copyright © 2003 pearson education, inc.slide 19-1 prepared by shafiq jadallah to accompany...

Copyright © 2003 Pearson Education, Inc.

Slide 19-1

Prepared by Shafiq Jadallah

To Accompany

Fundamentals of Multinational FinanceFundamentals of Multinational FinanceMichael H. Moffett, Arthur I. Stonehill, David K. Eiteman

Chapter 19Chapter 19International Portfolio TheoryInternational Portfolio Theory

& Diversification& Diversification


Slide 19-2

Chapter 19International 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


Slide 19-3

Chapter 19International 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

• Explore whether international portfolio theory may be extended to the estimation of a company’s cost of equity using the international CAPM


Slide 19-4

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


Slide 19-5


Portfolio ofU.S. stocks

By diversifying the portfolio, the variance of the portfolio’s return relative to the variance of the market’s return (beta) is reduced to the level of systematic risk -- the risk of the market itself.

Systematicrisk

Totalrisk

Total Risk = Diversifiable Risk + Market Risk (unsystematic) (systematic)

Percentrisk =

Variance of portfolio returnVariance of market return

20

40

60

80

Number of stocks in portfolio

10 20 30 40 501

100


Slide 19-6


Portfolio of international stocks

By diversifying the portfolio, the variance of the portfolio’s return relative to the variance of the market’s return (beta) is reduced to the level of systematic risk -- the risk of the market itself.

Percentrisk =

Variance of portfolio returnVariance of market return

20

40

60

80

Number of stocks in portfolio

10 20 30 40 501

100

Portfolio ofU.S. stocks


Slide 19-7

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


Slide 19-8

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%)


Slide 19-9

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

1r1r1R shares,¥¥/$$

300.1250.01400.01R $

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


Slide 19-10

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


Slide 19-11


Expected Returnof Portfolio, Rp

Expected Riskof Portfolio,p

Domestic portfolioopportunity set

An investor may choose a portfolio of assets enclosed by the Domestic portfolio opportunity set. The optimal domestic portfolio is found at DP, where the Security Market Line is tangent to the domestic portfolio opportunity set. The domestic portfolio with the minimum risk is MR DP.

Rf

Capital MarketLine (Domestic)

•

DP

R DP

•Minimum risk (MRDP )domestic portfolio

MRDP

DP

Optimal domesticportfolio (DP)


Slide 19-12


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


Slide 19-13




An investor may choose a portfolio of assets enclosed by the Domestic portfolio opportunity set. The optimal domestic portfolio is found at DP, where the Capital Market Line is tangent to the domestic opportunity set. The domestic portfolio with the minimum risk is designated MR DP.

Rf

Capital MarketLine (Domestic)

•

DP

R DP


DP

Internationally diversified portfolio opportunity set


Slide 19-14


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


Slide 19-15




An investor may choose a portfolio of assets enclosed by the Domestic portfolio opportunity set. The optimal domestic portfolio is found at DP, where the Security Market Line is tangent to the domestic portfolio opportunity set. The domestic portfolio with the minimum risk is MR DP.

Rf

CML (Domestic)

•

DP

R DP


DP

Internationally diversified portfolio opportunity set

R IP •

IP

IP

Optimal international portfolio

CML (International)


Slide 19-16

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

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

B = second asset

w = weights (respectively)

E(r) = expected return of assets


Slide 19-17


The expected risk is calculated as

ABBABA2B

2B

2A

2AP ww2ww

Where: A = first asset

B = second asset

w = weights (respectively)

σ = standard deviation of assets

= correlation coefficient of the two assets


Slide 19-18


Example of two-asset model

US/GERGERUSGERUS2GER

2GER

2US

2USP ww2ww

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


Slide 19-19


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


Slide 19-20


11 12 130 14 15 16 17 18 19 20

ExpectedPortfolioRisk ( )

Expected PortfolioReturn (%)

12

13

14

15

16

17

18 •Maximumreturn &maximum risk(100% GER)

• Minimum risk combination(70% US & 30% GER)

• Domestic only portfolio(100% US)

• Initial portfolio(40% US & 60% GER)


Slide 19-21


The multiple asset model for portfolio return

)E(rw)E(r ii

N

1iP


Slide 19-22


The multiple asset model for portfolio risk

ijjiji

N

1ij

1-N

1i

2j

2i

N

1iP www


Slide 19-23

National Equity Market Performance


Slide 19-24

National Equity Market Performance


Slide 19-25

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


Slide 19-26


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

i

fi RR measure Sharpe

Where: Ri = average portfolio return

Rf = market return

σ = risk of the portfolio


Slide 19-27


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

i

fi RR measureTreynor

Where: Ri = average portfolio return

Rf = market return

β = beta of the portfolio


Slide 19-28


Example:

– Hong Kong average return was 1.5%

– Assume risk free rate of 5%

– Standard deviation is 9.61%

113.00.0961

0042.0015.0 measure Sharpe


Slide 19-29


Example:

– Hong Kong average return was 1.5%

– Assume risk free rate of 5%

– beta is 1.09

0100.01.09

0042.0015.0 measureTreynor


Slide 19-30


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


Slide 19-31

Are Markets Increasingly Integrated?


Slide 19-32

The International CAPM

Recall that CAPM is

The difference for the international CAPM is that the beta calculation would be relevant for the equity market for analysis instead of the domestic market

)kk(kk fmrfe

m

jjmi

Where: β = beta of the security

= correlation coefficient of the market and the security

σ = standard deviation of return


Slide 19-33

The International CAPM


Slide 19-34

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


Slide 19-35


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


Slide 19-36


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


Slide 19-37


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


Slide 19-38

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


Slide 19-39

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

In theory, the primary distinction in the estimation of the cost of equity for an individual firm using CAPM is the definition of the “market” and a recalculation of the firm’s beta for that market

copyright © 2003 pearson education, inc.slide 19-1 prepared by shafiq jadallah to accompany...

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