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Portfolio Composition
Weight in World Portfolio
Weight of U.S. in Portfolio
Std Dev
Average Return
A. Inclusion based on capitalization
1 U.S. only
0.33
1
5.17
2 0.20
2 Portfolio 1 plus Japan *
0.42
0.79
4.95
2 0.24
3 Portfolio 2 plus U.K. *
0.49
0.67
4.97
2 0.20
4 Portfolio 3 plus France *
0.54
0.61
5.02
2 0.16
5 Portfolio 4 plus Canada *
0.58
0.57
5.07
2 0.10
6 Portfolio 5 plus Hong Kong *
0.62
0.54
5.06
2 0.07
7 Portfolio 6 plus Germany *
0.65
0.51
5.11
2 0.06
8 Portfolio 7 plus Brazil *
0.68
0.49
5.19
0.03
9 Portfolio 8 plus Australia *
0.71
0.46
5.19
0.07
10 Portfolio 9 plus Switzerland *
0.74
0.45
5.18
0.08
11 Portfolio 10 plus China *
0.76
0.44
5.19
0.10
12 Portfolio 11 plus Taiwan *
0.77
0.43
5.19
0.10
13 Portfolio 12 plus Netherlands *
0.78
0.42
5.20
0.10
B. Inclusion based on beta
1 U.S. only
0.33
1
5.17
2 0.20
2 Portfolio 1 plus Pakistan *
0.33
1.00
5.16
2 0.20
3 Portfolio 2 plus Malaysia *
0.34
0.98
5.12
2 0.18
4 Portfolio 3 plus Japan *
0.43
0.78
4.85
2 0.22
5 Portfolio 4 plus Philippines *
0.43
0.77
4.84
2 0.22
6 Portfolio 5 plus Portugal *
0.43
0.77
4.84
2 0.22
7 Portfolio 6 plus Chile *
0.44
0.76
4.83
2 0.20
8 Portfolio 7 plus Israel *
0.44
0.75
4.83
2 0.19
9 Portfolio 8 plus Hong Kong *
0.48
0.70
4.83
2 0.15
10 Portfolio 9 plus Switzerland *
0.50
0.66
4.81
2 0.12
11 Portfolio 10 plus Colombia *
0.51
0.65
4.82
2 0.10
12 Portfolio 11 plus U.K. *
0.58
0.57
4.84
2 0.09
13 Portfolio 12 plus New Zealand *
0.58
0.57
4.84
2 0.09
Table 25.11
Standard deviation of international portfolios by degree of diversification
continued
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914
Portfolio Composition
Weight in World Portfolio
Weight of U.S. in Portfolio
Std Dev
Average Return
C. Inclusion based on standard deviation
1 U.S. only
0.33
1
5.17
2 0.20
2 Portfolio 1 plus Turkey *
0.34
0.98
5.25
2 0.18
3 Portfolio 2 plus Argentina *
0.34
0.98
5.25
2 0.17
4 Portfolio 3 plus Russia *
0.36
0.93
5.39
2 0.08
5 Portfolio 4 plus Indonesia *
0.36
0.92
5.41
2 0.05
6 Portfolio 5 plus Pakistan *
0.36
0.92
5.40
2 0.05
7 Portfolio 6 plus Brazil *
0.39
0.84
5.66
0.10
8 Portfolio 7 plus Finland *
0.40
0.83
5.69
0.10
9 Portfolio 8 plus Poland *
0.40
0.83
5.70
0.11
10 Portfolio 9 plus Hungary *
0.40
0.83
5.70
0.11
11 Portfolio 10 plus Korea *
0.42
0.79
5.80
0.15
12 Portfolio 11 plus India *
0.44
0.74
5.87
0.22
13 Portfolio 12 plus Thailand *
0.45
0.74
5.87
0.23
D. All countries with various weighting schemes
Equally weighted
0.99
0.33
6.14
0.76
By capitalization
0.99
0.33
5.60
0.27
World portfolio actual return
†
1.00
0.33
5.34
2 0.01
Minimum variance portfolio—no short sales
0.99
0.33
4.14
0.02
Minimum variance portfolio—no restrictions
0.99
0.33
2.21
0.32
Table 25.11
concluded
Standard deviation of international portfolios by degree of diversification
*
Portfolio weighted by capitalization of included countries.
†
All countries (including five omitted here) capitalization-weighted.
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4.60
4.80
5.00
5.20
5.40
5.60
5.80
5.85
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.70
0.65
0.75
0.80
Fraction of World Portfolio Capitalization
Standard Deviation (% per month)
Inclusion in Order of Market Capitalization
Inclusion in Order of Beta
Inclusion in Order of SD
A
20.20
20.30
20.10
0.00
0.10
0.20
0.30
0.40
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.70
0.65
0.75
0.80
Fraction of World Portfolio Capitalization
A
verage Return (% per month)
Inclusion in Order of Market Capitalization
Inclusion in Order of Beta
Inclusion in Order of Standard Deviation
B
C H A P T E R
2 5
International
Diversification
915
Figure 25.16 , panel B shows that average returns increase along with the standard devi-
ation of returns. Average returns also increase with beta, at least for low-beta countries,
suggesting that at a qualitative level, world-systematic risk affects asset pricing, consistent
with an international CAPM.
Broadly speaking, these results are consistent with logic of the previous chapters. First,
diversification pays, and risk is rewarded. Second, even with strong home-country bias,
Figure 25.16
Risks and rewards of international portfolios, 2000–2009.
Panel A, Standard deviations for international portfolios; Panel B, Average return
of international portfolios.
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916
P A R T V I I
Applied Portfolio Management
covariance risk still plays a role internationally. We also see that when confined to domes-
tic markets, risk aversion across the world is not too different: Higher country standard
deviations match up with higher average returns.
In panel D of Table 25.11 , we examine risk and reward from fuller international diversi-
fication. Observe first that an equally weighted portfolio of all countries is the riskiest in the
group. At the same time, because this portfolio assigns much larger weights to the smaller,
high-volatility–high-return countries, it also provides a higher average return. At the other
extreme, consider the minimum-variance portfolios, with and without short-sale constraints.
Without the short-sale restriction, the minimum-variance portfolio attains the amazingly low
SD of 2.21%, less than half that of the lowest-SD country (the U.S.). However, this portfolio
is probably not practical, including 22 short positions, the largest being 2 15% (in Sweden).
When short sales are disallowed, the minimum SD is far higher, 4.14%, offering much less
improvement over the capitalization-weighted portfolio. Moreover, these portfolio weights
also would be impractical, with the largest weight in Malaysia (29%), and only 7% in the U.S.
One puzzling and instructive feature of the results in Table 25.11 is the lower average
return on the actual world portfolio (ACWI) compared with the 44-country portfolios. The
difference arises because MSCI country-index portfolios are not capitalization-weighted
portfolios. MSCI uses industry-weighted portfolios, which places greater weights on the
larger stocks in each country. Since small stocks performed better over 2000–2009, the
ACWI portfolio had a lower average return. This pattern is not guaranteed, or necessarily
even likely, to apply to future returns.
25.5
International Investing and
Performance Attribution
The benefits from international diversification may be modest for passive investors, but for
active managers international investing offers greater opportunities. International investing
calls for specialization in additional fields of analysis: currency, country and worldwide
industry, as well as a greater universe for stock selection.
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