Chapter 16
International
Portfolio
Theory and
Diversification
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International Portfolio Theory &
Diversification: Learning Objectives
• Separate total risk of a portfolio into two components,
diversifiable and non-diversifiable
• Demonstrate how both the diversifiable and nondiversifiable risks of an investor’s portfolio may be
reduced through international diversification
• Explore how foreign exchange risk impacts the
individual investor investing internationally
• Define the optimal domestic portfolio and the optimal
international portfolio
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International Portfolio Theory &
Diversification: Learning Objectives
• Review the recent history of equity market
performance globally, including the degree to
which the markets are more or less correlated in
their movements
• Examine the question of whether markets appear
to be more or less integrated over time
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International Diversification & Risk
• Portfolio Risk Reduction
– The risk of a portfolio is measured by the ratio of the variance
of the portfolio’s return relative to the variance of the market
return
– This is defined as the beta of the portfolio
– As an investor increases the number of securities, the
portfolio’s risk declines rapidly at first and then
asymptotically approaches the level of systematic risk of the
market
– A fully diversified portfolio would have a beta
of 1.0
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Exhibit 16.1 Portfolio Risk Reduction
Through Diversification
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Exhibit 16.2 Portfolio Risk Reduction
Through International Diversification
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Foreign Exchange Risk
• The foreign exchange risks of a portfolio, whether it be
a securities portfolio or the general portfolio of
activities of the MNE, are reduced through
diversification
• Internationally diversified portfolios are the same in
principle because the investor is attempting to combine
assets which are less than perfectly correlated, reducing
the risk of the portfolio
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Foreign Exchange Risk
• An illustration with Japanese equity
– US investor takes $1,000,000 on 1/1/2002 and invests in
stock traded on the Tokyo Stock Exchange (TSE)
• On 1/1/2002, the spot rate was ¥130/$
– The investor purchases 6,500 shares valued at ¥20,000 for a
total investment of ¥130,000,000
– At the end of the year, the investor sells the shares at a price
of ¥25,000 per share yielding ¥162,500,000
• On 1/1/2003, the spot rate was ¥125/$
– The investor receives a 30% return on investment
($300,000/$1,00,000 = 30%)
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Foreign Exchange Risk
• An illustration with Japanese equity
– The total return reflects not only the appreciation in
stock price but also the appreciation of the yen
– The formula for the total return is

R  1 r
$
¥/$
1  r
Where: ¥130/¥125 = .04
shares,¥
1
¥25,000/¥20,000 = .25
R $  1  0.4001  0.250  1  .300
Or = 30.00%
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Internationalizing the Domestic
Portfolio
• Classic portfolio theory assumes that a typical investor is riskaverse
– The typical investor wishes to maximize expected return per unit of
expected risk
• An investor may choose from an almost infinite choice of
securities
• This forms the domestic portfolio opportunity set
• The extreme left edge of this set is termed the efficient frontier
– This represents the optimal portfolios of securities that possess the
minimum expected risk per unit of return
– The portfolio with the minimum risk among all those possible is the
minimum risk domestic portfolio
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Exhibit 16.3 Optimal Domestic
Portfolio Construction
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Internationalizing the Domestic
Portfolio
• If the investor is allowed to choose among an
internationally diversified set of securities, the
portfolio set of securities shifts to upward and to
the left
• This is called the internationally diversified
portfolio opportunity set
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Exhibit 16.4 The Internationally
Diversified Portfolio Opportunity Set
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Internationalizing the Domestic Portfolio
• This new opportunity set allows the investor a
new choice for portfolio optimization
• The optimal international portfolio (IP) allows
the investor to maximize return per unit of risk
more so than would be received with just a
domestic portfolio
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Exhibit 16.5 The Gains from
International Portfolio Diversification
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Calculating Portfolio Risk
and Return
• The two-asset model consists of two components
– The expected return of the portfolio
– The expected risk of the portfolio
• The expected return is calculated as
E(rA )  w A E(rA )  w BE(rB )
Where: A = one asset
B = second asset
w = weights (respectively)
E(r) = expected return of assets
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Calculating Portfolio Risk
and Return
• The expected risk is calculated as
 P  w   w   2w A w B A B  AB
2
A
2
A
2
B
2
B
Where: A = first asset
B = second asset
w = weights (respectively)
σ = standard deviation of assets
 = correlation coefficient of the two assets
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Calculating Portfolio Risk
and Return
• Example of two-asset model
2
2
2
 P  w 2US US
 w GER
 GER
 2w USw GER US GER  US/GER
US-GER
Where: US = US security
GER = German security
wUS = weight of US security – 40%
wGER = weight of German security – 60%
σUS = standard deviation of US security – 15%
ρ = correlation coefficient of the two assets – 0.34
0.151 
2
2
2
2
(0.40) (0.15)  (0.60) (0.20)  2(0.40)(0.60)(0.15)(0.20)(0.34)
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Calculating Portfolio Risk
and Return
• Example of two-asset model
E(r )  w USE(rUS )  w GER E(rGER )
Where: EUS
EGER
wUS
wUS
E(r)
= expected return on US security – 14%
= expected return on German security – 18%
= weight of US security
= weight of German security
= expected return of portfolio
0.164  (0.40)(0.14)  (0.60)(0.18)
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Exhibit 16.6 Alternative Portfolio
Profiles Under Varying Asset Weights
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Calculating Portfolio Risk
and Return
• The multiple asset model for portfolio return
N
E(rP )   w i E(ri )
i 1
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Calculating Portfolio Risk
and Return
• The multiple asset model for portfolio risk
N
N -1 N
 P   w     w i w j i j ij
i 1
2
i
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2
j
i 1 ji 1
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National Markets & Asset
Performance
• As previously discussed, asset portfolios are
traditionally constructed using both interest bearing
risk-free assets and risky assets
• The following exhibit presents the performance of
major individual national markets by asset category for
the entire 21st century (1900 – 2000)
• This exhibit demonstrates that, at least for the past 100
years ending in 2000, the risk of investing in equity
assets has been rewarded with substantial returns
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Exhibit 16.7 Real Returns and Risks
on the Three Major Asset Classes,
Globally, 1900–2000
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National Markets & Asset
Performance
• The next exhibit reports correlation coefficients
between world equity markets for the 1900 – 2000
period
– The correlation coefficients in the lower-bottom-left of the
exhibit are for the entire period
– The correlation coefficients in the upper-top-right of the
exhibit are for the 1996-2000 period
• The relatively low correlation coefficients among
returns for the 16 countries for either period indicates
great potential for international diversification
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Exhibit 16.8 Correlation Coefficients
Between World Equity Markets, 1900–2000
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Sharp and Treynor
Performance Measures
• Investors should not examine returns in isolation
but rather the amount of return per unit risk
• To consider both risk and return for portfolio
performance there are two main measures
applied
– The Sharpe measure
– The Treynor measure
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Sharp and Treynor
Performance Measures
• The Sharpe measure calculates the average
return over and above the risk-free rate per unit
of portfolio risk
Sharpe measure 
Ri  Rf
i
Where: Ri = average portfolio return
Rf = market return
σ = risk of the portfolio
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Sharp and Treynor
Performance Measures
• The Treynor measure is similar to Sharpe’s measure
except that it measures return over the portfolio’s beta
• The measures are similar dependant upon the
diversification of the portfolio
– If the portfolio is poorly diversified, the Treynor will show a
high ranking and vice versa for the Sharpe measure
Treynor measure 
Ri  Rf
i
Where: Ri = average portfolio return
Rf = market return
β = beta of the portfolio
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Sharp and Treynor
Performance Measures
• Example:
– Hong Kong average return was 1.5%
– Assume risk free rate of 5%
– Standard deviation is 9.61%
Sharpe measure 
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0.015  0.0042
0.0961
 0.113
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Sharp and Treynor
Performance Measures
• Example:
– Hong Kong average return was 1.5%
– Assume risk free rate of 5%
– beta is 1.09
0.015  0.0042
Treynor measure 
 0.0100
1.09
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Sharp and Treynor
Performance Measures
• For each unit of risk the Hong Kong market rewarded
an investor with a monthly excess return of 0.113%
• The Treynor measure for Hong Kong was the second
highest among the global markets and the Sharpe
measure was eighth
• This indicates that the Hong Kong market portfolio was
not very well diversified from the world market
perspective
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Exhibit 16.9 Summary Statistics of the Monthly Returns for
18 Major Stock Markets, 1977–1996 (all returns converted
into U.S. dollars and include all dividends paid)
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Are Markets Increasingly
Integrated?
• It is often said that as capital markets around the world
become more and more integrated over time, the
benefits of diversification will be reduced
• The following exhibit illustrates two periods (1977-86
and 1987-96) correlation coefficients
• The overall picture is that correlations have increased
over time, answering the question “Are markets
increasing integrated” with a resounding “Yes”
• However, the correlation coefficients are still far from
1.0, providing plenty of risk-reducing opportunities for
international portfolio diversification
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Exhibit 16.10 Comparison of Selected
Correlation Coefficients Between Stock
Markets for Two Time Periods (dollar returns)
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Summary of Learning Objectives
• The total risk of any portfolio is composed of
systematic (the market) and unsystematic (individual
securities) risk. Increasing the number of securities in a
portfolio reduces the unsystematic risk component
• An internationally diversified portfolio has a lower
beta. This means that the portfolio’s market risk is
lower than that of a domestic portfolio; this arises
because the returns on the foreign stocks are not closely
correlated with returns on US stocks
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Summary of Learning Objectives
• Investors construct internationally diversified portfolios
in an attempt to combine assets which are less than
perfectly correlated, reducing the total risk of the
portfolio. In addition, by adding assets outside the
home market, the investor has now tapped into a larger
pool of potential investments
• International portfolio construction is also different in
that when the investor acquires assets outside their
home market, the investor may also be acquiring a
foreign-currency denominated asset
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Summary of Learning Objectives
• The investor has actually acquired two assets – the
currency of denomination and the asset subsequently
purchased with the currency – two assets in principle
but two in expected returns and risks
• The foreign exchange risks of a portfolio are reduced
through international diversification
• The individual investor will search out the optimal
domestic portfolio which combines the risk-free asset
and a portfolio of domestic securities found on the
efficient frontier
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Summary of Learning Objectives
• This portfolio is defined as the optimal domestic
portfolio because it moves out into risky space at the
steepest slope – maximizing the slope of expected
return over expected risk – while still touching the
opportunity set of domestic portfolios
• The optimal international portfolio is found by finding
that point on the capital market line which extends from
the risk-free rate of return to a point of tangency along
the internationally diversified efficient frontier
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Summary of Learning Objectives
• The investor’s optimal portfolio possesses both higher
than expected portfolio return and lower expected risk
than the purely domestic portfolio
• Risk reduction is possible through international
diversification because the returns of different stock
market around the world are not perfectly positively
correlated
• The relatively low correlation coefficients among
returns of 18 major stock markets in the 20-year period
indicates great potential for international diversification
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Summary of Learning Objectives
• The overall picture is that the correlations have
increased over time
• Nevertheless, 91 of the 153 correlations had overall
means still below 0.5 in 1987-1996, thus markets are
increasingly integrated
• However, although capital market integration has
decreased some benefits of international portfolio
diversification, the correlations between markets are
still far from 1.0
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