1、4-14-2uTotal 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 re

2、turn =4-3uIt 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 yield4-4uYou bought a stock for $35

3、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 =4-5R =4-6The stock price for Stock A was $10 per share 1 year ago. The stock is currently

4、 trading at $9.50 per share and shareholders just received a $1 dividend. What return was earned over the past year?4-7uSuppose 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

5、yield?uWhat is the capital gains yield?4-8InvestmentAverage 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%4-9uThe “extra” return earned for taking on riskuTreasury bills are considered to be risk-freeuThe

6、risk premium is the return over and above the risk-free rate4-10uLarge 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%4-11uExpected returns are based on the probabilities of possible outcomesuIn this context,

7、“expected” means average if the process is repeated many timesuThe “expected” return does not even have to be a possible return4-1200.050.10.150.20.250.30.350.4-15%-3%9%21%33% Discrete Continuous00.0050.010.0150.020.0250.030.035-50%-41%-32%-23%-14%-5%4%13%22%31%40%49%58%67%4-13 R = S ( Ri )( Pi )R i

8、s the expected return （期望報酬（期望報酬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.ni=14-14uSuppose you have predicted the following returns for stocks C and T in three possible states of nature. What are the e

9、xpected returns?uStateProbabilityCTuBoom0.30.150.25uNormal0.50.100.20uRecession?0.020.01uRC = uRT =4-15Stock 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%4-16方差）方差）. .Note, this is for a discrete N

10、ote, this is for a discrete distribution.distribution.ni=14-17Stock 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 .017284-18ni=14-19uConsider the previous example. What are the variance and standa

11、rd deviation for each stock?uStock Cu2 = u =uStock Tu2 =u =4-20The 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 = 1.464-21 R = S ( Ri ) / ( n )R is the expected return for the asset,Ri is the retu

12、rn for the ith observation,n is the total number of observations.ni=14-22ni=1population mean in this population mean in this example.example.4-23You 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

13、 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.4-24What are the Risk Attitude tendencies of each?Mary shows “risk aversion” because her “

14、certainty equivalent” the expected value of the gamble.4-254-26uRisk 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.4-27uRisk factors that affect a limited number of assetsuAlso k

15、nown as unique risk and asset-specific riskuIncludes such things as labor strikes, part shortages, etc.4-28STD 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.4-29STD DEV OF PORTFOLI

16、O 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.4-30uTotal risk = systematic risk + unsystematic riskuThe standard deviation of returns is a measure of total riskuFor we

17、ll diversified portfolios, unsystematic risk is very smalluConsequently, the total risk for a diversified portfolio is essentially equivalent to the systematic risk4-31uA portfolio is a collection of assetsuAn assets risk and return is important in how it affects the risk and return of the portfolio

18、uThe risk-return trade-off for a portfolio is measured by the portfolio expected return and standard deviation, just as with individual assets4-32A standardized statistical measure of the linear relationship between two variables.Its range is from -1.0 (perfect negative correlation), through 0 (no c

19、orrelation), to +1.0 (perfect positive correlation).4-33Combining securities that are not perfectly, positively correlated reduces risk.INVESTMENT RETURNTIMETIMETIME4-34uSuppose you have $15,000 to invest and you have purchased securities in the following amounts. What are your portfolio weights in

20、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 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

21、 the jth asset,m is the total number of assets in the portfolio.mj=14-36uConsider 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) =4-371、選擇足夠數量的

22、證券組合2、把投資報酬呈負相關的證券放在一起3、把風險大、中等、小的證券放在一起4-38CAPM 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.4-391.Capital markets are e

23、fficient.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 portfolio contains only systematic risk (use S&P 500 Indexor similar as a proxy).4-40Time Pd.MarketMy Stock19.6%12%2-15.4%-5%326.7

24、%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 systematic risk.It measures the sensitivity of a stocks returns to changes in returns on the market portfolio.The beta f

25、or a portfolio is simply a weighted average of the individual stock betas in the portfolio.4-42uConsider the previous example with the following four securitiesuSecurity WeightBetauDCLK.1334.03uKO.20.84uINTC.1671.05uKEI.40.59uWhat is the portfolio beta?4-43uHow do we measure systematic risk?uWe use

26、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 market4-44EXCESS RETURNON STOCKEXCESS RETURNON MARKET PORTFOLIOEach characteri

27、stic line has a different slope.4-45uConsider the following information:u 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?4-464-474-48Lisa 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