財(cái)務(wù)管理第五章風(fēng)險(xiǎn)和收益

1、5-15-2uStandard Deviation標(biāo)準(zhǔn)差或者標(biāo)準(zhǔn)離差標(biāo)準(zhǔn)差或者標(biāo)準(zhǔn)離差 uExpected return 期望回報(bào)率期望回報(bào)率uNormal distribution 正態(tài)分布正態(tài)分布uCoefficient of variation 離差系數(shù)離差系數(shù)uvariance方差方差uContinuous Distributions連續(xù)分布連續(xù)分布udiscrete distribution離散分布離散分布uCertainty Equivalent (CE)資本回收保證量資本回收保證量uRisk Preference風(fēng)險(xiǎn)偏好風(fēng)險(xiǎn)偏好uRisk Indifference風(fēng)險(xiǎn)中立風(fēng)險(xiǎn)中立

2、 uRisk Aversion風(fēng)險(xiǎn)規(guī)避風(fēng)險(xiǎn)規(guī)避uThe Capital Asset Pricing Model (CAPM)資本資產(chǎn)定價(jià)模型資本資產(chǎn)定價(jià)模型uSystematic Risk系統(tǒng)風(fēng)險(xiǎn)系統(tǒng)風(fēng)險(xiǎn)u Unsystematic Risk非系統(tǒng)風(fēng)險(xiǎn)非系統(tǒng)風(fēng)險(xiǎn)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 ago. The stock is curre

3、ntly 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 year?+ ( - ) = 5-65-7

4、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 .033 Sum 1.00 The ex

5、pected 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（離離散分布）散分布） .5-10Stock BW RiPi (Ri)(Pi) (Ri - R )2(Pi) -.15

6、.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 = / = 1.465-1300.050.10.150.20.250.30.

7、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 = S S ( Ri - R )2 ( n )

8、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 there are only 10 returns

9、).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 inputting data only for

10、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 observations. Population standa

11、rd deviation is 13.32%.uThis can be much quicker than calculating by hand, but slower than using a spreadsheet.5-20()資本回收保證資本回收保證量量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 amount expected to be

12、 received with risk at the same point in time.5-21Certainty equivalent Expected value風(fēng)險(xiǎn)偏好風(fēng)險(xiǎn)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 $100,000 (50% chance)

13、 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 Risk Attitude tendencies

14、 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 is the total number of

15、 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 in the portfolio.5-2

16、6 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 linear relationship betwe

17、en 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 s3,3s sj,k = is the

18、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 deviation of is and respectiv

19、ely. 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 - covariance matrix for

20、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)This represents the a

21、ctual 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%) + .6(10.65%)s sP =

22、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 correlated reduces risk.INVE

23、STMENT 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.= + 5-39STD DEV OF PORT

24、FOLIO 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 example, the death of

25、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 efficient.2.Homogeneous i

26、nvestor 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.MarketMy Stock19.6%12%

27、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 market portfolio (it

28、 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%, -1%, 12%, and 10%.5-

29、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 Y = 1.4448 + 0.595 X

30、 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-free rate of return,is the beta of stock j (measures systematic risk o