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Chapter 8 Diversification and Portfolio ManagementDiversification – Eliminating RiskSlide 3Slide 4When Diversification WorksBeta – Measure of Risk in a PortfolioSlide 7Using BetaSlide 9Company: A Portfolio of ProjectsRisk and Return in a Portfolio that is Not Well DiversifiedProblemsChapter 8Chapter 8Diversification and Portfolio Diversification and Portfolio ManagementManagementDiversification – Eliminating riskDiversification – Eliminating riskWhen diversification worksWhen diversification worksBeta – Measure of Risk in a PortfolioBeta – Measure of Risk in a PortfolioUsing BetaUsing BetaCompany: A Portfolio of ProjectsCompany: A Portfolio of ProjectsRisk and Return in a Portfolio that is Not Risk and Return in a Portfolio that is Not Well DiversifiedWell DiversifiedDiversification – Eliminating RiskDiversification – Eliminating RiskEasy way to lower or eliminate riskEasy way to lower or eliminate riskChoose risk-free investmentChoose risk-free investmentGet a lower returnGet a lower returnTask – eliminate some risk without giving Task – eliminate some risk without giving up returnup returnDon’t put all your eggs in one basketDon’t put all your eggs in one basketSpread out your investment across many Spread out your investment across many assetsassetsCalculate expected return and riskCalculate expected return and riskDiversification – Eliminating RiskDiversification – Eliminating RiskExample, Mars Bars and KlingonExample, Mars Bars and KlingonFour states of economyFour states of economyBoom, Good, Normal, and BustBoom, Good, Normal, and BustEach with probability of stateEach with probability of stateReturns in each state for two assetsReturns in each state for two assetsCalculating Expected Return Calculating Expected Return E(r) = probability of state x conditional returnE(r) = probability of state x conditional returnMars Bars Inc. = 10%Mars Bars Inc. = 10%Klingon LTD = 10%Klingon LTD = 10%Diversification – Eliminating RiskDiversification – Eliminating RiskCalculate “risk” as the standard deviation Calculate “risk” as the standard deviation of the conditional returnsof the conditional returnsσσ = [ = [ΣΣ (probability (probabilityii x (return x (returnii – average – average)2)2]]1/21/2Mars Bars Inc. Mars Bars Inc. σσ = 12.02% = 12.02%Klingon LTD Klingon LTD σσ = 7.63% = 7.63%Combining Mars Bars and Klingon (50/50)Combining Mars Bars and Klingon (50/50)Same return, 10%Same return, 10%Lower risk, 0.82%Lower risk, 0.82%Spreading investment lowers riskSpreading investment lowers riskWhen Diversification WorksWhen Diversification WorksCo-movement of stock returnsCo-movement of stock returnsCorrelation CoefficientCorrelation CoefficientCovariance of two assets divided by their standard Covariance of two assets divided by their standard deviations (equation 8.2)deviations (equation 8.2)Positive Correlation Positive Correlation No benefit if perfectly positively correlatedNo benefit if perfectly positively correlatedExample Peat and Repeat CompaniesExample Peat and Repeat CompaniesNegative CorrelationNegative CorrelationEliminate all risk if perfectly negatively correlatedEliminate all risk if perfectly negatively correlatedExample Zig and Zag CompaniesExample Zig and Zag CompaniesBeta – Measure of Risk in a Beta – Measure of Risk in a PortfolioPortfolioSystematic Risk – risk you cannot avoidSystematic Risk – risk you cannot avoidUnsystematic Risk – risk you can avoidUnsystematic Risk – risk you can avoidBeta is measure of systematic riskBeta is measure of systematic riskStandard Deviation is measure of both Standard Deviation is measure of both systematic and unsystematic risksystematic and unsystematic riskDiversification can eventually eliminate all Diversification can eventually eliminate all unsystematic riskunsystematic riskOnly systematic risk counts, so use Only systematic risk counts, so use ββBeta – Measure of Risk in a Beta – Measure of Risk in a PortfolioPortfolioUsing Beta for finding the risk of a portfolioUsing Beta for finding the risk of a portfolioIn a well diversified portfolio only systematic risk In a well diversified portfolio only systematic risk remainsremainsSystematic risk of portfolio is weighted betasSystematic risk of portfolio is weighted betasExample 8.1 (Tom’s Portfolio)Example 8.1 (Tom’s Portfolio)Peat’s Peat’s ββ = 0.8, Repeat’s = 0.8, Repeat’s ββ = 1.2, = 1.2, Zig’s Zig’s ββ = 0.6, Zag’s = 0.6, Zag’s ββ = 1.4= 1.4Equally weighted portfolio (Tom’s Portfolio)Equally weighted portfolio (Tom’s Portfolio)Portfolio’s Portfolio’s ββ = 1.0 = 1.01.0 = 0.25 x 0.8 + 0.25 x 1.2 + 0.25 x 0.6 + 0.25 x 1.41.0 = 0.25 x 0.8 + 0.25 x 1.2 + 0.25 x 0.6 + 0.25 x 1.4Using BetaUsing BetaBeta FactsBeta FactsBeta of zero means no risk (i.e. T-Bill)Beta of zero means no risk (i.e. T-Bill)Beta of 1 means average risk (same as market risk)Beta of 1 means average risk (same as market risk)Beta < 1, risk lower than marketBeta < 1, risk lower than marketBeta > 1, risk greater than marketBeta > 1, risk greater than marketExpected Return and Beta use asset weights in Expected Return and Beta use asset weights in portfolio for portfolio e(r) and portfolio for portfolio e(r) and ββExpected Return = Expected Return = ΣΣ w wii x return x returniiBeta = Beta = ΣΣ w wii x x ββiiUsing BetaUsing BetaBeta also determines expected return of Beta also determines expected return of individual assetindividual assetKnown, risk-free rateKnown, risk-free rateEstimate, expected return on marketEstimate, expected return on marketEach asset’s expected return function of its risk as Each asset’s expected return function of its risk as measured by beta and the risk-reward tradeoff (slope measured by beta and the risk-reward tradeoff (slope of SML)of SML) fmifirrErrE )(Company: A Portfolio of ProjectsCompany: A Portfolio of ProjectsAll companies are a portfolio of individual All companies are a portfolio of individual projects (or products and services)projects (or products and services)Concept of portfolio helps explainConcept of portfolio helps explainViewing each project or product with different level of Viewing each project or product with different

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