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IBUS 302: International Finance
Topic 16–Portfolio Analysis
Lawrence Schrenk, Instructor
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Learning Objectives
1. Calculate the return, standard deviation and correlation of foreign equity.▪
2. Describe international diversification.
3. Explain the International Asset Pricing Model (IAPM)
4. 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) = sP
2 = Si Sj xi xj sij
where sij = rij si sj
The algebra of portfolio diversification
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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
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Variance of a PortfolioCorrelation
E[ri] si A J
A American 11.1% 16.9% 1.0000.302
J Japanese 15.7% 34.6% 0.3021.000
sP2 = xA
2 sA
2 + 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
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Diversification
10%
12%
14%
16%
0% 10% 20% 30% 40%
Return
s
r = +1
r = -1
r = +0.302
A
J
The benefits of international portfolio diversification
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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
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Potential for…higher returnslower portfolio risk
InternationalPortfolio Diversification
s
Return
rF
MW
The benefits of international portfolio diversification
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Domestic versus International Diversification
1.0
0.5
International diversification
U.S. diversification only
Number of stocks in portfolio
5 10 15 20 25
26%12%
The benefits of international portfolio diversification
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International Stock Returns (1970-2006)
Mean Stdev βW SI Value ($bn)
Australia 11.5 24.2 0.194 0.976 932Canada 11.9 19.5 0.262 0.975 994France 14.4 27.9 0.272 1.109 1,698Germany 13.8 29.8 0.235 1.117 1,213Japan 15.7 34.6 0.257 1.355 2,969Switzerland 14.4 24.2 0.314 0.973 970U.K. 14.5 27.5 0.280 1.124 3,252U.S. 11.1 16.9 0.254 0.849 14,968World 11.3 17.0 0.265 1.000 32,785
U.S. T-bills 6.8 3.2 0.000 -0.015 -
βW versus the MSCI world stock market indexSharpe Index (SI) = (rP - rF) / σP
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International Equity Correlations (1970-2006)
Aus Can Fra Ger Jap Swi UK US
Canada 0.603
France 0.405 0.485
Germany 0.342 0.404 0.665
Japan 0.315 0.326 0.392 0.355
Switzerland 0.408 0.465 0.629 0.679 0.418
U.K. 0.479 0.514 0.571 0.465 0.361 0.576
U.S. 0.496 0.719 0.501 0.463 0.302 0.515 0.534
World 0.584 0.732 0.676 0.637 0.666 0.683 0.695 0.854
The benefits of international portfolio diversification
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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 0.65AT&T 0.90IBM 0.95Wal-Mart 1.10General Motors 1.15Microsoft 1.30Harley-Davidson 1.65
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Beta CalculationDisney versus S & P 500: January 1992 - 1996
-15.00%
-10.00%
-5.00%
0.00%
5.00%
10.00%
15.00%
-6.00% -4.00% -2.00% 0.00% 2.00% 4.00% 6.00% 8.00%
S & P 500
Dis
ney
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CAPM Equation
r = rF + β(E[rM] - rF)
r = Required Return on Asset
rF = Risk-Free Rate of Return
β = Beta Coefficient for Asset
E[rM] = Expected Market Return
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Capital Asset Pricing Model (CAPM) Review
0.0
1.6
0.0 2.5
M
s ▪
E[rj]Capital Market Line
(CML)
Efficient Frontier
E[rM]
rF
Investmentopportunity set
σM
Asset pricing models: CAPM
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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 DataCountry Share in World Market
ValueProportion 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 ExplanationsBarriers to International InvestmentRegulatory and Tax ReasonsHigh Share of Non-Tradables in
ConsumptionSubstitution of Investment in Foreign
Assets by investment In Multinational Corporations (MNC)
Informational Imperfections