1 (of 25)

IBUS 302: International Finance

Topic 16–Portfolio Analysis

Lawrence Schrenk, Instructor

2 (of 25)

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.▪

3 (of 25)

Returns, Volatility, Correlation

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

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 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

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

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

Potential for…higher returnslower portfolio risk

InternationalPortfolio Diversification

s

Return

rF

MW

The benefits of international portfolio diversification

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

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

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

13 (of 25)

International Asset Pricing Model (IAPM)

14 (of 25)

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.

15 (of 25)

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.

16 (of 25)

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

17 (of 25)

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

18 (of 25)

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

19 (of 25)

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

20 (of 25)

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.

21 (of 25)

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.

22 (of 25)

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%  

23 (of 25)

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