Investments, tenth edition

 Figure 25.12 

Ex post efficient frontier of country portfolios, 2001–2005  

World

Austria

Korea

New Zealand

−0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0

2

4

6

U.S.

8

10

12

Standard Deviation (% per month)

Realized A

verage Monthly Excess Return (%)

Efficient Frontier with Short Sales

Efficient Frontier w/ No Short Sales

Country Portfolios

bod61671_ch25_882-925.indd   908

bod61671_ch25_882-925.indd   908

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  C H A P T E R  

2 5

 International 

Diversification 

909

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 capital 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 

simply shift the curve upward. 

 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 

expected return on individual markets, assuming the expected excess return on the world 

portfolio is .6% per month. This excess return is in line with the average return over the 

previous 50 years. Varying this estimate would not qualitatively affect the results shown 

in  Figure 25.13  (which is drawn on the same scale as  Figure 25.12 ). The figure shows a 

realistic assessment that reveals modest but significant benefits from international diver-

sification using only developed markets. Incorporating emerging markets would further 

increase these benefits.