Presentation on theme: "6 Efficient Diversification Bodie, Kane and Marcus"— Presentation transcript:
1 6 Efficient Diversification Bodie, Kane and Marcus Essentials of Investments 9th Global Edition
2 6.1 Diversification and Portfolio Risk Market/Systematic/Non diversifiable RiskRisk factors common to whole economyUnique/Firm-Specific/Nonsystematic/ Diversifiable RiskRisk that can be eliminated by diversification
3 Figure 6.1 Risk as Function of Number of Stocks in Portfolio
11 6.2 Asset Allocation with Two Risky Assets Using Historical DataVariability/covariability change slowly over timeUse realized returns to estimateCannot estimate averages preciselyFocus for risk on deviations of returns from average value
12 6.2 Asset Allocation with Two Risky Assets Three RulesRoR: Weighted average of returns on components, with investment proportions as weightsERR: Weighted average of expected returns on components, with portfolio proportions as weightsVariance of RoR:
13 6.2 Asset Allocation with Two Risky Assets Risk-Return Trade-OffInvestment opportunity setAvailable portfolio risk-return combinationsMean-Variance CriterionIf E(rA) ≥ E(rB) and σA ≤ σBPortfolio A dominates portfolio B
24 6.4 Efficient Diversification with Many Risky Assets Efficient Frontier of Risky AssetsGraph representing set of portfolios that maximizes expected return at each level of portfolio riskThree methodsMaximize risk premium for any level standard deviationMinimize standard deviation for any level risk premiumMaximize Sharpe ratio for any standard deviation or risk premium
25 Figure 6.9 Portfolios Constructed with Three Stocks
26 Figure 6.10 Efficient Frontier: Risky and Individual Assets
27 6.4 Efficient Diversification with Many Risky Assets Choosing Optimal Risky PortfolioOptimal portfolio CAL tangent to efficient frontierPreferred Complete Portfolio and Separation PropertySeparation property: implies portfolio choice, separated into two tasksDetermination of optimal risky portfolioPersonal choice of best mix of risky portfolio and risk-free asset
28 6.4 Efficient Diversification with Many Risky Assets Optimal Risky Portfolio: IllustrationEfficiently diversified global portfolio using stock market indices of six countriesStandard deviation and correlation estimated from historical dataRisk premium forecast generated from fundamental analysis
31 6.5 A Single-Index Stock Market Index modelRelates stock returns to returns on broad market index/firm-specific factorsExcess returnRoR in excess of risk-free rateBetaSensitivity of security’s returns to market factorFirm-specific or residual riskComponent of return variance independent of market factorAlphaStock’s expected return beyond that induced by market index
34 6.5 A Single-Index Stock Market Statistical and Graphical Representation of Single- Index ModelSecurity Characteristic Line (SCL)Plot of security’s predicted excess return from excess return of marketAlgebraic representation of regression line
35 6.5 A Single-Index Stock Market Statistical and Graphical Representation of Single- Index ModelRatio of systematic variance to total variance
36 6.5 A Single-Index Stock Market Diversification in Single-Index Security MarketIn portfolio of n securities with weightsIn securities with nonsystematic riskNonsystematic portion of portfolio returnPortfolio nonsystematic variance
37 6.5 A Single-Index Stock Market Using Security Analysis with Index ModelInformation ratioRatio of alpha to standard deviation of residualActive portfolioPortfolio formed by optimally combining analyzed stocks
38 5) The standard deviation of the market-index portfolio is 15% 5) The standard deviation of the market-index portfolio is 15%. Stock A has a beta of 2.2 and a residual standard deviation of 25%.What would make for a larger increase in the stock’s variance: an increase of .2 in its beta or an increase of 3.84% (from 30% to 33%) in its residual standard deviation?An investor who currently holds the market-index portfolio decides to reduce the portfolio allocation to the market index to 90% and to invest 10% in stock A. Which of the changes in (a) will have a greater impact on the portfolio’s standard deviation?
39 20) Investors expect the market rate of return this year to be 10. 5% 20) Investors expect the market rate of return this year to be 10.5%. The expected rate of return on a stock with a beta of 1.3 is currently 13.65%. If the market return this year turns out to be 9%, how would you revise your expectation of the rate of return on the stock?
40 21. The following figure shows plots of monthly rates of return and the stock market for two stocks. Which stock is riskier to an investor currently holding her portfolio in a diversified portfolio of common stock?Which stock is riskier to an undiversified investor who puts all of his funds in only one of these stocks?
44 My Problems 5 Systematic Var & Residual Var in a Single Index Model 14 Risky Portfolio with Two Assets, Corr = -117 Efficient Frontier Diagram20 Single Index Model21 Systematic vs Unsystematic risksCFA 4, 5, 6 Diversification in a portfolio & across portfolios
45 TA Problems 3 Sharpe Ratio 6 Calculate Mean, Var, Cov 10 Sharpe Ratio for most feasible CAL (Solve differently)11 CAL (SD, weights of two risky assets & T-bills)12 Two Risky Assets (weights, comparison to CAL)19 SD of ReturnCFA 1 Portfolio Expected ReturnCFA 2 Choice of Index Fund