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 ManagementManagementDiversification – Eliminating riskDiversification – Eliminating riskWhen diversification worksWhen diversification worksBeta – Measure of Risk in a PortfolioBeta – Measure of Risk in a PortfolioUsing BetaUsing BetaCompany: A Portfolio of ProjectsCompany: A Portfolio of ProjectsRisk and Return in a Portfolio that is Not Risk and Return in a Portfolio that is Not Well DiversifiedWell DiversifiedDiversification – Eliminating RiskDiversification – Eliminating RiskEasy way to lower or eliminate riskEasy way to lower or eliminate riskChoose risk-free investmentChoose risk-free investmentGet a lower returnGet a lower returnTask – eliminate some risk without giving Task – eliminate some risk without giving up returnup returnDon’t put all your eggs in one basketDon’t put all your eggs in one basketSpread out your investment across many Spread out your investment across many assetsassetsCalculate expected return and riskCalculate expected return and riskDiversification – Eliminating RiskDiversification – Eliminating RiskExample, Mars Bars and KlingonExample, Mars Bars and KlingonFour states of economyFour states of economyBoom, Good, Normal, and BustBoom, Good, Normal, and BustEach with probability of stateEach with probability of stateReturns in each state for two assetsReturns in each state for two assetsCalculating Expected Return Calculating Expected Return E(r) = probability of state x conditional returnE(r) = probability of state x conditional returnMars Bars Inc. = 10%Mars Bars Inc. = 10%Klingon LTD = 10%Klingon LTD = 10%Diversification – Eliminating RiskDiversification – Eliminating RiskCalculate “risk” as the standard deviation Calculate “risk” as the standard deviation of the conditional returnsof the conditional returnsσσ = [ = [ΣΣ (probability (probabilityii x (return x (returnii – average – average)2)2]]1/21/2Mars 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 WorksCo-movement of stock returnsCo-movement of stock returnsCorrelation CoefficientCorrelation CoefficientCovariance 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 correlatedExample Peat and Repeat CompaniesExample Peat and Repeat CompaniesNegative CorrelationNegative CorrelationEliminate all risk if perfectly negatively correlatedEliminate all risk if perfectly negatively correlatedExample Zig and Zag CompaniesExample Zig and Zag CompaniesBeta – Measure of Risk in a Beta – Measure of Risk in a PortfolioPortfolioSystematic Risk – risk you cannot avoidSystematic Risk – risk you cannot avoidUnsystematic Risk – risk you can avoidUnsystematic Risk – risk you can avoidBeta is measure of systematic riskBeta is measure of systematic riskStandard Deviation is measure of both Standard Deviation is measure of both systematic and unsystematic risksystematic and unsystematic riskDiversification can eventually eliminate all Diversification can eventually eliminate all unsystematic riskunsystematic riskOnly systematic risk counts, so use Only systematic risk counts, so use ββBeta – Measure of Risk in a Beta – Measure of Risk in a PortfolioPortfolioUsing Beta for finding the risk of a portfolioUsing Beta for finding the risk of a portfolioIn a well diversified portfolio only systematic risk In a well diversified portfolio only systematic risk remainsremainsSystematic risk of portfolio is weighted betasSystematic risk of portfolio is weighted betasExample 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= 1.4Equally weighted portfolio (Tom’s Portfolio)Equally weighted portfolio (Tom’s Portfolio)Portfolio’s Portfolio’s ββ = 1.0 = 1.01.0 = 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 BetaBeta FactsBeta FactsBeta 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 marketBeta > 1, risk greater than marketBeta > 1, risk greater than marketExpected 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 ββExpected Return = Expected Return = ΣΣ w wii x return x returniiBeta = Beta = ΣΣ w wii x x ββiiUsing BetaUsing BetaBeta also determines expected return of Beta also determines expected return of individual assetindividual assetKnown, risk-free rateKnown, risk-free rateEstimate, expected return on marketEstimate, expected return on marketEach 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 ProjectsAll 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 explainViewing each project or product with different level of Viewing each project or product with different