财务管理第五章风险和收益.ppt

Chapter 5,Risk and Return,Glossary,Standard Deviation标准差或者标准离差 Expected return 期望回报率Normal distribution 正态分布Coefficient of variation 离差系数variance方差Continuous Distributions连续分布discrete distribution离散分布Certainty Equivalent(CE)资本回收保证量Risk Preference风险偏好Risk Indifference风险中立 Risk Aversion风险规避The Capital Asset Pricing Model(CAPM)资本资产定价模型Systematic Risk系统风险 Unsystematic Risk非系统风险,Defining Return,Income received on an investment plus any change in market price,usually expressed as a percent of the beginning market price of the investment.,Dt+(Pt-Pt-1),Pt-1,R=,Return Example,The stock price for Stock A was$10 per share 1 year ago.The stock is currently trading at$9.50 per share,and shareholders just received a$1 dividend.What return was earned over the past year?,Return Example,The stock price for Stock A was$10 per share 1 year ago.The stock is currently trading at$9.50 per share,and shareholders just received a$1 dividend.What return was earned over the past year?,$1.00+($9.50-$10.00),$10.00,R=,=5%,Defining Risk,Greater the variability,the riskier the security is said to be,The variability of returns from those that are expected.,Determining Expected Return(Discrete Dist.),R=S(Ri)(Pi)R is the expected return for the asset,Ri is the return for the ith possibility,Pi is the probability of that return occurring,n is the total number of possibilities.,n,i=1,How to Determine the Expected Return and Standard Deviation,Stock BW RiPi(Ri)(Pi)-.15.10-.015-.03.20-.006.09.40.036.21.20.042.33.10.033 Sum 1.00.090,The expected return,R,for Stock BW is.09 or 9%,Determining Standard Deviation标准差或者标准离差(Risk Measure),n,i=1,s=S(Ri-R)2(Pi)Standard Deviation,s,is a statistical measure of the variability of a distribution around its mean.It is the square root of variance(方差）.Note,this is for a discrete distribution（离散分布）.,How to Determine the Expected Return and Standard Deviation,Stock BW RiPi(Ri)(Pi)(Ri-R)2(Pi)-.15.10-.015.00576-.03.20-.006.00288.09.40.036.00000.21.20.042.00288.33.10.033.00576 Sum 1.00.090.01728,Determining Standard Deviation(Risk Measure),s=S(Ri-R)2(Pi)s=.01728s=.1315 or 13.15%,n,i=1,Coefficient of Variation,The ratio of the standard deviation of a distribution to the mean of that distribution.It is a measure of RELATIVE risk.CV=s/RCV of BW=.1315/.09=1.46,Discrete vs.Continuous Distributions连续分布,Discrete Continuous,Determining Expected Return(Continuous Dist.),R=S(Ri)/(n)R is the expected return for the asset,Ri is the return for the ith observation,n is the total number of observations.,n,i=1,Determining Standard Deviation(Risk Measure),n,i=1,s=S(Ri-R)2(n)Note,this is for a continuous distribution where the distribution is for a population.R represents the population mean in this example.,Continuous Distribution Problem,Assume that the following list represents the continuous distribution of population returns for a particular investment(even though there are only 10 returns).9.6%,-15.4%,26.7%,-0.2%,20.9%,28.3%,-5.9%,3.3%,12.2%,10.5%Calculate the Expected Return and Standard Deviation for the population assuming a continuous distribution.,Lets Use the Calculator!,Enter“Data”first.Press:2nd Data 2nd CLR Work9.6 ENTER-15.4 ENTER 26.7 ENTER Note,we are inputting data only for the“X”variable and ignoring entries for the“Y”variable in this case.,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,Lets Use the Calculator!,Examine Results!Press:2nd Stat through the results.Expected return is 9%for the 10 observations.Population standard deviation is 13.32%.This can be much quicker than calculating by hand,but slower than using a spreadsheet.,Certainty Equivalent(CE)资本回收保证量is the amount of cash someone would require with certainty at a point in time to make the individual indifferent between that certain amount and an amount expected to be received with risk at the same point in time.,Risk Attitudes,Certainty equivalent Expected valueRisk Preference风险偏好Certainty equivalent=Expected valueRisk Indifference风险中立 Certainty equivalent Expected valueRisk Aversion风险规避Most individuals are Risk Averse.,Risk Attitudes,Risk Attitude Example,You 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.Mary requires a guaranteed$25,000,or more,to call off the gamble.Raleigh is just as happy to take$50,000 or take the risky gamble.Shannon requires at least$52,000 to call off the gamble.,What are the Risk Attitude tendencies of each?,Risk Attitude Example,Mary shows“risk aversion”because her“certainty equivalent”the expected value of the gamble.,RP=S(Wj)(Rj)RP is the expected return for the portfolio,Wj is the weight(investment proportion)for the jth asset in the portfolio,Rj is the expected return of the jth asset,m is the total number of assets in the portfolio.,Determining PortfolioExpected Return,m,j=1,Determining Portfolio Standard Deviation,m,j=1,m,k=1,sP=S S Wj Wk sjk Wj is the weight(investment proportion)for the jth asset in the portfolio,Wk is the weight(investment proportion)for the kth asset in the portfolio,sjk is the covariance between returns for the jth and kth assets in the portfolio.,What is Covariance协方差?,s jk=s j s k r jk sj is the standard deviation of the jth asset in the portfolio,sk is the standard deviation of the kth asset in the portfolio,rjk is the correlation coefficient between the jth and kth assets in the portfolio.,Correlation Coefficient,A standardized statistical measure of the linear relationship between two variables.Its range is from-1.0(perfect negative correlation),through 0(no correlation),to+1.0(perfect positive correlation).,Variance-Covariance Matrix,A three-asset portfolio:Col 1 Col 2 Col 3Row 1W1W1s1,1 W1W2s1,2 W1W3s1,3Row 2W2W1s2,1 W2W2s2,2 W2W3s2,3Row 3W3W1s3,1 W3W2s3,2 W3W3s3,3sj,k=is the covariance between returns for the jth and kth assets in the portfolio.,You are creating a portfolio of Stock D and Stock BW(from earlier).You are investing$2,000 in Stock BW and$3,000 in Stock D.Remember that the expected return and standard deviation of Stock BW is 9%and 13.15%,respectively.The expected return and standard deviation of Stock D is 8%and 10.65%,respectively.The correlation coefficient between BW and D is 0.75.What is the expected return and standard deviation of the portfolio?,Portfolio Risk and Expected Return Example,Determining Portfolio Expected Return,WBW=$2,000/$5,000=.4WD=$3,000/$5,000=.6RP=(WBW)(RBW)+(WD)(RD)RP=(.4)(9%)+(.6)(8%)RP=(3.6%)+(4.8%)=8.4%,Two-asset portfolio:Col 1 Col 2Row 1WBW WBW sBW,BW WBW WD sBW,DRow 2 WD WBW sD,BW WD WD sD,DThis represents the variance-covariance matrix for the two-asset portfolio.,Determining Portfolio Standard Deviation,Two-asset portfolio:Col 1 Col 2Row 1(.4)(.4)(.0173)(.4)(.6)(.0105)Row 2(.6)(.4)(.0105)(.6)(.6)(.0113)This represents substitution into the variance-covariance matrix.,Determining Portfolio Standard Deviation,Two-asset portfolio:Col 1 Col 2Row 1(.0028)(.0025)Row 2(.0025)(.0041)This represents the actual element values in the variance-covariance matrix.,Determining Portfolio Standard Deviation,Determining Portfolio Standard Deviation,sP=.0028+(2)(.0025)+.0041sP=SQRT(.0119)sP=.1091 or 10.91%A weighted average of the individual standard deviations is INCORRECT.,Determining Portfolio Standard Deviation,The WRONG way to calculate is a weighted average like:sP=.4(13.15%)+.6(10.65%)sP=5.26+6.39=11.65%10.91%=11.65%This is INCORRECT.,Stock C Stock D PortfolioReturn 9.00%8.00%8.64%Stand.Dev.13.15%10.65%10.91%CV 1.46 1.33 1.26The portfolio has the LOWEST coefficient of variation due to diversification.,Summary of the Portfolio Return and Risk Calculation,Combining securities that are not perfectly,positively correlated reduces risk.,Diversification and the Correlation Coefficient,INVESTMENT RETURN,TIME,TIME,TIME,SECURITY E,SECURITY F,CombinationE and F,Systematic Risk is the variability of return on stocks or portfolios associated with changes in return on the market as a whole.Unsystematic Risk is the variability of return on stocks or portfolios not explained by general market movements.It is avoidable through diversification.,Total Risk=Systematic Risk+Unsystematic Risk,Total Risk=Systematic Risk+Unsystematic Risk,Total Risk=Systematic Risk+Unsystematic Risk,TotalRisk,Unsystematic risk,Systematic risk,STD DEV OF PORTFOLIO RETURN,NUMBER OF SECURITIES IN THE PORTFOLIO,Factors such as changes in nations economy,tax reform by the Congress,or a change in the world situation.,Total Risk=Systematic Risk+Unsystematic Risk,TotalRisk,Unsystematic risk,Systematic risk,STD DEV OF PORTFOLIO RETURN,NUMBER OF SECURITIES IN THE PORTFOLIO,Factors unique to a particular companyor industry.For example,the death of akey executive or loss of a governmentaldefense contract.,CAPM is a model that describes the relationship between risk and expected(required)return;in this model,a securitys expected(required)return is the risk-free rate plus a premium based on the systematic risk of the security.,Capital Asset Pricing Model(CAPM),1.Capital markets are efficient.2.Homogeneous investor expectations over a given period.3.Risk-free asset return is certain(use short-to intermediate-term Treasuries as a proxy 代理).4.Market portfolio contains only systematic risk(use S&P 500 Indexor similar as a proxy).,CAPM Assumptions,Characteristic Line,EXCESS RETURNON STOCK,EXCESS RETURNON MARKET PORTFOLIO,Beta=,RiseRun,Narrower spreadis higher correlation,Characteristic Line,Calculating“Beta”on Your Calculator,The Market and My Stock returns are“excess returns”and have the riskless rate already subtracted.,Calculating“Beta”on Your Calculator,Assume 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).Enter 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%.Enter the excess stock returns as“Y”observations of:12%,-5%,19%,3%,13%,14%,-9%,-1%,12%,and 10%.,Calculating“Beta”on Your Calculator,Let us examine again the statistical results(Press 2nd and then Stat)The market expected return and standard deviation is 9%and 13.32%.Your stock expected return and standard deviation is 6.8%and 8.76%.The 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.,An index of systematic risk.It measures the sensitivity of a stocks returns to changes in returns on the market portfolio.The beta for a portfolio is simply a weighted average of the individual stock betas in the portfolio.,What is Beta?,Characteristic Lines and Different Betas,EXCESS RETURNON STOCK,EXCESS RETURNON MARKET PORTFOLIO,Beta 1(defensive),Beta=1,Beta 1(aggressive),Each characteristic line has a different slope.,Rj is the required rate of return for stock j,Rf is the risk-free rate of return,bj is the beta of stock j(measures systematic risk of stock j),RM is the expected return for the market portfolio.,Security Market Line,Rj=Rf+bj(RM-Rf),Security Market Line,Rj=Rf+bj(RM-Rf),bM=1.0Systematic Risk(Beta),Rf,RM,Required Return,RiskPremium,Risk-freeReturn,Lisa Miller at Basket Wonders is attempting to determine the rate of return required by their stock investors.Lisa is using a 6%Rf and a long-term market expected rate of return of 10%.A stock analyst following the firm has calculated that the firm beta is 1.2.What is the required rate of return on the stock of Basket Wonders?,Determination of the Required Rate of Return,RBW=Rf+bj(RM-Rf)RBW=6%+1.2(10%-6%)RBW=10.8%The required rate of return exceeds the market rate of return as BWs beta exceeds the market beta(1.0).,BWs Required Rate of Return,Lisa Miller at BW is also attempting to determine the intrinsic value of the stock.She is using the constant growth model.Lisa estimates that the dividend next period will be$0.50 and that BW will grow at a constant rate of 5.8%.The stock is currently selling for$15.What is the intrinsic value of the stock?Is the stock over or underpriced?,Determination of the Intrinsic Value of BW,The stock is OVERVALUED as the market price($15)exceeds the intrinsic value($10).,Determination of the Intrinsic Value of BW,$0.50,10.8%-5.8%,IntrinsicValue,=,=,$10,Security Market Line,Systematic Risk(Beta),Rf,Required Return,Direction ofMovement,Direction ofMovement,Stock Y(Overpriced),Stock X(Underpriced),Small-firm EffectPrice/Earnings EffectJanuary EffectThese anomalies have presented serious challenges to the CAPM theory.,Determination of the Required Rate of Return,