Chapter Efficient Diversification Bodie, Kane, and Marcus Essentials of Investments 12th Edition Adopted for ECON5009 Financial Markets Securities and Derivatives , University of Glasgow, 2022/2023 6 2Copyright
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distribution without the prior written consent of McGraw Hill. 6.1 Diversification and Portfolio Risk Market, Systematic, & Nondiversifiable Risk Risk factors common to whole economy Unique, Firm-Specific, Nonsystematic & Diversifiable Risk Risk that can be eliminated by diversification 3Copyright
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distribution without the prior written consent of McGraw Hill. Figure 6.1 Risk as Function of Number of Stocks in Portfolio 4Copyright
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distribution without the prior written consent of McGraw Hill. Figure 6.2 Risk versus Diversification 5Copyright
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distribution without the prior written consent of McGraw Hill. Spreadsheet 6.1 Capital Market Expectations 6Copyright
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distribution without the prior written consent of McGraw Hill. 6.2 Asset Allocation with Two Risky Assets Covariance and Correlation Portfolio risk depends on covariance between returns of assets Expected return on two-security portfolio 2211)( rWrWrE p += 2security on return Expected 1security on return Expected 2security in funds of Proportion 1security in funds of Proportion 2 1 2 1 = = = = r r W W 7Copyright
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distribution without the prior written consent of McGraw Hill. Spreadsheet 6.2 Variance & Standard Deviations of Returns 8Copyright
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distribution without the prior written consent of McGraw Hill. Spreadsheet 6.3 Portfolio Performance 9Copyright
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distribution without the prior written consent of McGraw Hill. Spreadsheet 6.4 Return Covariance 10Copyright
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distribution without the prior written consent of McGraw Hill. 6.2 Asset Allocation with Two Risky Assets Covariance Calculations Correlation Coefficient ])()()][()()[(),Cov( 1 BS = = S i BBSS rEirrEiriprr BS BS SB rr σσ ),Cov( ρ = BSSBBS rr σσρ),Cov( = 11Copyright
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distribution without the prior written consent of McGraw Hill. 6.2 Asset Allocation with Two Risky Assets Using Historical Data Variability/covariability change slowly over time Use realized returns to estimate Cannot estimate averages precisely Focus for risk on deviations of returns from average value 12Copyright
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distribution without the prior written consent of McGraw Hill. 6.2 Asset Allocation with Two Risky Assets RoR: Weighted average of returns on components, with investment proportions as weights ERR: Weighted average of expected returns on components, with portfolio proportions as weights Variance of RoR: 13Copyright
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distribution without the prior written consent of McGraw Hill. 6.2 Asset Allocation with Two Risky Assets Risk-Return Trade-Off Investment opportunity set Available portfolio risk-return combinations Mean-Variance Criterion If E(rA) ≥ E(rB) and σA ≤ σB Portfolio A dominates portfolio B 14Copyright
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distribution without the prior written consent of McGraw Hill. Spreadsheet 6.5 Investment Opportunity Set 15Copyright
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distribution without the prior written consent of McGraw Hill. Figure 6.3 Investment Opportunity Set 16Copyright
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distribution without the prior written consent of McGraw Hill. Figure 6.4 Opportunity Sets: Various Correlation Coefficients 17Copyright
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distribution without the prior written consent of McGraw Hill. 6.3 The Optimal Risky Portfolio with a Risk-Free Asset Slope of CAL is Sharpe Ratio of Risky Portfolio Optimal Risky Portfolio Best combination of risky and safe assets to form portfolio ( )P f P P E r r S = 19Copyright
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distribution without the prior written consent of McGraw Hill. 6.3 The Optimal Risky Portfolio with a Risk-Free Asset Calculating Optimal Risky Portfolio Two risky assets BSSBfsfBBfsSfB BSSBfsSfB B rrErrErrErrE rrErrE w ])()([])([])([ ])([])([ 22 2 + + = BS ww =1 20Copyright
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distribution without the prior written consent of McGraw Hill. Figure 6.5 Two Capital Allocation Lines 21Copyright
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distribution without the prior written consent of McGraw Hill. Figure 6.6 Bond, Stock and T-Bill Optimal Allocation 22Copyright
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distribution without the prior written consent of McGraw Hill. Figure 6.7 The Complete Portfolio 23Copyright
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distribution without the prior written consent of McGraw Hill. Figure 6.8 Portfolio Composition: Asset Allocation Solution 24Copyright
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distribution without the prior written consent of McGraw Hill. 6.4 Efficient Diversification with Many Risky Assets Efficient Frontier of Risky Assets Graph representing set of portfolios that maximizes expected return at each level of portfolio risk Three methods Maximize risk premium for any level standard deviation Minimize standard deviation for any level risk premium Maximize Sharpe ratio for any standard deviation or risk premium 25Copyright
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distribution without the prior written consent of McGraw Hill. Figure 6.9 Portfolios Constructed with Three Stocks 26Copyright
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distribution without the prior written consent of McGraw Hill. Figure 6.10 Efficient Frontier: Risky and Individual Assets 27Copyright
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distribution without the prior written consent of McGraw Hill. 6.4 Efficient Diversification with Many Risky Assets Choosing Optimal Risky Portfolio Optimal portfolio CAL tangent to efficient frontier Separation Property implies portfolio choice, separated into two tasks 1. Determination of optimal risky portfolio 2. Personal choice of best mix of risky portfolio and risk- free asset 28Copyright
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distribution without the prior written consent of McGraw Hill. 6.4 Efficient Diversification with Many Risky Assets Optimal Risky Portfolio: Illustration Efficiently diversified global portfolio using stock market indices of six countries Standard deviation and correlation estimated from historical data Risk premium forecast generated from fundamental analysis 29Copyright
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distribution without the prior written consent of McGraw Hill. Figure 6.11 Efficient Frontiers & CAL: Table 6.1 30Copyright
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distribution without the prior written consent of McGraw Hill. 6.5 A Single-Index Stock Market Index model: Relates stock returns to returns on broad market index & firm-specific factors Excess return: RoR in excess of risk-free rate Beta: Sensitivity of security’s returns to market factor Firm-specific or residual risk: Component of return variance independent of market factor Alpha: Stock’s expected return beyond that induced by market index 31Copyright
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distribution without the prior written consent of McGraw Hill. 6.5 A Single-Index Stock Market Excess Return = β + α + Where: β: component of return due to movements in overall market β: security’s responsiveness to market α: stock’s expected excess return if market factor is neutral, i.e. market-index excess return is zero : Component attributable to unexpected events relevant only to this security (firm-specific) 32Copyright
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distribution without the prior written consent of McGraw Hill. 6.5 A Single-Index Stock Market Statistical Representation of Single-Index Model Security Characteristic Line (SCL) Plot of security’s predicted excess return from excess return of market Algebraic representation of regression line ( )D M D D ME R R R = + 33Copyright
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distribution without the prior written consent of McGraw Hill. 6.5 A Single-Index Stock Market Statistical and Graphical Representation of Single-Index Model Ratio of systematic variance to total variance 2 2 2 2 2 2 2 2 2 Systematic Variance Total Variance ( ) D M D M D D M De = = = + 34Copyright
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distribution without the prior written consent of McGraw Hill. Figure 6.12 Scatter Diagram for Disney 35Copyright
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distribution without the prior written consent of McGraw Hill. Figure 6.13 Various Scatter Diagrams 36Copyright
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distribution without the prior written consent of McGraw Hill. 6.5 A Single-Index Stock Market Diversification in Single-Index Security Market In portfolio of n securities with weights In securities with nonsystematic risk Nonsystematic portion of portfolio return Portfolio nonsystematic variance 2 2 2 1 P i n e i e i w = = 1 n P i i i e w e = = 37Copyright
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distribution without the prior written consent of McGraw Hill. 6.5 A Single-Index Stock Market Using Security Analysis with Index Model Information ratio Ratio of alpha to standard deviation of residual Active portfolio Portfolio formed by optimally combining analyzed stocks 38Copyright
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distribution without the prior written consent of McGraw Hill. 6.6 Risk of Long-Term Investments Why the Unending Confusion Vast majority of financial advisers believe stocks are less risky if held for long run Risk premium grows at rate of horizon, T Standard deviation grows at √T Sharpe ratio, 1√, grows with investment horizon 39Copyright
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distribution without the prior written consent of McGraw Hill. Table 6.4 Investment Risk for Different Horizons
