




F I G U R E 21.7
Efficient frontier with short sales
3.5
Realized average monthly excess return (%)




Ex-post-efficient
Efficient frontier without short sales
3.0 frontier of country
Country portfolios
portfolios,
2.5 1997“2001.
Finland
2.0

1.5
Greece
1.0
Israel
U.S.
0.5
World
0.0 U.K.
0 2 4 6 8 10 12 14
EAFE Taiwan
0.5
Singapore
New Zealand
Japan
1.0
Standard deviation (% per month)



suggests using the beta of the stock against the world portfolio. To generate expected excess
returns (over the risk-free rate) for all assets, we specify the expected excess return on the
world portfolio. We obtain the expected excess return on each asset by multiplying the beta of
the asset by the world portfolio expected excess return. This procedure presupposes that the
world portfolio will lie on the efficient frontier, at the point of tangency with the world capi-
tal market line. The curvature of the efficient frontier will not be affected by the estimate of
the world portfolio excess return. A higher estimate will shift the curve upward. The capital
market line will have a steeper slope.
We perform this procedure with risk measures estimated from actual returns and further
impose the likely applicable constraint on short sales. We use the betas to compute the ex-
pected return on individual markets, assuming the expected excess return on the world port-
folio is .6% per month. This is a larger excess return than the average realized over the period
1996“2001, but is in line with the average return over the previous 50 years. Varying this es-
timate would not qualitatively affect the results shown in Figure 21.8 (which is drawn on the
same scale as Figure 21.7). The figure shows a realistic assessment that reveals modest but
significant benefits from international diversification using only developed markets. Incorpo-
rating emerging markets would slightly increase these benefits.


Are Benefits from International Diversification Preserved
in Bear Markets?
Some studies (e.g., Longin and Solnik, 1995, or Jacquier and Marcus, 2001) suggest that
correlation in country portfolio returns increase during periods of turbulence in capital mar-
kets. If so, benefits from diversification would be lost exactly when they are needed the most.
For example, a study by Roll (1988) of the crash of October 1987 shows that all 23 country
indexes studied declined over the crash period of October 12“26. This correlation is reflected
in the movements of regional indexes depicted in Figure 21.9. Roll found that the beta of a
country index on the world index (estimated prior to the crash) was the best predictor of that
index™s response to the October crash of the U.S. stock market. This suggests a common
factor underlying the movement of stocks around the world. This model predicts that a
Bodie’Kane’Marcus: VI. Active Investment 21. International Investing © The McGraw’Hill
Essentials of Investments, Management Companies, 2003
Fifth Edition




744 Part SIX Active Investment Management




F I G U R E 21.8 3.5
Efficient frontier of
3.0
country portfolios Efficient frontier without short sales
Expected monthly excess return (%)

(world expected excess
Country portfolios
2.5
return .6% per
month)
2.0

World CML
1.5
Finland
1.0
World
Sweden
Greece
0.5 Israel
U.K. Belgium
0.0
0 2 4 6 8 10 12 14
0.5

1.0
Standard deviation (% per month)




F I G U R E 21.9 Value of one currency unit
1.05

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