财务管理基础ch02

CHAPTER 2Risk and Rates of ReturnStand-alone riskPortfolio riskRisk&return:CAPM/SMLInvestment returnsThe rate of return on an investment can be calculated as follows:(Amount received Amount invested)Return=_ Amount investedFor example,if$1,000 is invested and$1,100 is returned after one year,the rate of return for this investment is:($1,100-$1,000)/$1,000=10%.What is investment risk?nTwo types of investment riskStand-alone riskPortfolio risk nInvestment risk is related to the probability of earning a low or negative actual return.nThe greater the chance of lower than expected or negative returns,the riskier the investment.Outcome(1)Probability(2)Rain0.40=40%No Rain0.60=60%1.00 100%Probability DistributionsIt either will rain,or it will not only two possible outcomesProbability DistributionsMartin Products and U.S.ElectricMartin ProductsU.S.ElectricBoom0.2110%20%Normal0.522%16%Recession0.3-60%10%1.0Probability of This State OccurringState of the EconomyRate of Return on Stock if This State OccursProbability distributionsnA listing of all possible outcomes,and the probability of each occurrence.nCan be shown graphically.Expected Rate of ReturnRate ofReturn(%)100150-70Firm XFirm YInvestment alternativesEconomyProb.T-BillHTCollUSRMPRecession0.18.0%-22.0%28.0%10.0%-13.0%Below avg0.28.0%-2.0%14.7%-10.0%1.0%Average0.48.0%20.0%0.0%7.0%15.0%Above avg0.28.0%35.0%-10.0%45.0%29.0%Boom0.18.0%50.0%-20.0%30.0%43.0%Return:Calculating the expected return for each alternative 17.4%(0.1)(50%)(0.2)(35%)(0.4)(20%)(0.2)(-2%)(0.1)(-22.%)kP k k return of rate expected kHTn1iiiHow do the returns of HT and Coll.behave in relation to the market?nHT Moves with the economy,and has a positive correlation.This is typical.nColl.Is countercyclical with the economy,and has a negative correlation.This is unusual.Expected Rate of Return(1)(2)(3)=(4)(5)=(6)Boom0.2110%22%20%4%Normal0.522%11%16%8%Recession0.3-60%-18%10%3%1.0km=15%km=15%State of the EconomyMartin ProductsU.S.ElectricReturn if This State Occurs(ki)Product:(2)x(5)Probability of This State Occurring(Pri)Return if This State Occurs(ki)Product:(2)x(3)Summary of expected returns for all alternativesExp returnHT 17.4%Market 15.0%USR 13.8%T-bill 8.0%Coll.1.7%HT has the highest expected return,and appears to be the best investment alternative,but is it really?Have we failed to account for risk?Discrete Probability Distributions-60 -45 -30 -15 0 15 22 30 45 60 75 90 110Rate of Return(%)Expected Rate of Return(15%)a.Martin ProductsProbability of Occurrence-10 -5 0 5 10 16 20 25Rate of Return(%)Expected Rate of Return(15%)b.U.S.ElectricProbability of Occurrence0.5-0.4-0.3-0.2-0.1-0.5-0.4-0.3-0.2-0.1-Continuous Probability Distributions-60 0 15 110Rate of Return(%)Expected Rate of ReturnMartin ProductsProbability DensityU.S.ElectricMeasuring Risk:The Standard Deviationn1iiikk return of rate ExpectedPrn1ii2i2k-k VariancePrn1ii2i2k-k deviation StandardPrMeasuring Risk:The Standard DeviationCalculating Martin Products Standard Deviation(1)(2)(1)-(2)=(3)(4)(5)(4)x(5)=(6)110%15%959,025 0.2 1,805.0 22%15%749 0.5 24.5 -60%15%-755,625 0.3 1,687.5 Payoff ki(ki-k)2PriProbabilityExpected Return kki-k(ki-k)2%3.59 517,3 Deviation Standard0.517,3 Variance2mm2Standard deviation calculation15.3%18.8%20.0%13.4%0.0%(0.1)8.0)-(8.0 (0.2)8.0)-(8.0 (0.4)8.0)-(8.0 (0.2)8.0)-(8.0(0.1)8.0)-(8.0 P)k (k MUSRHTCollbillsT22222billsTn1ii2i21Comparing standard deviationsUSRProb.T-billHT0 8 13.8 17.4 Rate of Return(%)Comparing risk and returnSecurityExpected returnRisk,T-bills8.0%0.0%HT17.4%20.0%Coll*1.7%13.4%USR*13.8%18.8%Market15.0%15.3%Measuring Risk:Coefficient of VariationkReturnRisk CV Coefficient of variation Standardized measure of risk per unit of returnCalculated as the standard deviation divided by the expected returnUseful where investments differ in risk and expected returnsRisk rankings,by coefficient of variation CVT-bill0.000HT1.149Coll.7.882USR1.362Market1.020nCollections has the highest degree of risk per unit of return.nHT,despite having the highest standard deviation of returns,has a relatively average CV.Investor attitude towards risknRisk aversion assumes investors dislike risk and require higher rates of return to encourage them to hold riskier securities.nRisk premium the difference between the return on a risky asset and less risky asset,which serves as compensation for investors to hold riskier securities.Portfolio construction:Risk and returnAssume a two-stock portfolio is created with$50,000 invested in both HT and Collections.nExpected return of a portfolio is a weighted average of each of the component assets of the portfolio.nStandard deviation is a little more tricky and requires that a new probability distribution for the portfolio returns be devised.Calculating portfolio expected return9.6%(1.7%)0.5 (17.4%)0.5 kkw k :average weighted a is kpn1iiippAn alternative method for determining portfolio expected returnEconomyProb.HTCollRecession0.1-22.0%28.0%Below avg0.2-2.0%14.7%Average0.420.0%0.0%Above avg0.235.0%-10.0%Boom0.150.0%-20.0%9.6%(15.0%)0.10 (12.5%)0.20 (10.0%)0.40 (6.4%)0.20 (3.0%)0.10 kpCalculating portfolio standard deviation and CV0.34 9.6%3.3%CV3.3%9.6)-(15.0 0.10 9.6)-(12.5 0.20 9.6)-(10.0 0.40 9.6)-(6.4 0.20 9.6)-(3.0 0.10 p2122222pComments on portfolio risk measuresnp=3.3%is much lower than the i of either stock(HT=20.0%;Coll.=13.4%).np=3.3%is lower than the weighted average of HT and Coll.s (16.7%).n Portfolio provides average return of component stocks,but lower than average risk.nWhy?Negative correlation between stocks.Returns distribution for two perfectly negatively correlated stocks(r=-1.0)-101515252525150-10Stock W0Stock M-100Portfolio WMReturns distribution for two perfectly positively correlated stocks(r=1.0)Stock M01525-10Stock M01525-10Portfolio MM01525-10Combining stocks that are not perfectly correlated will reduce the portfolio risk by diversificationThe riskiness of a portfolio is reduced as the number of stocks in the portfolio increasesThe smaller the positive correlation,the lower the riskPortfolio RiskGeneral comments about risknMost stocks are positively correlated with the market(rk,m 0.65).n 35%for an average stock.nCombining stocks in a portfolio generally lowers risk.Creating a portfolio:Beginning with one stock and adding randomly selected stocks to portfolionp decreases as stocks added,because they would not be perfectly correlated with the existing portfolio.nEventually the diversification benefits of adding more stocks dissipates(after about 10 stocks),and for large stock portfolios,p tends to converge to 20%.Illustrating diversification effects of a stock portfolio#Stocks in Portfolio10 20 30 40 2,000+Diversifiable RiskMarket Risk20 0Portfolio Risk,p p(%)35Breaking down sources of riskStand-alone risk=Market risk+Firm-specific risknMarket risk portion of a securitys stand-alone risk that cannot be eliminated through diversification.Measured by beta.nFirm-specific risk portion of a securitys stand-alone risk that can be eliminated through proper diversification.Capital Asset Pricing Model(CAPM)nModel based upon concept that a stocks required rate of return is equal to the risk-free rate of return plus a risk premium that reflects the riskiness of the stock after diversification.nPrimary conclusion:The relevant riskiness of a stock is its contribution to the riskiness of a well-diversified portfolio.BetanMeasures a stocks market risk,and shows a stocks volatility relative to the market.nIndicates how risky a stock is if the stock is held in a well-diversified portfolio.The Concept of BetalA measure of the extent to which the returns on a given stock move with the stock marketb=0.5:stock is only half as volatile,or risky,as the average stockb=1.0:stock is of average riskb=2.0:stock is twice as risky as the average stockPortfolio Beta CoefficientslThe beta of any set of securities is the weighted average of the individual securities betasN1jjjnn2211ww.wwbbbbbpComments on betanIf beta=1.0,the security is just as risky as the average stock.nIf beta 1.0,the security is riskier than average.nIf beta 1.0,the security is less risky than average.nMost stocks have betas in the range of 0.5 to 1.5.Can the beta of a security be negative?nYes,if the correlation between Stock i and the market is negative(i.e.,ri,m 0).nIf the correlation is negative,the regression line would slope downward,and the beta would be negative.nHowever,a negative beta is highly unlikely.Beta coefficients for HT,Coll,and T-Billski_kM_-20 0 20 404020-20HT:=1.30T-bills:=0Coll:=-0.87Comparing expected return and beta coefficientsSecurityExp.Ret.Beta HT 17.4%1.30Market 15.0 1.00USR 13.8 0.89T-Bills 8.0 0.00Coll.1.7-0.87Riskier securities have higher returnsstock j on the premiumrisk k-k RPpremiumrisk market k-k RPreturn of rate kstock j on thereturn of rate kstock j on thereturn of rate kthjRFMjRFMMRFthjthjbfreeriskrequiredexpectedThe Relationship Between Risk and Rates of ReturnMarket Risk Premium is the additional return over the risk-free rate needed to compensate investors for assuming an average amount of riskTreasury bonds yield=6%Average stock required return=14%Then the market risk premium is 8 percent:RPM=kM-kRF=14%-6%=8%Risk Premium for a Stock=RPj=RPM x bjThe Required Rate of Return for a Stockjstock for return of rate kjrequiredjRFMRFjMRFjkk kRP k kbbThe line that shows the relationship between risk as measured by beta and the required rate of return for individual securitiesSecurity Market LineRequired Rate of Return(%)Risk-Free Rate:6%0 0.5 1.0 1.5 2.0 Risk,bjkhigh=22kM=kA=14kLOW=10kRF=6Safe Stock Risk Premium:4%Market(Average Stock)Risk Premium:8%jRFMRFjkk k k:SMLbRelatively Risky Stocks Risk Premium:16%The Security Market Line(SML):Calculating required rates of returnSML:ki=kRF+(kM kRF)i nAssume kRF=8%and kM=15%.nThe market(or equity)risk premium is RPM=kM kRF=15%8%=7%.Calculating required rates of returnnkHT =8.0%+(15.0%-8.0%)(1.30)=8.0%+(7.0%)(1.30)=8.0%+9.1%=17.10%nkM=8.0%+(7.0%)(1.00)=15.00%nkUSR=8.0%+(7.0%)(0.89)=14.23%nkT-bill=8.0%+(7.0%)(0.00)=8.00%nkColl=8.0%+(7.0%)(-0.87)=1.91%Expected vs.Required returnsk)k(Overvalued 1.9 1.7 Coll.k)k(uedFairly val 8.0 8.0 bills-Tk)k(Overvalued 14.2 13.8 USRk)k(uedFairly val 15.0 15.0 Market k)k(dUndervalue 17.1%17.4%HT k k An example:Equally-weighted two-stock portfolionCreate a portfolio with 50%invested in HT and 50%invested in Collections.nThe beta of a portfolio is the weighted average of each of the stocks betas.P=wHT HT+wColl Coll P=0.5(1.30)+0.5(-0.87)P=0.215Calculating portfolio required returnsnThe required return of a portfolio is the weighted average of each of the stocks required returns.kP=wHT kHT+wColl kColl kP=0.5(17.1%)+0.5(1.9%)kP=9.5%nOr,using the portfolios beta,CAPM can be used to solve for expected return.kP=kRF+(kM kRF)P kP=8.0%+(15.0%8.0%)(0.215)kP=9.5%Factors that change the SMLnWhat if investors raise inflation expectations by 3%,what would happen to the SML?SML1ki(%)SML20 0.5 1.01.5181511 8D D I=3%Risk,iFactors that change the SMLnWhat if investors risk aversion increased,causing the market risk premium to increase by 3%,what would happen to the SML?SML1ki(%)SML20 0.5 1.01.5 181511 8D D RPM=3%Risk,iWhat is market equilibrium?nIn equilibrium,stock prices are stable and there is no general tendency for people to buy versus to sell.nIn equilibrium,expected returns must equal required returns.b)k(k k k g PD kRFMRFs01sMarket equilibriumnExpected returns are obtained by estimating dividends and expected capital gains.nRequired returns are obtained by estimating risk and applying the CAPM.How is market equilibrium established?nIf expected return exceeds required return The current price(P0)is“too low”and offers a bargain.Buy orders will be greater than sell orders.P0 will be bid up until expected return equals required returnFactors that affect stock pricenRequired return(ks)could changeChanging inflation could cause kRF to changeMarket risk premium or exposure to market risk()could changenGrowth rate(g)could changeDue to economic(market)conditionsDue to firm conditionsWhat is the Efficient Market Hypothesis(EMH)?nSecurities are normally in equilibrium and are“fairly priced.”nInvestors cannot“beat the market”except through good luck or better information.nLevels of market efficiencyWeak-form efficiencySemistrong-form efficiencyStrong-form efficiencyWeak-form efficiencynCant profit by looking at past trends.A recent decline is no reason to think stocks will go up(or down)in the future.Semistrong-form efficiencynAll publicly available information is reflected in stock prices,so it doesnt pay to over analyze annual reports looking for undervalued stocks.nLargely true,but superior analysts can still profit by finding and using new informationStrong-form efficiencynAll information,even inside information,is embedded in stock prices.nNot true-insiders can gain by trading on the basis of insider information,but thats illegal.Is the stock market efficient?nEmpirical studies have been conducted to test the three forms of efficiency.Most of which suggest the stock market was:Highly efficient in the weak form.Reasonably efficient in the semistrong form.Not efficient in the strong form.Insiders could and did make abnormal(and sometimes illegal)profits.