财务管理第五章风险和收益

1、财务管理第五章风险和收益财务管理第五章风险和收益5-2uStandard Deviation标准差或者标准离差标准差或者标准离差 uExpected return 期望回报率期望回报率uNormal distribution 正态分布正态分布uCoefficient of variation 离差系数离差系数uvariance方差方差uContinuous Distributions连续分布连续分布udiscrete distribution离散分布离散分布uCertainty Equivalent (CE)资本回收保证量资本回收保证量uRisk Preference风险偏好风险偏好uRisk

2、 Indifference风险中立风险中立 uRisk Aversion风险规避风险规避uThe Capital Asset Pricing Model (CAPM)资本资产定价模型资本资产定价模型uSystematic Risk系统风险系统风险u Unsystematic Risk非系统风险非系统风险5-3on an investment plus any , usually expressed as a percent of the of the investment.+ ()R =5-4The stock price for Stock A was per share 1 year ag

3、o. 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 a . What return was earned over the past y

4、ear?+ ( - ) = 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 .20 -.006 .09 .40 .036 .21 .20 .042 .33 .10

5、 .033 Sum 1.00 The expected return, R, for Stock BW is .09 or 9%5-9ni=1 = 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( (方差）方差）.Note, this is for a discrete distribution（离离散分布）散分布） .5-10Stock BW RiPi (Ri)(Pi)

6、 (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 of BW = / = 1.465-1300.

7、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 observations.ni=15-15ni=1 =

8、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.5-16uAssume that the following list represents the continuous distribution of population returns for a particular investment (even though ther

9、e are only 10 returns).u9.6%, -15.4%, 26.7%, -0.2%, 20.9%, 28.3%, -5.9%, 3.3%, 12.2%, 10.5%uCalculate the Expected Return and Standard Deviation for the population assuming a continuous distribution.5-17Enter “Data” first. Press:2nd Data 2nd CLR Work9.6 ENTER -15.4 ENTER 26.7 ENTER uNote, we are inp

10、utting data only for the “X” variable and ignoring entries for the “Y” variable in this case.5-18Enter “Data” first. Press: -0.2 ENTER 20.9 ENTER 28.3 ENTER -5.9 ENTER 3.3 ENTER 12.2 ENTER 10.5 ENTER 5-19Examine Results! Press:2nd Stat through the results.uExpected return is 9% for the 10 observatio

11、ns. Population standard deviation is 13.32%.uThis can be much quicker than calculating by hand, but slower than using a spreadsheet.5-20()资本回收保证资本回收保证量量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

12、amount expected to be received with risk at the same point in time.5-21Certainty equivalent Expected value风险偏好风险偏好Certainty equivalent = Expected valueCertainty equivalent Expected valueMost individuals are .5-22You have the choice between (1) a guaranteed dollar reward or (2) a coin-flip gamble of

13、$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.5-23What are the Ris

14、k Attitude tendencies of each?Mary shows because her “certainty equivalent” the expected value of the gamble5-24 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 the jth asset,m i

15、s the total number of assets in the portfolio.mj=15-25mj=1mk=1 = SSSS Wj Wk s sjk Wj is the weight (investment proportion) for the jth asset in the portfolio,Wk is the weight (investment proportion) for the kth asset in the portfolio,s sjk is the covariance between returns for the jth and kth assets

16、 in the portfolio.5-26 jk = ssj ssk jkssj is the standard deviation of the jth asset in the portfolio,s sk is the standard deviation of the kth asset in the portfolio,rjk is the correlation coefficient between the jth and kth assets in the portfolio.5-27A standardized statistical measure of the line

17、ar relationship between two variables.Its range is from (perfect negative correlation), through (no correlation), to (perfect positive correlation).5-28A three-asset portfolio: Col 1 Col 2 Col 3Row 1W1W1s s1,1 W1W2s s1,2 W1W3s s1,3Row 2W2W1s s2,1 W2W2s s2,2 W2W3s s2,3Row 3W3W1s s3,1 W3W2s s3,2 W3W3s

18、 s3,3s sj,k = is the covariance between returns for the jth and kth assets in the portfolio.5-29You are creating a portfolio of and (from earlier). You are investing in and in . Remember that the expected return and standard deviation of is and respectively. The expected return and standard deviatio

19、n of is and respectively. The between BW and D is .5-30WBW = $2,000 / $5,000 = .4 = $3,000 / $5,000 =RP = (WBW)(RBW) + ()() RP = (.4)(9%) + ()()RP = (3.6%) + () = 5-31Two-asset portfolio: Col 1 Col 2Row 1WBW WBW s sBW,BW WBW WD s sBW,DRow 2 WD WBW s sD,BW WD WD s sD,DThis represents the variance - c

20、ovariance matrix for the two-asset portfolio.5-32Two-asset portfolio: Col 1 Col 2Row 1 (.4)(.4)(.0173) (.4)(.6)(.0105)Row 2 (.6)(.4)(.0105) (.6)(.6)(.0113)This represents substitution into the variance - covariance matrix.5-33Two-asset portfolio: Col 1 Col 2Row 1 (.0028) (.0025)Row 2 (.0025) (.0041)

21、This represents the actual element values in the variance - covariance matrix.5-34s sP = .0028 + (2)(.0025) + .0041s sP = SQRT(.0119)s sP = .1091 or 10.91%A weighted average of the individual standard deviations is INCORRECT.5-35The WRONG way to calculate is a weighted average like:s sP = .4 (13.15%

22、) + .6(10.65%)s sP = 5.26 + 6.39 = 11.65%10.91% = 11.65%This is INCORRECT.5-36Stock C Stock D Portfolio 9.00% 8.00% 8.64%13.15% 10.65% 10.91% 1.46 1.33 1.26The portfolio has the LOWEST coefficient of variation due to diversification.5-37Combining securities that are not perfectly, positively correla

23、ted reduces risk.INVESTMENT RETURNTIMETIMETIME5-38is the variability of return on stocks or portfolios associated with changes in return 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.=

24、+ 5-39STD 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.5-40STD DEV OF PORTFOLIO RETURNNUMBER OF SECURITIES IN THE PORTFOLIOFactors unique to a particular companyor industry. For e

25、xample, the death of akey executive or loss of a governmentaldefense contract.5-41CAPM 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.5-421.Capital markets are effi

26、cient.2.Homogeneous investor expectations over a given period.3. asset return is certain (use short- to intermediate-term Treasuries as a proxy 代理代理).4.Market portfolio contains only (use S&P 500 Indexor similar as a proxy).5-43EXCESS RETURNON STOCKEXCESS RETURNON MARKET PORTFOLIO =5-44Time Pd.M

27、arketMy 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.5-45uAssume that the previous continuous distribution problem represents the “excess returns” of the

28、 market portfolio (it may still be in your calculator data worksheet - 2nd Data ).uEnter the excess market returns as “X” observations of: 9.6%, -15.4%, 26.7%, -0.2%, 20.9%, 28.3%, -5.9%, 3.3%, 12.2%, and 10.5%.uEnter the excess stock returns as “Y” observations of: 12%, -5%, 19%, 3%, 13%, 14%, -9%,

29、 -1%, 12%, and 10%.5-46uLet us examine again the statistical results (Press 2nd and then Stat )uThe market expected return and standard deviation is 9% and 13.32%. Your stock expected return and standard deviation is 6.8% and 8.76%.uThe regression equation is Y=a+bX. Thus, our characteristic line is

30、 Y = 1.4448 + 0.595 X and indicates that our stock has a beta of 0.595.5-47An index of .It measures the sensitivity of a stocks 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.5-48EXCESS RETURNON STOCKEXCESS RETURNON MARKET PORTFOLIOEach has a different slope.5-49 is the required rate of return for stock j, is the risk-fre