1. International Portfolio Theory and Diversification
Chapter 16
International Portfolio Theory and Diversification

2. 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 non-diversifiable 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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3. 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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4. 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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5. Exhibit 16.1 Portfolio Risk Reduction Through Diversification
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6. Exhibit 16.2 Portfolio Risk Reduction Through International Diversification
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7. 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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8. 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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9. Foreign Exchange Risk An illustration with Japanese equity Or = 30.00%
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
Where: ¥130/¥125 = .04 ¥25,000/¥20,000 = .25
Or = 30.00%
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10. Internationalizing the Domestic Portfolio
Classic portfolio theory assumes that a typical investor is risk-averse
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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11. Exhibit 16.3 Optimal Domestic Portfolio Construction
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12. 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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13. Exhibit 16.4 The Internationally Diversified Portfolio Opportunity Set
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14. 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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15. Exhibit 16.5 The Gains from International Portfolio Diversification
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16. 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
Where: A = one asset
B = second asset
w = weights (respectively)
E(r) = expected return of assets
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17. Calculating Portfolio Risk and Return
The expected risk is calculated as
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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18. Calculating Portfolio Risk and Return
Example of two-asset model
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
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19. Calculating Portfolio Risk and Return
Example of two-asset model
Where: EUS = expected return on US security – 14%
EGER = expected return on German security – 18%
wUS = weight of US security
wUS = weight of German security
E(r) = expected return of portfolio
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20. Exhibit 16.6 Alternative Portfolio Profiles Under Varying Asset Weights
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21. Calculating Portfolio Risk and Return
The multiple asset model for portfolio return
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22. Calculating Portfolio Risk and Return
The multiple asset model for portfolio risk
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23. 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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24. Exhibit 16.7 Real Returns and Risks on the Three Major Asset Classes, Globally, 1900–2000
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25. 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 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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26. Exhibit 16.8 Correlation Coefficients Between World Equity Markets, 1900–2000
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27. 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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28. Sharp and Treynor Performance Measures
The Sharpe measure calculates the average return over and above the risk-free rate per unit of portfolio risk
Where: Ri = average portfolio return
Rf = market return
σ = risk of the portfolio
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29. 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
Where: Ri = average portfolio return
Rf = market return
β = beta of the portfolio
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30. Sharp and Treynor Performance Measures
Example:
Hong Kong average return was 1.5%
Assume risk free rate of 5%
Standard deviation is 9.61%
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31. Sharp and Treynor Performance Measures
Example:
Hong Kong average return was 1.5%
Assume risk free rate of 5%
beta is 1.09
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32. 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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33. Exhibit 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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34. 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 ( and ) 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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35. Exhibit Comparison of Selected Correlation Coefficients Between Stock Markets for Two Time Periods (dollar returns)
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36. 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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37. 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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38. 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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39. 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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40. 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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41. 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 , 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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