Efficient Diversification PDF - Bodie, Kane, and Marcus Essentials of Investments

Chapter 6 Efficient Diversification Bodie, Kane, and Marcus Essentials of Investments 2024 Release © McGraw Hill LLC. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or fu...

Chapter 6 Efficient Diversification Bodie, Kane, and Marcus Essentials of Investments 2024 Release © McGraw Hill LLC. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC.  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 © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 2  Figure 6.1 Risk as Function of Number of Stocks in Portfolio © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 3  Figure 6.2 Risk versus Diversification © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 4  Spreadsheet 6.1 Capital Market Expectations © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 5  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 E (rp ) W1r1  W2 r2 W1 Proportion of funds in security 1 W2 Proportion of funds in security 2 r1 Expected return on security 1 r 2 Expected return on security 2 © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 6  Spreadsheet 6.2 Variance & Standard Deviations of Returns © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 7  Spreadsheet 6.3 Portfolio Performance © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 8  Spreadsheet 6.4 Return Covariance © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 9  6.2 Asset Allocation with Two Risky Assets Covariance Calculations S Cov( rS , rB )  p (i )[rS (i )  E (rS )][rB (i )  E (rB )] i 1 Correlation Coefficient Cov( rS , rB ) ρ SB  σ S σ B Cov( rS , rB ) ρ SB σ S σ B © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 10  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: © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 11  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 © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 12  Spreadsheet 6.5 Investment Opportunity Set © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 13  Figure 6.3 Investment Opportunity Set © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 14  Figure 6.4 Opportunity Sets: Various Correlation Coefficients © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 15  Spreadsheet 6.6 Opportunity Set -Various Correlation Coefficients © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 16  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 © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 17  6.3 The Optimal Risky Portfolio with a Risk-Free Asset Slope of CAL is Sharpe Ratio of Risky Portfolio E (rP )  rf SP  P Optimal Risky Portfolio Best combination of risky and safe assets to form portfolio © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 18  6.3 The Optimal Risky Portfolio with a Risk-Free Asset Calculating Optimal Risky Portfolio Two risky assets [ E (rB )  rf ] S2  [ E (rs )  rf ] B S  BS wB  [ E (rB )  rf ] S2  [ E (rs )  rf ] B2  [ E (rB )  rf  E (rs )  rf ] B S  BS wS 1  wB © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 19  Figure 6.5 Two Capital Allocation Lines © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 20  Figure 6.6 Bond, Stock and T-Bill Optimal Allocation © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 21  Figure 6.7 The Complete Portfolio © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 22  Figure 6.8 Portfolio Composition: Asset Allocation Solution © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 23  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 © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 24  Figure 6.9 Portfolios Constructed with Three Stocks © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 25  Figure 6.10 Efficient Frontier: Risky and Individual Assets © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 26  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 © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 27  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 © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 28  Figure 6.11 Efficient Frontiers & CAL: Table 6.1 © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 29  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 © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 30  6.5 A Single-Index Stock Market Excess Return Where: : component of return due to movements in overall market : security’s responsiveness to market : 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) © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 31  6.5 A Single-Index Stock Market Statistical Interpretation 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 E ( RD RM )  D   D RM © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 32  6.5 A Single-Index Stock Market Statistical and Graphical Representation of Single-Index Model Ratio of systematic variance to total variance Systematic Variance 2   Total Variance 2 2 2 2      2  2 2 D M D M 2 D  D M   (eD ) © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 33  Figure 6.12 Scatter Diagram for U.S. Steel © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 34  Figure 6.13 Various Scatter Diagrams © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 35  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 n eP  wi ei i 1 Portfolio nonsystematic variance n   w  2 eP 2 i 2 ei i 1 © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 36  6.5 A Single-Index Stock Market Using Security Analysis with the Index Model Information ratio Ratio of alpha to standard deviation of residual Active portfolio Portfolio formed by optimally combining analyzed stocks © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 37  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, , grows with investment horizon © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 38  Table 6.4 Investment Risk for Different Horizons © McGraw Hill LLC. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill LLC. 39