copyright © 2009 pearson prentice hall. all rights reserved. chapter 16 international portfolio...

Copyright © 2009 Pearson Prentice Hall. All rights reserved.

Chapter 16

International Portfolio Theory and Diversification

Copyright © 2009 Pearson Prentice Hall. All rights reserved. 16-2

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


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


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


Exhibit 16.1 Portfolio Risk Reduction Through Diversification


Exhibit 16.2 Portfolio Risk Reduction Through International Diversification


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



• 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%)


( )( )[ ] 1r1r1R shares,¥¥/$$ −++=

( )( )[ ] 300.1250.01400.01R $ =−++=

Where: ¥130/¥125 = .04 ¥25,000/¥20,000 = .25

Or = 30.00%


• 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


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


Exhibit 16.3 Optimal Domestic Portfolio Construction



• 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


Exhibit 16.4 The Internationally Diversified Portfolio Opportunity Set



• 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


Exhibit 16.5 The Gains from International Portfolio Diversification


)E(rw)E(rw)E(r BBAAA +=Where: A = one asset

B = second asset

w = weights (respectively)

E(r) = expected return of assets

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


ABBABA2B

2B

2A

2AP ww2ww ρσσσσσ ++=

Where: A = first asset

B = second asset

w = weights (respectively)

σ = standard deviation of assets

ρ = correlation coefficient of the two assets


• The expected risk is calculated as


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

)34.0)(20.0)(15.0)(60.0)(40.0(22

)20.0(2

)60.0(2

)15.0(2

)40.0(151.0 ++=

US/GERGERUSGERUS2GER

2GER

2US

2USP ww2ww ρσσσσσ ++=

US-GER


• Example of two-asset model


)E(rw)E(rw)E(r GERGERUSUS +=

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

)18.0)(60.0()14.0)(40.0(164.0 +=


• Example of two-asset model


Exhibit 16.6 Alternative Portfolio Profiles Under Varying Asset Weights


)E(rw)E(r ii

N

1iP =

Σ=


• The multiple asset model for portfolio return


ijjiji

N

1ij

1-N

1i

2j

2i

N

1iP www ρσσσσ

+===ΣΣ+Σ=


• The multiple asset model for portfolio risk


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


Exhibit 16.7 Real Returns and Risks on the Three Major Asset Classes, Globally, 1900–2000


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


Exhibit 16.8 Correlation Coefficients Between World Equity Markets, 1900–2000


Sharp and TreynorPerformance 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


i

fi RR measure Sharpe

σ−

=

Where: Ri = average portfolio return

Rf = market return

σ = risk of the portfolio


• The Sharpe measure calculates the average return over and above the risk-free rate per unit of portfolio risk


i

fi RR measureTreynor

β−

=Where: Ri = average portfolio return

Rf = market return

β = beta of the portfolio


• 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


113.00.0961

0042.0015.0 measure Sharpe =

−=


• Example: – Hong Kong average return was 1.5%– Assume risk free rate of 5%– Standard deviation is 9.61%


0100.01.09

0042.0015.0 measureTreynor =

−=


• Example: – Hong Kong average return was 1.5%– Assume risk free rate of 5%– beta is 1.09



• 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


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)


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


Exhibit 16.10 Comparison of Selected Correlation Coefficients Between Stock Markets for Two Time Periods (dollar returns)


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



• 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



• 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



• 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



• 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



• 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

copyright © 2009 pearson prentice hall. all rights reserved. chapter 16 international portfolio...

Documents