IBUS 302:
International Finance
Topic 16–Portfolio Analysis
Lawrence Schrenk, Instructor
1 (of 25)
Learning Objectives
1.
2.
3.
4.
Calculate the return, standard deviation and
correlation of foreign equity.▪
Describe international diversification.
Explain the International Asset Pricing
Model (IAPM)
Discuss home bias.▪
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Returns, Volatility,
Correlation
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The Algebra of Portfolio
Theory
Assumptions


Nominal returns are normally distributed
Investors want more return and less risk in their
functional currency
Expected Return on a Portfolio
E[rP] = Si xi E[ri]
Portfolio Variance
Var(rP) = sP2 = Si Sj xi xj sij
where sij = rij si sj
The algebra of portfolio diversification
Expected Return on a
Portfolio
E[ri]
σi
American (A)
11.1% 16.9%
Japanese (J)
15.7% 34.6%
Example: Equal weights of A and J
E[rP] = xA E[rA] + xJ E[rJ]
= (½)(0.111)+(½)(0.157)
= 0.134, or 13.4%
The algebra of portfolio diversification
Variance of a Portfolio
A American
J Japanese
E[ri]
si
11.1% 16.9%
15.7% 34.6%
Correlation
A
J
1.000 0.302
0.302 1.000
sP2 = xA2 sA2 + xJ2 sJ2 + 2 xA xJ rAJ sA sJ
= (½)2(0.169)2 + (½)2(0.346)2
+ 2(½)(½)(0.302)(0.169)(0.346) = 0.0459
sP = (0.0459)1/2 = 0.214, or 21.4%
The algebra of portfolio diversification
Diversification
J
16%
Return
r = -1
14%
r = +1
r = +0.302
12%
A
10%
0%
10%
The benefits of international portfolio diversification
20%
30%
40%
s
Key Results of
Portfolio Theory

The extent to which risk is reduced by portfolio
diversification depends on the correlation of assets
in the portfolio.

As the number of assets increases, portfolio
variance becomes more dependent on the
covariances (or correlations) and less dependent
on variances.

The risk of an asset when held in a large portfolio
depends on its covariance (or correlation) with
other assets in the portfolio.
The benefits of international portfolio diversification
International
Portfolio Diversification
Return
W
M
rF
Potential for…
 higher returns
 lower portfolio risk
The benefits of international portfolio diversification
s
Domestic versus
International Diversification
U.S. diversification only
International diversification
1.0
0.5
26%
12%
5
10
15
20
Number of stocks in portfolio
The benefits of international portfolio diversification
25
International Stock
Returns (1970-2006)
Mean Stdev
βW
SI
Australia
11.5
24.2
0.194
0.976
Canada
11.9
19.5
0.262
0.975
France
14.4
27.9
0.272
1.109
Germany
13.8
29.8
0.235
1.117
Japan
15.7
34.6
0.257
1.355
Switzerland
14.4
24.2
0.314
0.973
U.K.
14.5
27.5
0.280
1.124
U.S.
11.1
16.9
0.254
0.849
World
11.3
17.0
0.265
1.000
U.S. T-bills
6.8
3.2
0.000
-0.015
βW versus the MSCI world stock market index
Sharpe Index (SI) = (rP - rF) / σP
Value ($bn)
932
994
1,698
1,213
2,969
970
3,252
14,968
32,785
-
International Equity
Correlations (1970-2006)
Canada
France
Germany
Japan
Switzerland
U.K.
U.S.
World
Aus
Can
Fra
Ger
Jap
Swi
UK
US
0.603
0.405
0.342
0.315
0.408
0.479
0.496
0.584
0.485
0.404
0.326
0.465
0.514
0.719
0.732
0.665
0.392
0.629
0.571
0.501
0.676
0.355
0.679
0.465
0.463
0.637
0.418
0.361
0.302
0.666
0.576
0.515
0.683
0.534
0.695
0.854
The benefits of international portfolio diversification
International Asset
Pricing Model (IAPM)
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Capital Asset Pricing Model
(CAPM) Review



All investors will choose to hold the market
portfolio, i.e., all assets, in proportion to their
market values.
This market portfolio is the optimal risky
portfolio.
The part of a stock’s risk that is diversifiable
does not matter to investors.
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Capital Asset Pricing Model
(CAPM) Review

Risk






Diversifiable/Non-Market/Company Risk
Non-Diversifiable/Market/Risk
Only Market Risk Relevant!
Uses variance as a measure of risk
Specifies that only that portion of variance that is not
diversifiable is rewarded.
Measures the non-diversifiable risk with beta, which
is standardized around one.
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Beta

Market Beta = 1.0 = average level of risk



A Beta of .5 is half as risky as average
A Beta of 2.0 is twice as risky as average
A negative beta asset moves in opposite direction to
market
Exxon
AT&T
IBM
Wal-Mart
General Motors
Microsoft
Harley-Davidson
0.65
0.90
0.95
1.10
1.15
1.30
1.65
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Beta Calculation
Disney versus S & P 500: January 1992 - 1996
15 .00 %
10 .00 %
D is n e y
5.0 0%
0.0 0%
-6.00 %
-4.00 %
-2.00 %
0.0 0%
2.0 0%
4.0 0%
6.0 0%
8.0 0%
-5.00 %
-10.0 0%
-15.0 0%
S & P 5 00
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CAPM Equation
r = rF + β(E[rM] - rF)
r
=
rF
=
β
=
E[rM] =
Required Return on Asset
Risk-Free Rate of Return
Beta Coefficient for Asset
Expected Market Return
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Capital Asset Pricing Model
(CAPM) Review
1.6
Capital Market Line
(CML)
E[rj]
M
E[rM]
Efficient Frontier
Investment
opportunity set
rF
0.0
0.0
σM
s▪
2.5
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Asset pricing models: CAPM
International Asset Pricing
Model (IAPM)


Global market portfolio in the IAPM includes
all assets in the world weighted according to
their market values.
IAPM assumes that investors in each country
share the same consumption basket and
purchasing power parity holds.
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Home Bias


Home bias refers to the extent to which portfolio
investments are concentrated in domestic equities.
Possible Explanations
1. Domestic equities may provide a superior
inflation hedge.
2. Home bias may reflect institutional and legal
restrictions on foreign investment.
3. Extra taxes and transactions/information costs
for foreign securities may give rise to home bias.
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Home Bias Data
Country
Share in World Market
Value
Proportion of Domestic
Equities in Portfolio
France
2.6%
64.4%
Germany
3.2%
75.4%
Italy
1.9%
91.0%
Japan
43.7%
86.7%
Spain
1.1%
94.2%
Sweden
0.8%
100.0%
United Kingdom
10.3%
78.5%
United States
36.4%
98.0%
Total
100.0%
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Home Bias Explanations





Barriers to International Investment
Regulatory and Tax Reasons
High Share of Non-Tradables in
Consumption
Substitution of Investment in Foreign
Assets by investment In Multinational
Corporations (MNC)
Informational Imperfections
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