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?+ ( - ) = 5-55-6 R = ( Ri )( Pi )R is the expected return for the asset,Ri is the return for the ith possibility,Pi is the probabilit
3、y of that return occurring,n is the total number of possibilities.ni=15-7 = ( Ri - R )2( Pi ), , is a statistical measure of the variability of a distribution around its mean.It is the square root of variance.ni=15-8Stock BW RiPi (Ri)(Pi) (Ri - R )2(Pi) -.15 .10 -.015 .00576 -.03 .20 -.006 .00288 .0
4、9 .40 .036 .00000 .21 .20 .042 .00288 .33 .10 .033 .00576 Sum 1.00 5-9 = ( Ri - R )2( Pi ) = .01728 = or ni=15-10The ratio of the of a distribution to the of that distribution.It is a measure of risk.CV = / CV of BW = / = 1.465-11() is the amount of cash someone would require with certainty at a poi
5、nt in time to make the individual indifferent between that certain amount and an amount expected to be received with risk at the same point in time.5-12Certainty equivalent Expected valueCertainty equivalent = Expected valueCertainty equivalent Expected valueMost individuals are .5-13You have the ch
6、oice between (1) $25,000 guaranteed or (2) an unknown outcome of $100,000 (50% chance) or $0 (50% chance). The expected value of the gamble is $50,000.You are if you choose $25,000You are if you cant chooseYou have a if you choose the gamble of $0 or $100,0005-14 RP = ( Wj )( Rj )RP is the expected
7、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=15-15mj=1mk=1 = Wj Wk jk Wj is the weight (investment proportion) for the jth asset in the portfolio,Wk
8、is the weight (investment proportion) for the kth asset in the portfolio, jk is the covariance between returns for the jth and kth assets in the portfolio.5-16Slides 5-17 through 5-19 assume that the student has read Appendix A in Chapter 55-17 jk = j k jkj is the standard deviation of the jth asset
9、 in the portfolio, k 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.5-18A standardized statistical measure of the linear relationship between two variables.Its range is from (perfect negative correlation)
10、, through (no correlation), to (perfect positive correlation).5-19A three asset portfolio: Col 1 Col 2 Col 3Row 1W1W1 1,1 W1W2 1,2 W1W3 1,3Row 2W2W1 2,1 W2W2 2,2 W2W3 2,3Row 3W3W1 3,1 W3W2 3,2 W3W3 3,3 j,k = is the covariance between returns for the jth and kth assets in the portfolio.5-20You are cr
11、eating a portfolio of and (from earlier). You are investing in and in . The expected return and standard deviation of is and respectively. The between BW and D is .5-21WBW = $2,000 / $5,000 = .4 = $3,000 / $5,000 =RP = (WBW)(RBW) + ()() RP = (.4)(9%) + ()()RP = (3.6%) + () = 5-22Two-asset portfolio:
12、 Col 1 Col 2Row 1WBW WBW BW,BW WBW WD BW,DRow 2 WD WBW D,BW WD WD D,DThis represents the variance - covariance matrix for the two-asset portfolio.5-23Two-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 varian
13、ce - covariance matrix.5-24Two-asset portfolio: Col 1 Col 2Row 1 (.0028) (.0025)Row 2 (.0025) (.0041)This represents the actual element values in the variance - covariance matrix.5-25 P = .0028 + (2)(.0025) + .0041 P = SQRT(.0119) P = .1091 or 10.91%A weighted average of the individual standard devi
14、ations is INCORRECT.5-26Stock 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.5-27Combining securities that are not perfectly, positively correlated reduces risk.INVESTMENT RETURNTIMETIMETIME5-28is t
15、he 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.= + 5-29STD DEV OF PORTFOLIO RETURNNUMBER OF SECURITIES
16、IN THE PORTFOLIOFactors such as changes in nations economy, tax reform by the Congress,or a change in the world situation.5-30STD 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 gover
17、nmentaldefense contract.5-31CAPM 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.5-321.Capital markets are efficient.2.Homogeneous investor expectations over a given
18、 period.3. asset return is certain (use short- to intermediate-term Treasuries as a proxy).4.Market portfolio contains only (use S&P 500 Indexor similar as a proxy).5-33EXCESS RETURNON STOCKEXCESS RETURNON MARKET PORTFOLIO =5-34An index of .It measures the sensitivity of a stocks returns to changes
19、in returns on the market portfolio.The of a portfolio is simply a weighted average of the individual stock betas in the portfolio.5-35EXCESS RETURNON STOCKEXCESS RETURNON MARKET PORTFOLIOEach has a different slope.5-36 is the required rate of return for stock j, is the risk-free rate of return,is th
20、e beta of stock j (measures systematic risk of stock j), is the expected return for the market portfolio. = + j( - )5-37 = + j( - ) = Systematic Risk (Beta)5-38Lisa Miller at Basket Wonders is attempting to determine the rate of return required by their stock investors. Lisa is using a and a long-te
21、rm of . A stock analyst following the firm has calculated that the firm is . What is the on the stock of Basket Wonders?5-39 = + j( - ) = + ( - ) = The required rate of return exceeds the market rate of return as BWs beta exceeds the market beta (1.0).5-40Lisa Miller at BW is also attempting to dete
22、rmine the of the stock. 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 ?5-41The stock is OVERVALUED as the market price ($15) exceeds the (). - =5-42Systematic Risk (Beta)Direction ofMovementDirection ofMovement(Overpriced)Stock X (Underpriced)5-43These anomalies have presented serious challenges to the CAPM theory.
