Discussion Thread: Parable of the Talents
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EfficientDiversification.pptxEfficient Diversification
Bodie, Kane, and Marcus
Essentials of Investments Eleventh Edition
6
Chapter
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
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Figure 6.1 Risk as Function of Number of Stocks in Portfolio
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Figure 6.2 Risk versus Diversification
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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
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6.2 Asset Allocation with Two Risky Assets
Covariance Calculations
Correlation Coefficient
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Spreadsheet 6.1 Capital Market Expectations
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Spreadsheet 6.2 Variance of Returns
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Spreadsheet 6.3 Portfolio Performance
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Spreadsheet 6.4 Return Covariance
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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
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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:
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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
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Spreadsheet 6.5 Investment Opportunity Set
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Figure 6.3 Investment Opportunity Set
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Figure 6.4 Opportunity Sets: Various Correlation Coefficients
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Spreadsheet 6.6 Opportunity Set -Various Correlation Coefficients
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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
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6.3 The Optimal Risky Portfolio with a Risk-Free Asset
Calculating Optimal Risky Portfolio
Two risky assets
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Figure 6.5 Two Capital Allocation Lines
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Figure 6.6 Bond, Stock and T-Bill Optimal Allocation
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Figure 6.7 The Complete Portfolio
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Figure 6.8 Portfolio Composition: Asset Allocation Solution
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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
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Figure 6.9 Portfolios Constructed with Three Stocks
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Figure 6.10 Efficient Frontier: Risky and Individual Assets
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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
Determination of optimal risky portfolio
Personal choice of best mix of risky portfolio and risk-free asset
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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
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Figure 6.11 Efficient Frontiers/CAL: Table 6.1
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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
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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)
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6.5 A Single-Index Stock Market
Statistical and Graphical 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
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6.5 A Single-Index Stock Market
Statistical and Graphical Representation of Single-Index Model
Ratio of systematic variance to total variance
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Figure 6.12 Scatter Diagram for Ford
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Figure 6.13 Various Scatter Diagrams
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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
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6.5 A Single-Index Stock Market
Using Security Analysis with Index Model
In
