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Chapter 13 Risk, Return and The CAPM Homework: 9, 11, 15, 19, 24 & 26.

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Presentation on theme: "Chapter 13 Risk, Return and The CAPM Homework: 9, 11, 15, 19, 24 & 26."— Presentation transcript:

1 Chapter 13 Risk, Return and The CAPM Homework: 9, 11, 15, 19, 24 & 26

2 Lecture Organization Expected Return and Variance Portfolio Variance The Power of Diversification The CAPM and the Security Market Line

3 Expected Returns and Variances: Basic Ideas The quantification of risk and return is a crucial aspect of modern finance. It is not possible to make “good” (i.e., value-maximizing) financial decisions unless one understands the relationship between risk and return. Consider the following proxies for return and risk: Expected return - weighted average of the distribution of possible returns in the future. Variance of returns - a measure of the dispersion of the distribution of possible returns in the future.

4 Example: Calculating the Expected Return s E(R) = (p i x r i ) i =1 p i r i Probability Return in State of Economyof state i state i +1% change in GNP.25-5% +2% change in GNP.5015% +3% change in GNP.2535% 

5 Calculation of Expected Return Stock L Stock U (3)(5) (2)Rate ofRate of (1)ProbabilityReturn(4)Return(6) State ofof State ofif StateProductif StateProduct EconomyEconomyOccurs(2) x (3)Occurs(2) x (5) Recession.80-.20.30 Boom.20.70.10 E(R L ) = E(R U ) =

6 Example: Calculating the Variance s Var(R) 2 = [p i x (r i - r ) 2 ] i =1 p i r i ProbabilityReturn in State of Economyof state istate i +1% change in GNP.25-5% +2% change in GNP.5015% +3% change in GNP.2535% 

7 Calculating the Variance (concluded) i (r i - r) 2 p i x (r i - r ) 2 i=1 i=2 i=3 Var(R) = What is the standard deviation?

8 Example: Expected Returns and Variances State of theProbabilityReturn onReturn on economyof stateasset Aasset B Boom0.4030%-5% Bust0.60-10%25% 1.00 A.Expected returns

9 Example: Expected Returns and Variances (concluded) B.Variances C.Standard deviations

10 Portfolios of Securities Investors’ opportunity set is comprised not only of sets of individual securities but also combinations, or portfolios, of securities The return on a portfolio is the weighted average of returns on component securities: The expected return is also a weighted average

11 Portfolios Value-weighted Portfolios: Example: You have $2,500 in IBM stock and $7,500 in GM stock. What are the portfolio weights? Equal-weighted Portfolios:

12 Covariance and Correlation What is covariance? Is there a difference between covariance and correlation?

13 Covariance and Correlation -1 < Correlation Coefficient < 1

14 Portfolio Risk The standard deviation of a portfolio is NOT just a weighted average of securities standard deviations. We also need to account for their covariances. Example with 2 risky securities: X and Y

15 Portfolio Risk What happens to risk if two securities are perfectly positively correlated? Perfectly negatively? What about general case? Intuitively, what implications can we infer for efficient portfolio selection strategies?

16 Example: Portfolio Expected Returns and Variances Portfolio weights: put 50% in Asset A and 50% in Asset B: State of the ProbabilityReturnReturnReturn on economyof stateon Aon Bportfolio Boom0.4030%-5% Bust0.60-10%25% 1.00

17 What is the expected return and variance of the previous portfolio?

18 Example: Portfolio Expected Returns and Variances (concluded) New portfolio weights: put 3/7 in A and 4/7 in B: State of the ProbabilityReturnReturnReturn on economyof stateon Aon Bportfolio Boom0.4030%-5% Bust0.60-10%25% 1.00 E(R P ) = SD(R P ) =

19 The Effect of Diversification on Portfolio Variance Stock A returns 0.05 0.04 0.03 0.02 0.01 0 -0.01 -0.02 -0.03 -0.04 -0.05 0.05 0.04 0.03 0.02 0.01 0 -0.01 -0.02 -0.03 Stock B returns 0.04 0.03 0.02 0.01 0 -0.01 -0.02 -0.03 Portfolio returns: 50% A and 50% B

20 Portfolio Risk For N securities, in general, the formula is: Intuitively, what happens to the portfolio’s variance as N gets large?

21 What Affects Risk? Market risk  Risk factors common to the whole economy  Systematic or non-diversifiable Firm specific risk  Risk that can be eliminated by diversification  Unique risk  Nonsystematic or diversifiable

22 Standard Deviations of Annual Portfolio Returns (Table 13.8) ( 3) (2)Ratio of Portfolio (1)Average StandardStandard Deviation to Number of StocksDeviation of AnnualStandard Deviation in PortfolioPortfolio Returnsof a Single Stock 149.24%1.00 1023.93 0.49 5020.20 0.41 10019.69 0.40 30019.34 0.39 50019.27 0.39 1,00019.21 0.39

23 Portfolio Diversification Average annual standard deviation (%) Number of stocks in portfolio Diversifiable risk Nondiversifiable risk 49.2 23.9 19.2 1102030401000

24 CAPM - Rewards and Beta We have a simple expression for expected returns on any asset or portfolio. So only _________ risk matters.

25 Measuring Systematic Risk Beta coefficient is a measure of how much systematic risk an asset has relative to an average risk asset.

26 The Capital Asset Pricing Model The Capital Asset Pricing Model (CAPM) - an equilibrium model of the relationship between risk and return. What determines an asset’s expected return?    The CAPM: E(R i ) = R f + [E(R M ) - R f ] x i

27 Security Market Line SML M A

28 Beta Coefficients for Selected Companies (Table 13.10) U.S. Beta Company Coefficient American Electric Power.65 Exxon.80 IBM.95 Wal-Mart 1.15 General Motors 1.05 Harley-Davidson 1.20 Papa Johns 1.45 America Online 1.65 Source: (Canadian) Scotia Capital markets and (US) Value Line Investment Survey, May 8, 1998. Canadian Beta Company Coefficient Bank of Nova Scotia0.65 Bombardier0.71 Canadian Utilities0.50 C-MAC Industries1.85 Investors Group1.22 Maple Leaf Foods0.83 Nortel Networks1.61 Rogers Communication1.26

29 Return, Risk, and Equilibrium Key issues:  What is the relationship between risk and return?  What does security market equilibrium look like? The fundamental conclusion is that the ratio of the risk premium to beta is the same for every asset. In other words, the reward-to-risk ratio is constant and equal to E(R i ) - R f Reward/risk ratio = i

30 Return, Risk, and Equilibrium (concluded) Example: Asset A has an expected return of 12% and a beta of 1.40. Asset B has an expected return of 8% and a beta of 0.80. Are these assets valued correctly relative to each other if the risk-free rate is 5%? What would the risk-free rate have to be for these assets to be correctly valued?

31 Example: Portfolio Beta Calculations AmountPortfolio StockInvestedWeightsBeta (1)(2)(3)(4) Haskell Mfg. $ 6,0000.90 Cleaver, Inc.4,0001.10 Rutherford Co.2,0001.30

32 Example: Portfolio Expected Returns and Betas Assume you wish to hold a portfolio consisting of asset A and a riskless asset. Given the following information, calculate portfolio expected returns and portfolio betas, letting the proportion of funds invested in asset A range from 0 to 125%. Asset A has a beta ( ) of 1.2 and an expected return of 18%. The risk-free rate is 7%. Asset A weights: 0%, 25%, 50%, 75%, 100%, and 125%.

33 Example: Portfolio Expected Returns and Betas (concluded) Proportion ProportionPortfolio Invested in Invested inExpectedPortfolio Asset A (%) Risk-free Asset (%) Return (%)Beta 01007.000.00 2575 5050 7525 1000 125-25

34 Summary of Risk and Return (Table 13.12) I.Total risk - the variance (or the standard deviation) of an asset’s return. II.Total return - the expected return + the unexpected return. III.Systematic and unsystematic risks Systematic risks are unanticipated events that affect almost all assets to some degree. Unsystematic risks are unanticipated events that affect single assets or small groups of assets. IV.The effect of diversification - the elimination of unsystematic risk via the combination of assets into a portfolio. V.The systematic risk principle and beta - the reward for bearing risk depends only on its level of systematic risk. VI.The reward-to-risk ratio - the ratio of an asset’s risk premium to its beta. VII. The capital asset pricing model - E(R i ) = R f + [E(R M ) - R f ]  i.

35 Chapter 13 Quick Quiz 1.Assume: the historic market risk premium has been about 8.5%. The risk-free rate is currently 5%. GTX Corp. has a beta of.85. What return should you expect from an investment in GTX? E(R GTX ) = 5% + _______ x.85 = 12.225% 2. What is the effect of diversification? 3. The slope of the SML = ______.

36 Example Consider the following information: State ofProb. of StateStock AStock BStock C Economyof EconomyReturnReturnReturn Boom0.350.140.150.33 Bust0.650.120.03-0.06 What is the expected return on an equally weighted portfolio of these three stocks? What is the variance of a portfolio invested 15 percent each in A and B, and 70 percent in C?

37 Solution to Example

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