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大家好大家好15-2Chapter 5Risk and Risk and ReturnReturn5-3Glossary Glossary uuStandard DeviationStandard Deviation标准差或者标准离差标准差或者标准离差标准差或者标准离差标准差或者标准离差 uuExpected return Expected return 期望回报率期望回报率期望回报率期望回报率uuNormal distribution Normal distribution 正态分布正态分布正态分布正态分布uuCoefficient of variation Coefficient of variation 离差系数离差系数离差系数离差系数uuvariancevariance方差方差方差方差uuContinuous DistributionsContinuous Distributions连续分布连续分布连续分布连续分布uudiscrete distributiondiscrete distribution离散分布离散分布离散分布离散分布uuCertainty Equivalent(CE)Certainty Equivalent(CE)资本回收保证量资本回收保证量资本回收保证量资本回收保证量uuRisk PreferenceRisk Preference风险偏好风险偏好风险偏好风险偏好uuRisk IndifferenceRisk Indifference风险中立风险中立风险中立风险中立 uuRisk AversionRisk Aversion风险规避风险规避风险规避风险规避uuThe Capital Asset Pricing Model(CAPM)The Capital Asset Pricing Model(CAPM)资本资产定价模型资本资产定价模型资本资产定价模型资本资产定价模型uuSystematic RiskSystematic Risk系统风险系统风险系统风险系统风险uu Unsystematic Risk Unsystematic Risk非系统风险非系统风险非系统风险非系统风险5-4Defining ReturnDefining ReturnIncome received Income received on an investment on an investment plus any plus any change in market pricechange in market price,usually expressed as a percent of usually expressed as a percent of the the beginning market price beginning market price of the of the investment.investment.Dt+(Pt-Pt-1)Pt-1R=5-5Return ExampleReturn ExampleThe stock price for Stock A was The stock price for Stock A was$10$10 per per share 1 year ago.The stock is currently share 1 year ago.The stock is currently trading at trading at$9.50$9.50 per share,and per share,and shareholders just received a shareholders just received a$1 dividend$1 dividend.What return was earned over the past year?What return was earned over the past year?5-6Return ExampleReturn ExampleThe stock price for Stock A was The stock price for Stock A was$10$10 per per share 1 year ago.The stock is currently share 1 year ago.The stock is currently trading at trading at$9.50$9.50 per share,and per share,and shareholders just received a shareholders just received a$1 dividend$1 dividend.What return was earned over the past year?What return was earned over the past year?$1.00+($9.50-$10.00)$10.00R=5%5-7Defining RiskDefining RiskGreater the variability,the riskier the Greater the variability,the riskier the security is said to besecurity is said to beThe variability of returns from The variability of returns from those that are expected.those that are expected.5-8Determining Expected Determining Expected Return(Discrete Dist.)Return(Discrete Dist.)R R=S S S S(R Ri i)()(P Pi i)R R is the expected return for the asset,is the expected return for the asset,R Ri i is the return for the i is the return for the ithth possibility,possibility,P Pi i is the probability of that return is the probability of that return occurring,occurring,n n is the total number of possibilities.is the total number of possibilities.ni=15-9How to Determine the Expected How to Determine the Expected Return and Standard DeviationReturn and Standard DeviationStock BWStock BW R Ri iP Pi i (R Ri i)()(P Pi i)-.15 -.15 .10 .10 -.015 -.015 -.03 -.03 .20 .20 -.006 -.006 .09 .09 .40 .40 .036 .036 .21 .21 .20 .20 .042 .042 .33 .33 .10 .10 .033 .033 SumSum 1.001.00 .090.090The expected return,R,for Stock BW is.09 or 9%5-10Determining Standard DeviationDetermining Standard Deviation标准差或者标准离差标准差或者标准离差标准差或者标准离差标准差或者标准离差(Risk (Risk Measure)Measure)ni=1s s s s=S S S S(R Ri i-R R)2 2(P Pi i)Standard DeviationStandard Deviation,s s s s,is a statistical,is a statistical measure of the variability of a distribution measure of the variability of a distribution around its mean.around its mean.It is the square root of varianceIt is the square root of variance(方差）方差）方差）方差）.Note,this is for a Note,this is for a discrete distributiondiscrete distribution（离离离离散分布）散分布）散分布）散分布）.5-11How to Determine the Expected How to Determine the Expected Return and Standard DeviationReturn and Standard DeviationStock BWStock BW R Ri iP Pi i (R Ri i)()(P Pi i)(R Ri i-R R)2 2(P Pi i)-.15 -.15 .10 .10 -.015 -.015 .00576 .00576 -.03 -.03 .20 .20 -.006 -.006 .00288 .00288 .09 .09 .40 .40 .036 .036 .00000 .00000 .21 .21 .20 .20 .042 .042 .00288 .00288 .33 .33 .10 .10 .033 .033 .00576 .00576 SumSum 1.001.00 .090.090 .01728.017285-12Determining Standard Determining Standard Deviation(Risk Measure)Deviation(Risk Measure)s s s s=S S S S(R Ri i-R R)2 2(P Pi i)s s s s=.01728.01728s s s s=.1315.1315 or or 13.15%13.15%ni=15-13Coefficient of VariationCoefficient of VariationThe ratio of the The ratio of the standard deviation standard deviation of of a distribution to the a distribution to the mean mean of that of that distribution.distribution.It is a measure of It is a measure of RELATIVERELATIVE risk.risk.CV=CV=s s s s/R RCV of BW =CV of BW =.1315.1315/.09.09=1.46=1.465-14Discrete vs.Continuous Distributions连续分布 Discrete Continuous5-15Determining Expected Determining Expected Return(Continuous Dist.)Return(Continuous Dist.)R R=S S S S(R Ri i)/()/(n n)R R is the expected return for the asset,is the expected return for the asset,R Ri i is the return for the ith observation,is the return for the ith observation,n n is the total number of observations.is the total number of observations.ni=15-16Determining Standard Determining Standard Deviation(Risk Measure)Deviation(Risk Measure)ni=1s s s s=S S S S(R Ri i-R R)2 2 (n n)Note,this is for a Note,this is for a continuous continuous distributiondistribution where the distribution is where the distribution is for a for a populationpopulation.R R represents the represents the population mean in this example.population mean in this example.5-17Continuous Distribution ProblemuAssume that the following list represents the continuous distribution of population returns for a particular investment(even though there are only 10 returns).u9.6%,-15.4%,26.7%,-0.2%,20.9%,28.3%,-5.9%,3.3%,12.2%,10.5%uCalculate the Expected Return and Standard Deviation for the population assuming a continuous distribution.5-18Lets Use the Calculator!Lets Use the Calculator!Enter“Data”first.Press:2nd Data 2nd CLR Work9.6 ENTER -15.4 ENTER 26.7 ENTER uNote,we are inputting data only for the“X”variable and ignoring entries for the“Y”variable in this case.5-19Lets Use the Calculator!Lets Use the Calculator!Enter“Data”first.Press:-0.2 ENTER 20.9 ENTER 28.3 ENTER -5.9 ENTER 3.3 ENTER 12.2 ENTER 10.5 ENTER 5-20Lets Use the Calculator!Lets Use the Calculator!Examine Results!Press:2nd Stat through the results.uExpected return is 9%for the 10 observations.Population standard deviation is 13.32%.uThis can be much quicker than calculating by hand,but slower than using a spreadsheet.5-21Certainty EquivalentCertainty Equivalent (CECE)资本回收保证资本回收保证资本回收保证资本回收保证量量量量is the amount of cash someone is the amount of cash someone would require with certainty at a would require with certainty at a point in time to make the individual point in time to make the individual indifferent between that certain indifferent between that certain amount and an amount expected to amount and an amount expected to be received with risk at the same be received with risk at the same point in time.point in time.Risk AttitudesRisk Attitudes5-22Certainty equivalent Expected valueCertainty equivalent Expected valueRisk PreferenceRisk Preference风险偏好风险偏好风险偏好风险偏好Certainty equivalent=Expected valueCertainty equivalent=Expected valueRisk IndifferenceRisk Indifference风险中立风险中立风险中立风险中立 Certainty equivalent Expected valueCertainty equivalent Expected valueRisk AversionRisk Aversion风险规避风险规避风险规避风险规避MostMost individuals are individuals are Risk AverseRisk Averse.Risk AttitudesRisk Attitudes5-23Risk Attitude ExampleYou have the choice between(1)a guaranteed dollar reward or(2)a coin-flip gamble of$100,000(50%chance)or$0(50%chance).The expected value of the gamble is$50,000.uMary requires a guaranteed$25,000,or more,to call off the gamble.uRaleigh is just as happy to take$50,000 or take the risky gamble.uShannon requires at least$52,000 to call off the gamble.5-24What are the Risk Attitude tendencies of each?Risk Attitude ExampleRisk Attitude ExampleMaryMary shows shows“risk aversion”“risk aversion”“risk aversion”because her because her“certainty equivalent”the expected value of“certainty equivalent”the expected value of“certainty equivalent”the expected value of the gamblethe gamble.5-25 R RP P=S S S S(WWj j)()(R Rj j)R RP P is the expected return for the portfolio,is the expected return for the portfolio,WWj j is the weight(investment proportion)is the weight(investment proportion)for the for the j jthth asset in the portfolio,asset in the portfolio,R Rj j is the expected return of the j is the expected return of the jthth asset,asset,mm is the total number of assets in the is the total number of assets in the portfolio.portfolio.Determining PortfolioDetermining PortfolioExpected ReturnExpected Returnmj=15-26Determining Portfolio Determining Portfolio Standard DeviationStandard Deviationmj=1mk=1s s s sP P=SSSSSSSS WWj j WWk k s s s sj jk k WWj j is the weight(investment proportion)is the weight(investment proportion)for the for the j jthth asset in the portfolio,asset in the portfolio,WWk k is the weight(investment proportion)is the weight(investment proportion)for the for the k kthth asset in the portfolio,asset in the portfolio,s s s sj jk k is the covariance between returns for is the covariance between returns for the the j jthth and and k kthth assets in the portfolio.assets in the portfolio.5-27What is CovarianceWhat is Covariance协方差协方差协方差协方差?s s s s j jk k=s s s s j j s s s s k k r r j jk k s s s sj j is the standard deviation of the is the standard deviation of the j jthth asset asset in the portfolio,in the portfolio,s s s sk k is the standard deviation of the is the standard deviation of the k kthth asset in the portfolio,asset in the portfolio,r rj jk k is the correlation coefficient between the is the correlation coefficient between the j jthth and and k kthth assets in the portfolio.assets in the portfolio.5-28Correlation CoefficientCorrelation CoefficientA standardized statistical measure A standardized statistical measure of the linear relationship between of the linear relationship between two variables.two variables.Its range is from Its range is from-1.0-1.0(perfect perfect negative correlationnegative correlation),through),through 0 0 (no correlationno correlation),to),to+1.0+1.0(perfect perfect positive correlationpositive correlation).).5-37Stock CStock C Stock DStock D PortfolioPortfolioReturnReturn 9.00%9.00%8.00%8.00%8.64%8.64%Stand.Stand.Dev.Dev.13.15%13.15%10.65%10.65%10.91%10.91%CVCV 1.46 1.46 1.33 1.33 1.26 1.26The portfolio has the The portfolio has the LOWESTLOWEST coefficient coefficient of variation due to diversification.of variation due to diversification.Summary of the Portfolio Summary of the Portfolio Return and Risk CalculationReturn and Risk Calculation5-38Combining securities that are not perfectly,Combining securities that are not perfectly,positively correlated reduces risk.positively correlated reduces risk.Diversification and the Diversification and the Correlation CoefficientCorrelation CoefficientINVESTMENT RETURNTIMETIMETIMESECURITY ESECURITY ESECURITY FSECURITY FCombinationCombinationE and FE and F5-39Systematic Risk Systematic Risk Systematic Risk is the variability of return is the variability of return on stocks or portfolios associated with on stocks or portfolios associated with changes in return on the market as a whole.changes in return on the market as a whole.Unsystematic Risk Unsystematic Risk Unsystematic Risk is the variability of return is the variability of return on stocks or portfolios not explained by on stocks or portfolios not explained by general market movements.It is avoidable general market movements.It is avoidable through diversification.through diversification.Total Risk=Systematic Total Risk=Systematic Risk+Unsystematic RiskRisk+Unsystematic RiskTotal Risk=Systematic Risk+Unsystematic Risk5-40Total Risk=Systematic Total Risk=Systematic Risk+Unsystematic RiskRisk+Unsystematic RiskTotalTotalRiskRiskUnsystematic riskUnsystematic riskSystematic riskSystematic riskSTD DEV OF PORTFOLIO RETURNNUMBER OF SECURITIES IN THE PORTFOLIOFactors such as changes in nations economy,tax reform by the Congress,or a change in the world situation.5-41Total Risk=Systematic Total Risk=Systematic Risk+Unsystematic RiskRisk+Unsystematic RiskTotalTotalRiskRiskUnsystematic riskUnsystematic riskSystematic riskSystematic riskSTD DEV OF PORTFOLIO RETURNNUMBER OF SECURITIES IN THE PORTFOLIOFactors unique to a particular companyor industry.For example,the death of akey executive or loss of a governmentaldefense contract.5-42CAPM is a model that describes the CAPM is a model that describes the relationshiprelationship between between riskrisk and and expected(required)expected(required)returnreturn;in this;in this model,a securitys expected model,a securitys expected(required)return is the(required)return is the risk-free rate risk-free rate plus plus a premium a premium based on the based on the systematic risk systematic risk of the security.of the security.Capital Asset Capital Asset Pricing Model(CAPM)Pricing Model(CAPM)5-431.1.Capital markets are efficient.Capital markets are efficient.2.2.Homogeneous investor expectations Homogeneous investor expectations over a given period.over a given period.3.3.Risk-freeRisk-freeRisk-free asset return is certain asset return is certain(use(use short-to intermediate-term short-to intermediate-term Treasuries as a proxy Treasuries as a proxy 代理代理代理代理).).4.4.Market portfolio contains Market portfolio contains onlyonly systematic risk systematic risk systematic risk(use S&P 500 Index(use S&P 500 Indexor similar as a proxy).or similar as a proxy).CAPM AssumptionsCAPM Assumptions5-44Characteristic LineCharacteristic LineEXCESS RETURNON STOCKEXCESS RETURNON MARKET PORTFOLIOBetaBeta=RiseRiseRunRunNarrower spreadNarrower spreadis higher correlationis higher correlationCharacteristic LineCharacteristic Line5-45Calculating“Beta”on Your CalculatorTime Pd.MarketMy Stock19.6%12%2-15.4%-5%326.7%19%4-.2%3%520.9%13%628.3%14%7-5.9%-9%83.3%-1%912.2%12%1010.5%10%The Market and My Stock returns are“excess returns”and have the riskless rate already subtracted.5-46Calculating“Beta”on Your CalculatoruAssume that the previous continuous distribution problem represents the“excess returns”of the market portfolio(it may still be in your calculator data worksheet -2nd Data).uEnter the excess market returns as“X”observations of:9.6%,-15.4%,26.7%,-0.2%,20.9%,28.3%,-5.9%,3.3%,12.2%,and 10.5%.uEnter the excess stock returns as“Y”observations of:12%,-5%,19%,3%,13%,14%,-9%,-1%,12%,and 10%.5-47Calculating“Beta”on Your CalculatoruLet us examine again the statistical results(Press 2nd and then Stat)uThe market expected return and standard deviation is 9%and 13.32%.Your stock expected return and standard deviation is 6.8%and 8.76%.uThe regression equation is Y=a+bX.Thus,our characteristic line is Y=1.4448+0.595 X and indicates that our stock has a beta of 0.595.5-48An index of An index of systematic risksystematic risk.It measures the It measures the sensitivitysensitivity of a of a stocks returns to changes in returns stocks returns to changes in returns on the market portfolio.on the market portfolio.The The betabeta for a portfolio is simply a for a portfolio is simply a weighted average of the individual weighted average of the individual stock betas in the portfolio.stock betas in the portfolio.What is Beta?What is Beta?5-49Characteristic Lines Characteristic Lines and Different Betasand Different BetasEXCESS RETURNON STOCKEXCESS RETURNON MARKET PORTFOLIOBeta 1Beta 1Beta 1(aggressive)(aggressive)Each characteristic characteristic line line has a different slope.5-50R Rj j is the required rate of return for stock j,is the required rate of return for stock j,R Rf f is the risk-free rate of return,is the risk-free rate of return,b b b bj j is the beta of stock j(measures is the beta of stock j(measures systematic risk of stock j),systematic risk of stock j),R RMM is the expected return for the market is the expected return for the market portfolio.portfolio.Security Market LineSecurity Market LineRj=Rf+b bj(RM-Rf)5-51Security Market LineSecurity Market LineRj=Rf+b bj(RM-Rf)b b b bMM=1.01.0Systematic Risk(Beta)R Rf fR RMMRequired ReturnRequired ReturnRiskRiskPremiumPremiumRisk-freeRisk-freeReturnReturn5-52Lisa Miller at Lisa Miller at Basket WondersBasket Wonders is is attempting to determine the rate of return attempting to determine the rate of return required by their stock investors.Lisa is required by their stock investors.Lisa is using a using a 6%R6%Rf f and a long-term and a long-term market market expected rate of return expected rate of return of of 10%10%.A stock.A stock analyst following the firm has calculated analyst following the firm has calculated that the firm that the firm betabeta is is 1.21.2.What is the.What is the required rate of returnrequired rate of return on the stock of on the stock of Basket WondersBasket Wonders?Determination of the Determination of the Required Rate of ReturnRequired Rate of Return5-53R RBWBW=R Rf f +b b b bj j(R RMM-R Rf f)R RBWBW=6%6%+1.21.2(10%10%-6%6%)R RBWBW=10.8%10.8%The required rate of return exceeds The required rate of return exceeds the market rate of return as BWs the market rate of return as BWs beta exceeds the market beta(1.0).beta exceeds the market beta(1.0).BWs Required BWs Required Rate of ReturnRate of Return5-54Lisa Miller at BW is also attempting to Lisa Miller at BW is also attempting to determine the determine the intrinsic value intrinsic value intrinsic value of the stock.of the stock.She is using the She is using the constant growth modelconstant growth model.Lisa estimates that the Lisa estimates that the dividend next period dividend next period dividend next period will be will be$0.50$0.50$0.50 and that BW will and that BW will growgrowgrow at a at a constant rate of constant rate of 5.8%5.8%5.8%.The stock is currently.The stock is currently selling for$15.selling for$15.What is the What is the intrinsic value intrinsic value of the stock?of the stock?Is the stock Is the stock overover or or underpricedunderpriced?Determination of the Determination of the Intrinsic Value of BWIntrinsic Value of BW5-55The stock is The stock is OVERVALUEDOVERVALUED as as the market price($15)exceeds the market price($15)exceeds the the intrinsic value intrinsic value($10$10).).Determination of the Determination of the Intrinsic Value of BWIntrinsic Value of BW$0.5010.8%-5.8%IntrinsicValue=$105-56Security Market LineSecurity Market LineSystematic Risk(Beta)R Rf fRequired ReturnRequired ReturnDirection ofMovementDirection ofMovementStock Y Stock Y(Overpriced)Stock X(Underpriced)
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