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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.▪ 2 (of 25) Returns, Volatility, Correlation 3 (of 25) 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) 13 (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. 14 (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. 15 (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 AT&T IBM Wal-Mart General Motors Microsoft Harley-Davidson 0.65 0.90 0.95 1.10 1.15 1.30 1.65 16 (of 25) 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 17 (of 25) 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 18 (of 25) 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 19 (of 25) 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. 20 (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. 21 (of 25) 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% 22 (of 25) 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 23 (of 25)