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1、5-15-2uDefining Risk and ReturnuUsing Probability Distributions to Measure RiskuAttitudes Toward RiskuRisk and Return in a Portfolio ContextuDiversificationuThe Capital Asset Pricing Model (CAPM)5-3on an investment plus any , usually expressed as a percent of the of the investment.+ ()R =5-4The stoc
2、k price for Stock A was per share 1 year ago. The stock is currently trading at per share, and shareholders just received a . What return was earned over the past year?5-5The stock price for Stock A was per share 1 year ago. The stock is currently trading at per share, and shareholders just received
3、 a . What return was earned over the past year?+ ( - ) = 5-65-7 R = S S ( Ri )( Pi )R is the expected return 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=15-8Stock BW RiPi (Ri)(Pi) -.15 .10 -.015 -.03
4、.20 -.006 .09 .40 .036 .21 .20 .042 .33 .10 .033 Sum 1.00 The expected return, R, for Stock BW is .09 or 9%5-9 = S S ( Ri - R )2( Pi ), , is a statistical measure of the variability of a distribution around its mean.It is the square root of variance.Note, this is for a discrete distribution.ni=15-10
5、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 5-11 = S S ( Ri - R )2( Pi ) = .01728 = or ni=15-12The ratio of the of a distribution to the of that distribution.It is a measure of risk.CV = / CV o
6、f BW = / = 1.465-1300.050.10.150.20.250.30.350.4-15%-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%5-14 R = S 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 observ
7、ations.ni=15-15ni=1 = S S ( Ri - R )2 ( n )Note, this is for a continuous distribution where the distribution is for a population. R represents the population mean in this example.5-165-17It tells us how many standard deviations R is from the mean.Appendix Table VuIf Z=(0-0.09)/0.1315= -0.68, what i
8、t tells us?uThere is 25% probability that the actual return will be zero or less.Z = (R R) / 5-18() is the amount of cash someone would require with certainty at a point in time to make the individual indifferent between that certain amount and an amount expected to be received with risk at the same
9、 point in time.5-19Certainty equivalent Expected valueCertainty equivalent = Expected valueCertainty equivalent Expected valueMost individuals are .5-20You 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
10、 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.5-21What are the Risk Attitude tendencies of each?Mary shows because her “certai
11、nty equivalent” the expected value of the gamble5-22uWheaton, Inc. pays a constant annual dividend. Last year, the dividend yield was 3.6 percent when the stock was selling for $28 a share. What is the current price of the stock if the current dividend yield is 3.2 percent?u$31.5uD=3.6%*$28=1.008uP0
12、=D/DY=1.008/3.2%=$31.55-23uOne year ago, Mike purchased 100 shares of PJ stock for $3,100. The stock does not pay any regular dividends but it did pay a special dividend of $2.40 a share last week. This morning, he sold his shares for $29.80 a share. What was his total return on this investment? u3.
13、87%=($29.8+$2.4-$31)/$315-24uYou own a portfolio that consists of $8,000 in stock A, $4,600 in stock B, $13,000 in stock C, and $5,500 in stock D. What is the portfolio weight of stock D? u17.68 percent5-25uThe stock of Hobby Town has an expected return of 8.8 percent. Given the information below, w
14、hat is the expected return on this stock if the economy is normal?u6.43%5-26Given the following information, what is the variance for this stock?5-27(1) State of Economy(2)Probability of state of economy(3)Return deviation(4)Squared return deviation(2)*(4)VarianceBoom 0.150.26-0.08750.0297560.004463
15、Normal0.650.13-0.08750.0018060.001174Recession0.20-0.18-0.08750.0715560.014311 0.019949E(R)=0.15*0.26+0.65*0.13+0.20*(-0.18)=0.08755-28Section 25-2929uA portfolio is a collection of assetsuAn assets risk and return are important in how they affect the risk and return of the portfoliouThe risk-return
16、 trade-off for a portfolio is measured by the portfolio expected return and standard deviation, just as with individual assets5-30 RP = S 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
17、 the jth asset,m is the total number of assets in the portfolio.mj=15-31State of EconomyProbabilityPortfolio Excepted ReturnBoom0.412%Normal0.459%Recession0.152%RP = 0.4*12%+0.45*9%+0.15*2% = 9.15%5-3232uPortfolio diversification is the investment in several different asset classes or sectorsuDivers
18、ification is not just holding a lot of assetsuFor example, if you own 50 Internet stocks, you are not diversifieduHowever, if you own 50 stocks that span 20 different industries, then you are diversified5-33A standardized statistical measure of the linear relationship between two variables.Its range
19、 is from (perfect negative correlation), through (no correlation), to (perfect positive correlation).5-34Combining securities that are not perfectly, positively correlated reduces risk.INVESTMENT RETURNTIMETIMETIME5-35is the variability of return on stocks or portfolios associated with changes in re
20、turn on the market as a whole.is the variability of return on stocks or portfolios not explained by general market movements. It is avoidable through diversification.= + 5-36STD DEV OF PORTFOLIO RETURNNUMBER OF SECURITIES IN THE PORTFOLIOFactors such as changes in nations economy, tax reform by the
21、Congress,or a change in the world situation.5-37STD 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.5-38An index of .It measures the sensitivity of a stoc
22、ks returns to changes in returns on the market portfolio.The for a portfolio is simply a weighted average of the individual stock betas in the portfolio.5-39EXCESS RETURNON STOCKEXCESS RETURNON MARKET PORTFOLIO =5-40EXCESS RETURNON STOCKEXCESS RETURNON MARKET PORTFOLIOEach has a different slope.5-41
23、uConsider the previous example with the following four securitiesSecurity WeightBetaDCLK.1332.685KO.20.195INTC.2672.161KEI.42.434uWhat is the portfolio beta?u.133(2.685) + .2(.195) + .267(2.161) + .4(2.434) = 1.9475-42RfE(RA) AE(RA)=20%A=1.6Rf=8%5-43uThe reward-to-risk ratio is the slope of the line
24、 illustrated in the previous exampleuSlope = (E(RA) Rf) / ( A 0)uReward-to-risk ratio for previous example = (20 8) / (1.6 0) = 7.5uWhat if an asset has a reward-to-risk ratio of 8 (implying that the asset plots above the line)?uWhat if an asset has a reward-to-risk ratio of 7 (implying that the ass
25、et plots below the line)?5-44uIn equilibrium, all assets and portfolios must have the same reward-to-risk ratio and they all must equal the MfMAfARRERRE)()(5-455-46uThe security market line (SML) is the representation of uThe slope of the SML is the reward-to-risk ratio: (E(RM) Rf) / MuBut since the
26、 beta for the market is ALWAYS equal to 1, the slope can be rewrittenuSlope = E(RM) Rf = 5-47CAPM is a model that describes the relationship between risk and expected (required) return; in this model, a securitys expected (required) return is the plus based on the of the security.5-48 is the require
27、d rate of return for stock j, is the risk-free rate of return,is the beta of stock j (measures systematic risk of stock j), is the expected return for the market portfolio. = + j( - )5-491.Capital markets are efficient.2.Homogeneous investor expectations over a given period.3. asset return is certai
28、n (use short- to intermediate-term Treasuries as a proxy).4.Market portfolio contains only (use S&P 500 Indexor similar as a proxy).5-50Lisa Miller at Basket Wonders is attempting to determine the rate of return required by their stock investors. Lisa is using a and a long-term of . A stock analyst
29、following the firm has calculated that the firm is . What is the on the stock of Basket Wonders?5-51 = + j( - ) = + ( - ) = The required rate of return exceeds the market rate of return as BWs beta exceeds the market beta (1.0).5-52Lisa Miller at BW is also attempting to determine the of the stock.
30、She is using the constant growth model. Lisa estimates that the will be and that BW will at a constant rate of . The stock is currently selling for $15.What is the of the stock? Is the stock or ?5-53The stock is OVERVALUED as the market price ($15) exceeds the (). - =5-54Systematic Risk (Beta)Direct
31、ion ofMovementDirection ofMovement(Overpriced)Stock X (Underpriced)5-55uThe stock of Jensen Shipping has a risk premium of 8.4 percent while the inflation rate is 2.6 percent and the risk-free rate is 4.2 percent. What is the expected return on this stock? uRisk premium= Expected return- risk-free r
32、ateuExpected Return=12.6%5-56uThe risk-free rate of return is 8 percent and the market risk premium is 13 percent. What is the expected rate of return on a stock with a beta of 1.37?uCAPMuE(Ri)=Rf+(E(Rm)-Rf)*iu= 25.81%5-57uStock A has an expected return of 21% and a beta of 1.3. Stock B has an expec
33、ted return of 20% and a beta of .7. Both stocks have the same reward-to-risk ratio. What is the risk-free rate?uReward-to-risk ratio=slope = E(RA)-Rf /Au18.83%5-58uYou own a $90,000 portfolio that is invested in stock A and B. The portfolio beta is equal to the market beta. Stock A has an expected r
34、eturn of 14.1 percent and a beta of 1.2. Stock B has a beta of .76. What is the value of your investment in stock A? 1.2*X+0.76*(1-X)=1X*$90,000$49,0915-59uGiven the following information, what is the variance of a portfolio that is invested 30 percent in both stocks A and C, and 40 percent in stock
35、 B?5-60ABCPortfolioBoom 0.250.210.110.170.158Normal0.750.080.070.110.08530%40%30%0.10325The portfolio return when the economy booms is calculated as:0.21*30%+0.11*40%+0.17*30%=0.158The expected return on the portfolio is:0.158*0.25+0.085*0.75=0.10325Variance=0.25*(0.158-0.10325)2+0.75*(0.085-0.10325)2=0.000999