財(cái)務(wù)管理ch04 風(fēng)險(xiǎn)和報(bào)酬

1、Chapter 4Risk and Return風(fēng)險(xiǎn)與報(bào)酬Dollar ReturnsTotal 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

2、=Capital gain = Total dollar return =Percentage ReturnsIt 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

3、gains yieldExample Calculating ReturnsYou 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 ReturnIncome received

4、 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-1R =Return ExampleThe 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 re

5、ceived a $1 dividend. What return was earned over the past year?ExerciseSuppose 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 Retu

6、rnsInvestmentAverage 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%Risk Premiums（風(fēng)險(xiǎn)溢價(jià)）The “extra” return earned for taking on riskTreasury bills are considered to be risk-freeThe risk premium is the return

7、 over and above the risk-free rateHistorical Risk PremiumsLarge 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%Expected ReturnsExpected returns are based on the probabilities of possible outcomesIn this context,

8、“expected” means average if the process is repeated many timesThe “expected” return does not even have to be a possible returnDiscrete vs. Continuous Distributions Discrete ContinuousDetermining Expected Return (Discrete Dist.離散型分布) R = S ( Ri )( Pi )R is the expected return （期望報(bào)酬）for the asset,Ri i

9、s the return for the ith possibility,Pi is the probability of that return occurring,n is the total number of possibilities.ni=1Example: Expected ReturnsSuppose you have predicted the following returns for stocks C and T in three possible states of nature. What are the expected returns?StateProbabili

10、tyCTBoom5Normal0Recession?0.020.01RC = RT =How to Determine the Expected Return and Standard DeviationStock BW RiPi (Ri)(Pi) -.15 .10 -.015 -.03 .20 -.006 .09 .40 .036 .21 .20 .042 .33 .10 .033 Sum 1.00 .090The expected return, R, for Stock BW is .09 or 9%Determining Standard Dev

11、iation (Risk Measure)s = S ( Ri - R )2( Pi )Standard Deviation（標(biāo)準(zhǔn)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.ni=1How to Determine the Expected Return and Standard DeviationStock B

12、W 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 .01728Determining Standard Deviation (Risk Measure)s = S ( Ri - R )2( Pi )s = .01728s = .1315 or 13.15%ni=1Example: Variance and Standard DeviationCons

13、ider the previous example. What are the variance and standard deviation for each stock?Stock C2 = =Stock T2 = =Coefficient of Variation（變化系數(shù)）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

14、Determining Expected Return (Continuous Dist.連續(xù)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.ni=1Determining Standard Deviation (Risk Measure)ni=1s = S ( Ri - R )2 ( n )Note, this is for a continuous dis

15、tribution where the distribution is for a population. R represents the population mean in this example.Risk 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.Ma

16、ry 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 ExampleMary shows “risk aversion” because her “cert

17、ainty equivalent” the expected 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 a

18、voidable through diversification.Total Risk = Systematic Risk + Unsystematic RiskTotal Risk = Systematic Risk + Unsystematic RiskSystematic RiskRisk factors that affect a large number of assetsAlso known as non-diversifiable risk or market riskIncludes such things as changes in GDP, inflation, inter

19、est rates, etc.Unsystematic RiskRisk 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 RiskTotalRiskUnsystematic riskSystematic riskSTD DEV OF PORTFOLIO

20、 RETURNNUMBER OF SECURITIES IN THE PORTFOLIOFactors such as changes in nations economy, tax reform by the Congress,or a change in the world situation.Total Risk = Systematic Risk + Unsystematic RiskTotalRiskUnsystematic riskSystematic riskSTD DEV OF PORTFOLIO RETURNNUMBER OF SECURITIES IN THE PORTFO

21、LIOFactors unique to a particular companyor industry. For example, the death of akey executive or loss of a governmentaldefense contract.Total RiskTotal risk = systematic risk + unsystematic riskThe standard deviation of returns is a measure of total riskFor well diversified portfolios, unsystematic

22、 risk is very smallConsequently, the total risk for a diversified portfolio is essentially equivalent to the systematic riskPortfolios(組合）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

23、portfolio is measured by the portfolio expected return and standard deviation, just as with individual assetsCorrelation Coefficient（相關(guān)系數(shù)）A standardized statistical measure of the linear relationship between two variables.Its range is from -1.0 (perfect negative correlation), through 0 (no correlati

24、on), to +1.0 (perfect positive correlation).Combining securities that are not perfectly, positively correlated reduces risk.Diversification and the Correlation CoefficientINVESTMENT RETURNTIMETIMETIMESECURITY ESECURITY FCombinationE and FExample: Portfolio Weights（權(quán)重）Suppose you have $15,000 to inve

25、st and you have purchased securities in the following amounts. What are your portfolio weights in each security?$2000 of DCLK$3000 of KO$4000 of INTC$6000 of KEIDCLK: 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 weig

26、ht (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 Returnmj=1Example: Expected Portfolio ReturnsConsider the portfolio weights computed previously. If the individual s

27、tocks have the following expected returns, what is the expected return for the portfolio?DCLK: 19.65%KO: 8.96%INTC: 9.67%KEI: 8.13%E(RP) =證券投資組合的具體做法1、選擇足夠數(shù)量的證券組合2、把投資報(bào)酬呈負(fù)相關(guān)的證券放在一起3、把風(fēng)險(xiǎn)大、中等、小的證券放在一起CAPM is a model that describes the relationship between risk and expected (required) return; in this m

28、odel, 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

29、intermediate-term Treasuries as a proxy).4.Market portfolio contains only systematic risk (use S&P 500 Indexor similar as a proxy).CAPM AssumptionsCalculating “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 Ma

30、rket 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 to changes in returns on the market portfolio.The beta for a portfolio is simply a weighted average of the individual stock betas i

31、n the portfolio.What is Beta?Example: Portfolio BetasConsider the previous example with the following four securitiesSecurityWeightBetaDCLK.1334.03KO.20.84INTC.1671.05KEI.40.59What is the portfolio beta?Measuring Systematic RiskHow do we measure systematic risk?We use the beta coefficient to measure

32、 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 systematic risk than the overall marketCharacteristic Lines and Different BetasEXCESS RETURNON STOCKEXCESS RETURNON MARKET PORTFOLIOBeta 1(aggres

33、sive)Each characteristic line has a different slope.Total versus Systematic RiskConsider the following information: Standard DeviationBetaSecurity 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

34、?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 LineRj = Rf + bj(RM - Rf)Security Market LineRj = Rf + bj(RM - Rf)bM = 1.0Systematic Ri

35、sk (Beta)RfRMRequired ReturnRiskPremiumRisk-freeReturnLisa 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 ReturnRBW = Rf + bj(RM - Rf)RBW =