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1、Chapter 4,Risk and Return风险与报酬,Dollar Returns,Total dollar return=income from investment+capital gain(loss)due to change in priceExample:You bought a bond for$950 1 year ago.You have received two coupons of$30 each.You can sell the bond for$975 today.What is your total dollar return?Income=Capital g
2、ain=Total dollar return=,Percentage Returns,It is generally more intuitive to think in terms of percentages than dollar returnsDividend yield=income/beginning priceCapital gains yield=(ending price beginning price)/beginning priceTotal percentage return=dividend yield+capital gains yield,Example Cal
3、culating Returns,You bought a stock for$35 and you received dividends of$1.25.The stock is now selling for$40.What is your dollar return?Dollar return=What is your percentage return?Dividend yield=Capital gains yield=Total percentage return=,Defining Return,Income received on an investment plus any
4、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
5、was earned over the past year?,Exercise,Suppose a firms stock is selling for$10.50.They just paid a$1 dividend and dividends are expected to grow at 5%per year.What is the required return?R=What is the dividend yield?What is the capital gains yield?,Average Returns,Risk Premiums（风险溢价）,The“extra”retu
6、rn earned for taking on riskTreasury bills are considered to be risk-freeThe risk premium is the return over and above the risk-free rate,Historical Risk Premiums,Large stocks:12.7 3.9=8.8%Small stocks:17.3 3.9=13.4%Long-term corporate bonds:6.1 3.9=2.2%Long-term government bonds:5.7 3.9=1.8%,Expect
7、ed Returns,Expected returns are based on the probabilities of possible outcomesIn this context,“expected”means average if the process is repeated many timesThe“expected”return does not even have to be a possible return,Discrete vs.Continuous Distributions,Discrete Continuous,Determining Expected Ret
8、urn(Discrete Dist.离散型分布),R=S(Ri)(Pi)R is the expected return（期望报酬）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,Example:Expected Returns,Suppose you have predicted the following returns for stocks C
9、 and T in three possible states of nature.What are the expected returns?StateProbabilityCTBoom0.30.150.25Normal0.50.100.20Recession?0.020.01RC=RT=,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
10、expected return,R,for Stock BW is.09 or 9%,Determining Standard Deviation(Risk Measure),s=S(Ri-R)2(Pi)Standard Deviation（标准差）,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.,n,i=1,How to D
11、etermine 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,Example:Variance and
12、Standard Deviation,Consider the previous example.What are the variance and standard deviation for each stock?Stock C2=Stock T2=,Coefficient of Variation（变化系数）,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/
13、.09=1.46,Determining Expected Return(Continuous Dist.连续型分布),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 distributi
14、on where the distribution is for a population.R represents the population mean in this example.,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 guara
15、nteed$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 exp
16、ected value of the gamble.,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 diversif
17、ication.,Total Risk=Systematic Risk+Unsystematic Risk,Total Risk=Systematic Risk+Unsystematic Risk,Systematic Risk,Risk factors that affect a large number of assetsAlso known as non-diversifiable risk or market riskIncludes such things as changes in GDP,inflation,interest rates,etc.,Unsystematic Ris
18、k,Risk factors that affect a limited number of assetsAlso known as unique risk and asset-specific riskIncludes such things as labor strikes,part shortages,etc.,Total Risk=Systematic Risk+Unsystematic Risk,TotalRisk,Unsystematic risk,Systematic risk,STD DEV OF PORTFOLIO RETURN,NUMBER OF SECURITIES IN
19、 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 part
20、icular companyor industry.For example,the death of akey executive or loss of a governmentaldefense contract.,Total Risk,Total risk=systematic risk+unsystematic riskThe standard deviation of returns is a measure of total riskFor well diversified portfolios,unsystematic risk is very smallConsequently,
21、the total risk for a diversified portfolio is essentially equivalent to the systematic risk,Portfolios(组合）,A portfolio is a collection of assetsAn assets risk and return is important in how it affects the risk and return of the portfolioThe risk-return trade-off for a portfolio is measured by the po
22、rtfolio expected return and standard deviation,just as with individual assets,Correlation Coefficient（相关系数）,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 correl
23、ation).,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,Example:Portfolio Weights（权重）,Suppose you have$15,000 to invest and you have purchased sec
24、urities in the following amounts.What are your portfolio weights in each security?$2000 of DCLK$3000 of KO$4000 of INTC$6000 of KEI,DCLK:2/15=.133KO:3/15=.2INTC:4/15=.267KEI:6/15=.4,RP=S(Wj)(Rj)RP is the expected return for the portfolio,Wj is the weight(investment proportion)for the jth asset in th
25、e 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,Example:Expected Portfolio Returns,Consider the portfolio weights computed previously.If the individual stocks have the following expected returns,what
26、is the expected return for the portfolio?DCLK:19.65%KO:8.96%INTC:9.67%KEI:8.13%E(RP)=,证券投资组合的具体做法,1、选择足够数量的证券组合2、把投资报酬呈负相关的证券放在一起3、把风险大、中等、小的证券放在一起,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
27、-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).4.Market portfol
28、io contains only systematic risk(use S&P 500 Indexor similar as a proxy).,CAPM Assumptions,Calculating“Beta”on Your Calculator,The Market and My Stock returns are“excess returns”and have the riskless rate already subtracted.,An index of systematic risk.It measures the sensitivity of a stocks returns
29、 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?,Example:Portfolio Betas,Consider the previous example with the following four securitiesSecurityWeightBetaDCLK.1334.03KO.20.84INTC.1671.0
30、5KEI.40.59What is the portfolio beta?,Measuring Systematic Risk,How do we measure systematic risk?We use the beta coefficient to measure systematic riskWhat does beta tell us?A beta of 1 implies the asset has the same systematic risk as the overall marketA beta 1 implies the asset has more systemati
31、c risk than the overall market,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.,Total versus Systematic Risk,Consider the following information:Standard Deviatio
32、nBetaSecurity C20%1.25Security K30%0.95Which security has more total risk?Which security has more systematic risk?Which security should have the higher expected return?,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
33、 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 require
34、d 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
35、(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 estimat
36、es 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)e
37、xceeds 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),Example-CAPM,Consider the betas for each of the assets given earlier.If the risk-free rate is 6.15%and the market risk premium is 9.5%,what is the expected return for each?SecurityBeta Expected ReturnDCLK4.036.15+4.03(9.5)=44.435%KO0.846.15+.84(9.5)=14.13%INTC1.056.15+1.05(9.5)=16.125%KEI0.596.15+.59(9.5)=11.755%,
