1. Chapter McGraw-Hill/Irwin Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 13 Return, Risk, and the Security Market Line

2. 13-1 Expected Returns Expected Rate of Return All possible outcomes and probabilities known Kμ = E(R) = P 1 K 1 + P 2 K 2 + P 3 K 3 Sample taken of past returns _ K = ΣK/n

3. 13-2 Example: Expected Returns Suppose you have predicted the following returns for stocks C and T in three possible states of nature. What are the expected returns? StateProbabilityCT Boom0.31525 Normal0.51020 Recession???21 R C =.3(15) +.5(10) +.2(2) = 9.99% R T =.3(25) +.5(20) +.2(1) = 17.7%

4. Sample of Observations Returns: 2008 8.6% 2007 14.2% 2006 -4.6% 2005 8.8% E(R) = Mean = (8.6+14.2-4.6+8.8)/4 = 6.75 13-3

5. 13-4 Variance and Standard Deviation Variance: σ 2 = P 1 (K 1 - K μ ) 2 + P 2 (K 2 - K μ ) 2 + P 3 (K 3 - K μ ) 2 _ _ _ Variance: S 2 = [(K 1 - K) 2 + (K 2 - K) 2 + (K 3 - K) 2 ]/n-1 Standard Deviation = Square Root of Variance

6. Sample of Observations Returns: 2008 8.6% 2007 14.2% 2006 -4.6% 2005 8.8% E(R) = Mean = (8.6+14.2-4.6+8.8)/4 = 6/75 13-5

7. 13-6 Example: Variance and Standard Deviation Consider the previous example. What are the variance and standard deviation for each stock? Stock C  2 =.3(15-9.9) 2 +.5(10-9.9) 2 +.2(2-9.9) 2 = 20.29  = 4.5 Stock T  2 =.3(25-17.7) 2 +.5(20-17.7) 2 +.2(1-17.7) 2 = 74.41  = 8.63

8. Sample Variance Variance = [(8.6 – 6.75)^2 + (14.2 – 6.75)^2 + (-4.6 – 6.75)^2 + (8.8 – 6.75)^2] /3 = [3.4224 + 55,5025 + 128.8225 + 4.2025]/3 = 63.98333 Standard Deviation = 63.98333^(1/2) = 7.998 Average Distance Around Mean [(8.6 – 6.75) + (14.2 – 6.75) + (-4.6 – 6.75) + (8.8 – 6.75)] /4 = 5.675 13-7

9. 13-8 Portfolios vs. Individual Stocks A portfolio is a collection of assets An asset’s risk and return are important in how they affect the risk and return of the portfolio The risk-return trade-off for a portfolio is measured by the portfolio expected return and standard deviation, just as with individual assets

10. 13-9 Individual Stocks’ Mean Return θ P K W 1.2-10 40 2.2 40 -10 3.2 -5 35 4.2 35 -5 5.2 15 15 Kμ =.2(-10) +.2(40) +.2(-5) +.2(35) +.2(15) = 15 Wμ =.2(40) +.2(-10) +.2(35) +.2(-5) +.2(15) = 15

11. 13-10 Individual Stocks’ Variance and Standard Deviation θ P K W(K-Kμ)2 (W-Wμ)2 1.2-10 40 625 625 2.2 40 -10 625 625 3.2 -5 35 400 400 4.2 35 -5 400 400 5.2 15 15 0 0 σK = [.2(625) +.2(625) +.2(400) +.2(400) +.2(0)] ½ = 20.25 σW = [.2(625) +.2(625) +.2(400) +.2(400) +.2(0)] ½ =20.25

12. 13-11 Equally Weighted Portfolio Returns θ P K W(K-Kμ) 2 (W-Wμ) 2.5K+.5W 1.2 -10 40 625625 15 2.2 40 -10 625625 15 3.2 -5 35 400400 15 4.2 35 -5 400400 15 5.2 15 15 0 0 15 Ex: (1).5 x -10 +.5 x 40 = 15 Ex: (2).5 x 40 +.5 x -10 = 15

13. 13-12 Unequally Weighted Portfolio Variance θ P K W(K-Kμ) 2 (W-Kμ) 2.75K+.25W 1.2 -10 40 625 625 2.5 2.2 40-10 625 625 27.5 3.2 -5 35 400 400 5.0 4.2 35 -5 400 400 25.0 5.2 15 15 0 0 15.0 Ex: (1).75 x -10 +.25 x 40 = 2.5 Ex: (2).75 x 40 +.25 x -10 = 27.5

14. 13-13 Correlation of Security Returns Perfect Positive = +1 Perfect Negative = -1 Uncorrelated = 0

15. 13-14 Diversification Total Risk = Nondiversifiable Risk + Diversifiable Risk Total Risk = Systematic Risk + Unsystematic Risk Total Risk = Market Risk + Firm Risk

16. 13-15 Systematic Risk Risk factors that affect a large number of assets Also known as non-diversifiable risk or market risk Includes such things as changes in GDP, inflation, interest rates, etc.

17. 13-16 Unsystematic Risk Risk factors that affect a limited number of assets Also known as unique risk and asset- specific risk Includes such things as labor strikes, part shortages, etc.

18. 13-17 Diversification Portfolio diversification is the investment in several different asset classes or sectors Diversification is not just holding a lot of assets For example, if you own 50 internet stocks, you are not diversified However, if you own 50 stocks that span 20 different industries, then you are diversified

19. 13-18 Table 13.7

20. 13-19 The Principle of Diversification Diversification can substantially reduce the variability of returns without an equivalent reduction in expected returns This reduction in risk arises because worse than expected returns from one asset are offset by better than expected returns from another However, there is a minimum level of risk that cannot be diversified away and that is the systematic portion

21. 13-20 Figure 13.1

22. 13-21 Diversifiable Risk The risk that can be eliminated by combining assets into a portfolio Often considered the same as unsystematic, unique or asset-specific risk If we hold only one asset, or assets in the same industry, then we are exposing ourselves to risk that we could diversify away

23. 13-22 Total Risk Total risk = systematic risk + unsystematic risk The standard deviation of returns is a measure of total risk For well-diversified portfolios, unsystematic risk is very small Consequently, the total risk for a diversified portfolio is essentially equivalent to the systematic risk

24. 13-23 Systematic Risk Principle There is a reward for bearing risk There is not a reward for bearing risk unnecessarily The expected return on a risky asset depends only on that asset’s systematic risk since unsystematic risk can be diversified away

25. 13-24 Measuring Systematic Risk How do we measure systematic risk? We use the beta coefficient to measure systematic risk What does beta tell us? A beta of 1 implies the asset has the same systematic risk as the overall market A beta < 1 implies the asset has less systematic risk than the overall market A beta > 1 implies the asset has more systematic risk than the overall market

26. 13-25 Total versus Systematic Risk Consider the following information: Standard DeviationBeta Security C20%1.25 Security K30%0.95 Which security has more total risk? Which security has more systematic risk? Which security should have the higher expected return?

27. 13-26 Examples of Betas Edison Electricity.55 Coor’s Brewing.75 Sony.85 General Motors 1.25 Intel 1.40 Dell 1.55

28. 13-27 Example: Portfolio Betas Consider the following four securities SecurityWeightBeta DCLK.1332.685 KO.20.195 INTC.2672.161 KEI.42.434 What is the portfolio beta?.133(2.685) +.2(.195) +.267(2.161) +.4(2.434) = 1.9467

29. 13-28 Beta and the Risk Premium Remember that the risk premium = expected return – risk-free rate The higher the beta, the greater the risk premium should be Can we define the relationship between the risk premium and beta so that we can estimate the expected return? YES!

30. 13-29 Example: Portfolio Expected Returns and Betas RfRf E(R A ) AA

31. 13-30 Reward-to-Risk Ratio: Definition and Example The reward-to-risk ratio is the slope of the line illustrated in the previous example Slope = (E(R A ) – R f ) / (  A – 0) Reward-to-risk ratio for previous example = (20 – 8) / (1.6 – 0) = 7.5 What if an asset has a reward-to-risk ratio of 8 (implying that the asset plots above the line)? What if an asset has a reward-to-risk ratio of 7 (implying that the asset plots below the line)?

32. 13-31 Market Equilibrium In equilibrium, all assets and portfolios must have the same reward-to-risk ratio and they all must equal the reward-to-risk ratio for the market

33. 13-32 Security Market Line The security market line (SML) is the representation of market equilibrium The slope of the SML is the reward-to-risk ratio: (E(R M ) – R f ) /  M But since the beta for the market is ALWAYS equal to one, the slope can be rewritten Slope = E(R M ) – R f = market risk premium

34. 13-33 The Capital Asset Pricing Model (CAPM) The capital asset pricing model defines the relationship between risk and return E(R A ) = R f +  A (E(R M ) – R f ) If we know an asset’s systematic risk, we can use the CAPM to determine its expected return This is true whether we are talking about financial assets or physical assets

35. 13-34 Factors Affecting Expected Return Pure time value of money – measured by the risk-free rate Reward for bearing systematic risk – measured by the market risk premium Amount of systematic risk – measured by beta

36. 13-35 Example - CAPM Consider the betas for each of the assets given earlier. If the risk-free rate is 2.13% and the market risk premium is 8.6%, what is the expected return for each? SecurityBetaExpected Return DCLK2.6852.13 + 2.685(8.6) = 25.22% KO0.1952.13 + 0.195(8.6) = 3.81% INTC2.1612.13 + 2.161(8.6) = 20.71% KEI2.4342.13 + 2.434(8.6) = 23.06%

37. 13-36 Figure 13.4

38. Chapter McGraw-Hill/Irwin Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 12 End of Chapter