# 1 (of 25) IBUS 302: International Finance Topic 16–Portfolio Analysis Lawrence Schrenk, Instructor.

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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[r P ] =  i x i E[r i ] Portfolio Variance Var(r P ) =  P 2 =  i  j x i x j  ij where  ij =  ij  i  j The algebra of portfolio diversification

Expected Return on a Portfolio E[r i ] σ i American (A)11.1%16.9% Japanese (J)15.7%34.6% Example: Equal weights of A and J E[r P ]= x A E[r A ] + x J E[r J ] = (½)(0.111)+(½)(0.157) = 0.134, or 13.4% The algebra of portfolio diversification

Variance of a Portfolio Correlation E[r i ]  i AJ A American 11.1% 16.9%1.0000.302 J Japanese 15.7% 34.6%0.3021.000  P 2 = x A 2  A 2 + x J 2  J 2 + 2 x A x J  AJ  A  J = (½) 2 (0.169) 2 + (½) 2 (0.346) 2 + 2(½)(½)(0.302)(0.169)(0.346) = 0.0459  P = (0.0459) 1/2 = 0.214, or 21.4% The algebra of portfolio diversification

Diversification Return   = +1  = -1  = +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 returns lower portfolio risk International Portfolio Diversification  Return rFrF M W 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 510152025 26% 12% The benefits of international portfolio diversification

International Stock Returns (1970-2006) Mean Stdev β W SI Value(\$bn) Australia11.524.20.1940.976 932 Canada11.919.50.2620.975 994 France14.427.90.2721.109 1,698 Germany13.829.80.2351.117 1,213 Japan15.734.60.2571.355 2,969 Switzerland14.424.20.3140.973 970 U.K.14.527.50.2801.124 3,252 U.S.11.116.90.2540.849 14,968 World11.317.00.2651.000 32,785 U.S. T-bills6.83.20.000-0.015- β W versus the MSCI world stock market index Sharpe Index (SI) = (r P  r F ) / σ P

International Equity Correlations (1970-2006) AusCanFraGerJapSwiUKUS Canada0.603 France0.4050.485 Germany0.3420.4040.665 Japan0.3150.3260.3920.355 Switzerland0.4080.4650.6290.6790.418 U.K.0.4790.5140.5710.4650.3610.576 U.S.0.4960.7190.5010.4630.3020.5150.534 World0.5840.7320.6760.6370.6660.6830.6950.854 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 Exxon0.65 AT&T0.90 IBM0.95 Wal-Mart1.10 General Motors1.15 Microsoft1.30 Harley-Davidson1.65

17 (of 25) Beta Calculation

18 (of 25) CAPM Equation r = r F + β(E[r M ] - r F ) r= Required Return on Asset r F = Risk-Free Rate of Return β = Beta Coefficient for Asset E[r M ] = Expected Market Return

19 (of 25) Capital Asset Pricing Model (CAPM) Review M  ▪ ▪ E[r j ] Capital Market Line (CML) Efficient Frontier E[r M ] rFrF Investment opportunity set σMσM 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 Data CountryShare in World Market Value Proportion of Domestic Equities in Portfolio France2.6%64.4% Germany3.2%75.4% Italy1.9%91.0% Japan43.7%86.7% Spain1.1%94.2% Sweden0.8%100.0% United Kingdom10.3%78.5% United States36.4%98.0% Total 100.0%

23 (of 25) Home Bias E xplanations 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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