Risk and Return

1、Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-1Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-2uDefining Risk and ReturnuUsing Probability Distributions to Measure RiskuAttitudes Toward RiskuRisk and Return in a Portfolio ContextuDiversificationuThe Capital Asset Pri

2、cing Model (CAPM)Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-3on an investment plus any , usually expressed as a percent of the of the investment.+ ()R =Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-4The stock price for Stock A was per share 1 year ago. The stock

3、is currently trading at per share, and shareholders just received a . What return was earned over the past year?Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-5The stock price for Stock A was per share 1 year ago. The stock is currently trading at per share, and shareholders just rec

4、eived a . What return was earned over the past year?+ ( - ) = Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-6Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-7 R = S S ( Ri )( Pi )R is the expected return for the asset,Ri is the return for the ith possibility,Pi is the

5、 probability of that return occurring,n is the total number of possibilities.ni=1Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-8Stock BW RiPi (Ri)(Pi) -.15 .10 -.015 -.03 .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%Sydne

6、y Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 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=1Sydney Institute of Language and Commerce, S. U. 上 海大学悉

7、尼工商学院 5-10Stock 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 Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-11 = S S ( Ri - R )2( Pi ) = .01728 = or ni=1Sydney Institute of Language an

8、d Commerce, S. U. 上 海大学悉尼工商学院 5-12The ratio of the of a distribution to the of that distribution.It is a measure of risk.CV = / CV of BW = / = 1.46Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-1300.050.10.150.20.250.30.350.4-15%-3%9%21%33% Discrete Continuous00.0050.010.0150.020.025

9、0.030.035-50%-41%-32%-23%-14%-5%4%13%22%31%40%49%58%67%Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-14() 确定性等价确定性等价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

10、be received with risk at the same point in time.Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-15Certainty equivalent Expected valueCertainty equivalent = Expected valueCertainty equivalent Expected valueMost individuals are .Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商

11、学院 5-16You 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 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

12、the risky gamble.uShannon requires at least $52,000 to call off the gamble.Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-17What are the Risk Attitude tendencies of each?Mary shows because her “certainty equivalent” the expected value of the gambleSydney Institute of Language and Com

13、merce, S. U. 上 海大学悉尼工商学院 5-18 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 assets in the portfolio.mj=1Sydney Institute of Language and

14、Commerce, S. U. 上 海大学悉尼工商学院 5-19mj=1mk=1 = S SS S 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.Sy

15、dney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-20 jk = s s j s s k jk s sj 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.Syd

16、ney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-21A standardized statistical measure of the linear relationship between two variables.Its range is from (perfect negative correlation), through (no correlation), to (perfect positive correlation).Sydney Institute of Language and Commerce, S

17、. U. 上 海大学悉尼工商学院 5-22A 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 covariance between returns for the jth and kth assets in the portfolio.Sydney Institute of Language and Commer

18、ce, S. U. 上 海大学悉尼工商学院 5-23You 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 respectively. The between BW and D is .Sydney Institute of

19、 Language and Commerce, S. U. 上 海大学悉尼工商学院 5-24WBW = $2,000 / $5,000 = .4 = $3,000 / $5,000 =RP = (WBW)(RBW) + ()() RP = (.4)(9%) + ()()RP = (3.6%) + () = Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-25Two-asset portfolio: Col 1 Col 2Row 1WBW WBW s sBW,BW WBW WD s sBW,DRow 2 WD WBW

20、s sD,BW WD WD s sD,DThis represents the variance - covariance matrix for the two-asset portfolio.Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-26Two-asset portfolio: Col 1 Col 2Row 1 (.4)(.4)(.0173) (.4)(.6)(.0105)Row 2 (.6)(.4)(.0105) (.6)(.6)(.0113)This represents substitution int

21、o the variance - covariance matrix.Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-27Two-asset portfolio: Col 1 Col 2Row 1 (.0028) (.0025)Row 2 (.0025) (.0041)This represents the actual element values in the variance - covariance matrix.Sydney Institute of Language and Commerce, S. U.

22、 上 海大学悉尼工商学院 5-28s sP = .0028 + (2)(.0025) + .0041s sP = SQRT(.0119)s sP = .1091 or 10.91%A weighted average of the individual standard deviations is INCORRECT.Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-29The WRONG way to calculate is a weighted average like:s sP = .4 (13.15%) +

23、.6(10.65%)s sP = 5.26 + 6.39 = 11.65%10.91% = 11.65%This is INCORRECT.Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-30Stock 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.Sydney Ins

24、titute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-31Combining securities that are not perfectly, positively correlated reduces risk.INVESTMENT RETURNTIMETIMETIMESydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-32is the variability of return on stocks or portfolios associated with ch

25、anges 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.= + Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-33STD DEV OF PORTFOLIO RETURNNUMBER OF SECURITIES IN THE

26、 PORTFOLIOFactors such as changes in nations economy, tax reform by the Congress,or a change in the world situation.Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-34STD DEV OF PORTFOLIO RETURNNUMBER OF SECURITIES IN THE PORTFOLIOFactors unique to a particular companyor industry. For

27、example, the death of akey executive or loss of a governmentaldefense contract.Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-35CAPM is a model that describes the relationship between risk and expected (required) return; in this model, a securitys expected (required) return is the pl

28、us based on the of the security.Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-361.Capital markets are efficient.2.Homogeneous investor expectations over a given period.3. asset return is certain (use short- to intermediate-term Treasuries as a proxy).4.Market portfolio contains only

29、 (use S&P 500 Indexor similar as a proxy).Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-37EXCESS RETURNON STOCKEXCESS RETURNON MARKET PORTFOLIO =Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-38Time Pd.MarketMy Stock19.6%12%2-15.4%-5%326.7%19%4-.2%3%520.9%13%628.3%14

30、%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.Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-39uAssume that the previous continuous distribution problem represents the “excess returns” of the ma

31、rket 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%, -1

32、%, 12%, and 10%.Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-40uLet 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 regre

33、ssion equation is Y=a+bX. Thus, our characteristic line is Y = 1.4448 + 0.595 X and indicates that our stock has a beta of 0.595.Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-41An index of .It measures the sensitivity of a stocks returns to changes in returns on the market portfolio

34、.The for a portfolio is simply a weighted average of the individual stock betas in the portfolio.Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-42EXCESS RETURNON STOCKEXCESS RETURNON MARKET PORTFOLIOEach has a different slope.Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商

35、学院 5-43 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 of stock j), is the expected return for the market portfolio. = + j( - )Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-44 = + j( - ) = Systematic Risk (Beta)Sydney Institute of Language and Commerce, S. U. 上 海大学悉尼工商学院 5-45Lisa Miller at Basket Wonders i