4-1Chapter 4Risk and ReturnRisk and Return风险与报酬风险与报酬风险与报酬风险与报酬4-2Dollar ReturnsuTotal dollar return = income from investment + capital gain (loss) due to change in priceuExample:uYou 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?uIncome =uCapital gain = uTotal dollar return =4-3Percentage ReturnsuIt is generally more intuitive to think in terms of percentages than dollar returnsuDividend yield = income / beginning priceuCapital gains yield = (ending price beginning price) / beginning priceuTotal percentage return = dividend yield + capital gains yield4-4Example Calculating ReturnsuYou bought a stock for $35 and you received dividends of $1.25. The stock is now selling for $40.uWhat is your dollar return?uDollar return =uWhat is your percentage return?uDividend yield =uCapital gains yield =uTotal percentage return =4-5Defining 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 =4-6Return 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 shareholders per share and shareholders just received a just received a $1 dividend$1 dividend. What return . What return was earned over the past year?was earned over the past year?4-7ExerciseuSuppose 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?uR = uWhat is the dividend yield?uWhat is the capital gains yield?4-8Average ReturnsInvestmentAverage ReturnLarge stocks 12.7%Small Stocks 17.3%Long-term Corporate Bonds 6.1%Long-term Government Bonds 5.7%U.S. Treasury Bills 3.9%Inflation 3.1%4-9Risk Premiums（风险溢价）风险溢价）uThe “extra” return earned for taking on riskuTreasury bills are considered to be risk-freeuThe risk premium is the return over and above the risk-free rate4-10Historical Risk PremiumsuLarge stocks: 12.7 3.9 = 8.8%uSmall stocks: 17.3 3.9 = 13.4%uLong-term corporate bonds: 6.1 3.9 =2.2%uLong-term government bonds: 5.7 3.9 = 1.8%4-11Expected ReturnsuExpected returns are based on the probabilities of possible outcomesuIn this context, “expected” means average if the process is repeated many timesuThe “expected” return does not even have to be a possible return4-12Discrete vs. Continuous Distributions Discrete Continuous4-13Determining Expected Return Determining Expected Return (Discrete Dist.(Discrete Dist.离散型分布离散型分布离散型分布离散型分布) R R = = S S S S ( ( R Ri i )( )( P Pi i ) )R R is the is the expected returnexpected return （期望报酬）期望报酬）期望报酬）期望报酬）for the for the asset,asset,R Ri i is the return for the is the return for the i ithth possibility, possibility,P Pi i is the probability of that return occurring, is the probability of that return occurring,n n is the total number of possibilities. is the total number of possibilities.ni=14-14Example: Expected ReturnsuSuppose you have predicted the following returns for stocks C and T in three possible states of nature. What are the expected returns?uStateProbabilityCTuBoom0.30.150.25uNormal0.50.100.20uRecession?0.020.01uRC = uRT =4-15How 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%4-16Determining Standard Determining Standard Deviation Deviation (Risk Measure)Risk Measure) = = S S S S ( ( R Ri i - - R R ) )2 2( ( P Pi i ) )Standard DeviationStandard Deviation（标准差）标准差）标准差）标准差）, , , is a , is a statistical measure of the variability of a statistical measure of the variability of a distribution around its mean.distribution 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. .ni=14-17How 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 .01728.017284-18Determining Standard Determining Standard Deviation (Risk Measure)Deviation (Risk Measure) = = S S S S ( ( R Ri i - - R R ) )2 2( ( P Pi i ) ) = = .01728.01728 = = .1315.1315 or or 13.15%13.15%ni=14-19Example: Variance and Standard DeviationuConsider the previous example. What are the variance and standard deviation for each stock?uStock Cu 2 = u =uStock Tu 2 =u =4-20Coefficient of VariationCoefficient of Variation（变化系数）变化系数）变化系数）变化系数）The 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 = / / R RCV of BW = CV of BW = .1315.1315 / / .09.09 = 1.46 = 1.464-21Determining Expected Return Determining Expected Return (Continuous Dist.(Continuous Dist.连续型分布连续型分布连续型分布连续型分布) 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 is the return for the ithith observation, observation,n n is the total number of observations. is the total number of observations.ni=14-22Determining Standard Determining Standard Deviation (Risk Measure)Deviation (Risk Measure)ni=1 = = 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.4-23Risk 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.4-24What 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. .4-25Systematic 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 Risk4-26Systematic RiskuRisk factors that affect a large number of assetsuAlso known as non-diversifiable risk or market riskuIncludes such things as changes in GDP, inflation, interest rates, etc.4-27Unsystematic RiskuRisk factors that affect a limited number of assetsuAlso known as unique risk and asset-specific riskuIncludes such things as labor strikes, part shortages, etc.4-28Total 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.4-29Total 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.4-30Total RiskuTotal risk = systematic risk + unsystematic riskuThe standard deviation of returns is a measure of total riskuFor well diversified portfolios, unsystematic risk is very smalluConsequently, the total risk for a diversified portfolio is essentially equivalent to the systematic risk4-31Portfolios(组合）组合）uA portfolio is a collection of assetsuAn assets risk and return is important in how it affects the risk and return of the portfoliouThe risk-return trade-off for a portfolio is measured by the portfolio expected return and standard deviation, just as with individual assets4-32Correlation CoefficientCorrelation Coefficient（相关系数）相关系数）相关系数）相关系数）相关系数）相关系数）A 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). ).4-33Combining 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 F4-34Example: Portfolio Weights（权重权重）uSuppose you have $15,000 to invest and you have purchased securities in the following amounts. What are your portfolio weights in each security?u$2000 of DCLKu$3000 of KOu$4000 of INTCu$6000 of KEIDCLK: 2/15 = .133KO: 3/15 = .2INTC: 4/15 = .267KEI: 6/15 = .44-35 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 is the expected return of the j 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=14-36Example: Expected Portfolio ReturnsuConsider the portfolio weights computed previously. If the individual stocks have the following expected returns, what is the expected return for the portfolio?uDCLK: 19.65%uKO: 8.96%uINTC: 9.67%uKEI: 8.13%uE(RP) =4-37证券投资组合的具体做法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4-38CAPM 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)4-391.1.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).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 Assumptions4-40Calculating “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.4-41An 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?4-42Example: Portfolio BetasuConsider the previous example with the following four securitiesuSecurityWeightBetauDCLK.1334.03uKO.20.84uINTC.1671.05uKEI.40.59uWhat is the portfolio beta?4-43Measuring Systematic RiskuHow do we measure systematic risk?uWe use the beta coefficient to measure systematic riskuWhat does beta tell us?uA beta of 1 implies the asset has the same systematic risk as the overall marketuA beta 1 implies the asset has more systematic risk than the overall market4-44Characteristic 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.4-45Total versus Systematic RiskuConsider the following information: Standard DeviationBetauSecurity C20%1.25uSecurity K30%0.95uWhich security has more total risk?uWhich security has more systematic risk?uWhich security should have the higher expected return?4-46R 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)4-47Security 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-freeReturnReturn4-48Lisa 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% 6% R 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 Return4-49R 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 Return4-50Lisa 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 BW4-51The 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=$104-52Security Market LineSecurity Market LineSystematic Risk (Beta)R Rf fRequired ReturnRequired ReturnDirection ofMovementDirection ofMovementStock Y Stock Y (Overpriced)Stock X (Underpriced)4-53Example - CAPMuConsider 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?uSecurityBeta Expected ReturnuDCLK4.036.15 + 4.03(9.5) = 44.435%uKO0.846.15 + .84(9.5) = 14.13%uINTC1.056.15 + 1.05(9.5) = 16.125%uKEI0.596.15 + .59(9.5) = 11.755%