1. Chapter McGraw-Hill Ryerson © 2013 McGraw-Hill Ryerson Limited Return, Risk, and the Security Market Line Prepared by Anne Inglis Edited by William Rentz 13

2. 13-1 Key Concepts and Skills Know how to calculate expected returns and standard deviations for individual securities and portfolios. Understand the principle of diversification and the role of correlation. Understand systematic and unsystematic risk. Understand beta as a measure of risk and the security market line. © 2013 McGraw-Hill Ryerson Limited

3. 13-2 Chapter Outline Expected Returns and Variances Portfolios Announcements, Surprises, and Expected Returns Risk: Systematic and Unsystematic Diversification and Portfolio Risk Systematic Risk and Beta The Security Market Line Arbitrage Pricing Theory Summary and Conclusions © 2013 McGraw-Hill Ryerson Limited

4. 13-3 Expected Returns 13.1 Expected returns are based on the probabilities of possible outcomes. In this context, “expected” means average if the process is repeated many times. The “expected” return does NOT even have to be a possible return. LO1 © 2013 McGraw-Hill Ryerson Limited

5. 13-4 Expected Returns – Example 1 Suppose you have predicted the following returns for stocks C and T in three possible states of nature. What are the expected returns? StateProbabilityCT Boom0.30.150.25 Normal 0.50.100.20 Recession0.20.020.01 Sum of prob = 1.0 R C =.3(.15) +.5(.10) +.2(.02) =.099 = 9.9% R T =.3(.25) +.5(.20) +.2(.01) =.177 = 17.7% LO1 © 2013 McGraw-Hill Ryerson Limited

6. 13-5 Expected Returns – Example 1 continued This example can also be done in a spreadsheet. Click on the Excel link to see this. LO1 © 2013 McGraw-Hill Ryerson Limited

7. 13-6 Variance and Standard Deviation Variance and standard deviation measure the volatility of returns. You may use unequal probabilities for the entire range of possibilities. Weighted average of squared deviations LO1 © 2013 McGraw-Hill Ryerson Limited

8. 13-7 Variance and Standard Deviation – Example 1 What is the variance & std. deviation for each stock in the previous example? Stock C σ 2 =.3(.15-.099) 2 +.5(.1-.099) 2 +.2(.02-.099) 2 =.002029 σ =.045 Stock T σ 2 =.3(.25-.177) 2 +.5(.2-.177) 2 +.2(.01-.177) 2 =.007441 σ =.0863 LO1 © 2013 McGraw-Hill Ryerson Limited

9. 13-8 Variance and Standard Deviation – Example continued This can also be done in a spreadsheet. Click on the Excel icon to see this. LO1 © 2013 McGraw-Hill Ryerson Limited

10. 13-9 Quick Quiz I Consider the following information: StateProbabilityABC, Inc. Boom.25.15 Normal.50.08 Slowdown.15.04 Recession.10-.03 What is the expected return? What is the variance? What is the standard deviation? LO1 © 2013 McGraw-Hill Ryerson Limited

11. 13-10 Portfolios 13.2 A portfolio is a collection of assets. An asset’s risk and return is important in how it affects 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. LO1 © 2013 McGraw-Hill Ryerson Limited

12. 13-11 Example: Portfolio Weights Suppose you have $15,000 to invest and you have purchased securities in the following amounts. What are your portfolio weights in each security? $2000 of ABC $3000 of DEF $4000 of GHI $6000 of JKL ABC: 2/15 =.133 DEF: 3/15 =.2 GHI: 4/15 =.267 JKL: 6/15 =.4 LO1 © 2013 McGraw-Hill Ryerson Limited

13. 13-12 Portfolio Expected Returns The expected return of a portfolio is the weighted average of the expected returns for each asset in the portfolio. You can also find the expected return by finding the portfolio return in each possible state and computing the expected value as we did with individual securities. LO1 © 2013 McGraw-Hill Ryerson Limited

14. 13-13 Example: Expected Portfolio Returns Consider the portfolio weights computed previously. If the individual stocks have the following expected returns, what is the expected return for the portfolio? ABC: 19.65% DEF: 8.96% GHI: 9.67% JKL: 8.13% E(R P ) =.133(19.65) +.2(8.96) +.267(9.67) +.4(8.13) = 10.24% Click the Excel icon for an example. LO1 © 2013 McGraw-Hill Ryerson Limited

15. 13-14 Portfolio Variance Compute the portfolio return for each state. R P = w 1 R 1 + w 2 R 2 + … + w m R m Compute the expected portfolio return using the same formula as for an individual asset. Compute the portfolio variance and standard deviation using the same formulas as for an individual asset. LO1 © 2013 McGraw-Hill Ryerson Limited

16. 13-15 Example: Portfolio Variance Consider the following information: Invest 60% of your money in Asset A. StateProbabilityAB Boom.570%10% Bust.5-20%30% What is the expected return and standard deviation for each asset? What is the expected return and standard deviation for the portfolio? LO1 © 2013 McGraw-Hill Ryerson Limited

17. Portfolio Variance Example continued First, calculate Portfolio Return for EACH State, Portfolio Return in Boom State: R p,boom =.6 x 70% +.4 x 10% = 46% Portfolio Return in Bust State: R p,bust =.6 x (- 20%) +.4 x 30% = 0% Expected Portfolio Return: E(R p ) =.5 x 46% +.5 x 0% = 23% 13-16

18. Portfolio Variance Example continued Next, calculate Expected Portfolio Variance. σ p 2 =.5 x (46% - 23%) 2 +.5 x (0% - 23%) 2 σ p 2 = (23%) 2 =.0529 Finally, calculate Expected Portfolio Standard Deviation. σ p = √(23%) 2 = 23% or σ p = √.0529 =.23 13-17

19. 13-18 Portfolio Variance Example continued This can also be done in a spreadsheet. Click on the Excel icon to see this. LO1 © 2013 McGraw-Hill Ryerson Limited

20. 13-19 Another Way to Calculate Portfolio Variance Portfolio variance can also be calculated using the following formula: Note: That is, there are gains to diversification whenever the correlation is LESS than ONE. LO1 © 2013 McGraw-Hill Ryerson Limited

21. 13-20 Figure 13.1 – Different Correlation Coefficients LO2 © 2013 McGraw-Hill Ryerson Limited

22. 13-21 Figure 13.1 – Different Correlation Coefficients LO2 © 2013 McGraw-Hill Ryerson Limited

23. 13-22 Figure 13.1 – Different Correlation Coefficients LO2 © 2013 McGraw-Hill Ryerson Limited

24. 13-23 Figure 13.2 – Graphs of Possible Relationships Between Two Stocks LO2 © 2013 McGraw-Hill Ryerson Limited

25. 13-24 Diversification There are benefits to diversification whenever the correlation between two stocks is less than perfect (ρ < 1.0). If two stocks are perfectly positively correlated, then there is simply a risk-return trade-off between the two securities. LO2 © 2013 McGraw-Hill Ryerson Limited

26. 13-25 Diversification – Figure 13.4 LO2 © 2013 McGraw-Hill Ryerson Limited

27. 13-26 Terminology Minimum Variance Frontier – the curve that comprises the set of portfolios with minimum variance for each possible expected return Efficient Frontier – the portion of the minimum variance frontier that only includes the efficient portfolios, where the maximum return is achieved for a given level of risk Minimum Variance Portfolio – the possible portfolio with the least amount of risk LO2 © 2013 McGraw-Hill Ryerson Limited

28. 13-27 Terminology (continued) Feasible Set (also called the Opportunity Set) – comprises all of the possible portfolio combinations Relationship between Minimum Variance Frontier & Opportunity Set In the two-asset case, Minimum Variance Frontier & Opportunity Set are the same. When there are more than 2 assets, the Minimum Variance Frontier is a subset of the Feasible Set. That is, there are feasible portfolios that lie to the right of the Minimum Variance Frontier. LO2 © 2013 McGraw-Hill Ryerson Limited

29. 13-28 Quick Quiz II Consider the following information StateProbabilityXZ Boom.2515%10% Normal.6010%9% Recession.155%10% What is the expected return and standard deviation for a portfolio with an investment of $6,000 in asset X and $4,000 in asset Z? LO1 © 2013 McGraw-Hill Ryerson Limited

30. 13-29 Expected versus Unexpected Returns 13.3 Realized returns are generally NOT equal to expected returns. There is the expected component and the unexpected component. At any point in time, the unexpected return can be either positive or negative. Over time, the average of the unexpected component is zero. LO2 © 2013 McGraw-Hill Ryerson Limited

31. 13-30 Announcements and News Announcements and news contain both an expected component and a surprise component. It is the surprise component that affects a stock’s price and therefore its return. This is very obvious when we watch how stock prices move when an unexpected announcement is made or earnings are different than anticipated. LO2 © 2013 McGraw-Hill Ryerson Limited

32. 13-31 Efficient Markets Efficient markets are a result of investors trading on the unexpected portion of announcements. The easier it is to trade on surprises, the more efficient markets should be. Efficient markets involve random price changes because we can NOT predict surprises. LO2 © 2013 McGraw-Hill Ryerson Limited

33. 13-32 Systematic Risk 13.4 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. LO3 © 2013 McGraw-Hill Ryerson Limited

34. 13-33 Unsystematic Risk Risk factors that affect a limited number of assets Also known as unique risk and asset- specific risk Includes such things as labour strikes, shortages, etc. LO3 © 2013 McGraw-Hill Ryerson Limited

35. 13-34 Returns Total Return = expected return + unexpected return Unexpected return = systematic part + unsystematic part Therefore, total return can be expressed as follows: Total Return = expected return + systematic part + unsystematic part LO3 © 2013 McGraw-Hill Ryerson Limited

36. 13-35 Diversification 13.5 Portfolio diversification is the investment in several different asset classes or sectors. Diversification is NOT just holding many assets. For example, if you own 50 internet stocks, you are NOT diversified! However, if you own 50 stocks that span 20 different industries, you are diversified, LO2 © 2013 McGraw-Hill Ryerson Limited

37. 13-36 Table 13.8 – Portfolio Diversification LO2 © 2013 McGraw-Hill Ryerson Limited

38. 13-37 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 can NOT be diversified away and that is the systematic portion. LO2 & LO3 © 2013 McGraw-Hill Ryerson Limited

39. 13-38 Figure 13.6 – Portfolio Diversification LO2 & LO3 © 2013 McGraw-Hill Ryerson Limited

40. 13-39 Diversifiable (Unsystematic) Risk The risk that can be eliminated by combining assets into a portfolio Synonymous with 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. On average, the market will NOT compensate investors for assuming unnecessary risk. LO3 © 2013 McGraw-Hill Ryerson Limited

41. 13-40 Total Risk Total risk = systematic risk + unsystematic risk NB. Using variance as risk measure The variance or 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. LO3 © 2013 McGraw-Hill Ryerson Limited

42. 13-41 Systematic Risk Principle 13.6 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. LO3 © 2013 McGraw-Hill Ryerson Limited

43. 13-42 Measuring Systematic Risk How do we measure systematic risk? We use the beta coefficient to measure relative systematic risk. What does beta tell us? Beta = 1 implies the asset has the SAME systematic risk as the overall market. Beta < 1 implies the asset has LESS systematic risk than the overall market. Beta > 1 implies the asset has MORE systematic risk than the overall market. LO3 © 2013 McGraw-Hill Ryerson Limited

44. 13-43 Figure 13.7 – High and Low Betas LO3 © 2013 McGraw-Hill Ryerson Limited

45. 13-44 Table 13.10 – Beta Coefficients for Selected Companies LO3 © 2013 McGraw-Hill Ryerson Limited

46. 13-45 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? LO3 © 2013 McGraw-Hill Ryerson Limited

47. 13-46 Example: Portfolio Betas Consider the Example from Slide 11 with the following four securities: SecurityWeightBeta ABC.1333.69 DEF.20.64 GHI.2671.64 JKL.41.79 What is the portfolio beta?.133(3.69) +.2(.64) +.267(1.64) +.4(1.79) = 1.773 LO3 © 2013 McGraw-Hill Ryerson Limited

48. 13-47 Beta and the Risk Premium 13.7 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! It is the Security Market Line (SML). LO3 © 2013 McGraw-Hill Ryerson Limited

49. 13-48 Figure 13.8A – Portfolio Expected Returns and Betas (SML) R f = 8% LO4 © 2013 McGraw-Hill Ryerson Limited

50. 13-49 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 ) / (β 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)? LO4 © 2013 McGraw-Hill Ryerson Limited

51. 13-50 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. LO4 © 2013 McGraw-Hill Ryerson Limited

52. 13-51 Security Market Line (SML) 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 ) / β M But since the beta for the market is ALWAYS equal to one, the slope can be rewritten as Slope = E(R M ) – R f = Market Risk Premium LO4 © 2013 McGraw-Hill Ryerson Limited

53. 13-52 Figure 13.11 – Security Market Line LO4 © 2013 McGraw-Hill Ryerson Limited

54. 13-53 Security Market Line (SML) of the Capital Asset Pricing Model (CAPM) The SML of the CAPM defines the relationship between risk and return: E(R i ) = R f + β i [E(R M ) – R f ] If we know an asset’s relative systematic risk, we can use the SML of the CAPM to determine its expected return. This is true whether we are talking about financial assets or physical assets. LO4 © 2013 McGraw-Hill Ryerson Limited

55. 13-54 Capital Market Line (CML) of the Capital Asset Pricing Model (CAPM) Consider a Portfolio i that is perfectly positively correlated with the Market Portfolio M (i.e. ρ iM = 1). We can use the SML to derive the CML, which is a relationship that only holds for perfectly diversified portfolios. LO4 © 2013 McGraw-Hill Ryerson Limited

56. 13-55 Factors Affecting Expected Return Pure time value of money – measured by the risk-free rate Reward for relative systematic risk – measured by the market risk premium Amount of relative systematic risk – measured by beta LO4 © 2013 McGraw-Hill Ryerson Limited

57. 13-56 Example - CAPM Consider the betas for each of the assets given earlier. If the risk-free rate is 4.5% and the market risk premium is 8.5%, what is the expected return for each? SecurityBetaExpected Return ABC3.694.5 + 3.69(8.5) = 35.865% DEF.644.5 +.64(8.5) = 9.940% GHI1.644.5 + 1.64(8.5) = 18.440% JKL1.794.5 + 1.79(8.5) = 19.715% LO4 © 2013 McGraw-Hill Ryerson Limited

58. 13-57 Arbitrage Pricing Theory (APT) 13.8 Similar to the CAPM, the APT can handle multiple factors that the CAPM ignores, Unexpected return is related to several market factors. LO1 © 2013 McGraw-Hill Ryerson Limited

59. 13-58 Quick Quiz What is the difference between systematic and unsystematic risk? What type of risk is relevant for determining the expected return? What is the SML? What is the CAPM? What is the APT? Consider an asset with a beta of 1.2, a risk-free rate of 5% and a market return of 13%. What is the reward-to-risk ratio in equilibrium? What is the expected return on the asset? © 2013 McGraw-Hill Ryerson Limited

60. 13-59 Summary 13.9 Total risk has two parts: systematic risk and unsystematic risk. Unsystematic risk can be eliminated through diversification. Systematic risk can NOT be eliminated and is rewarded with a risk premium. Relative systematic risk is measured by beta. The SML of the CAPM defines the equilibrium required return for a given level of risk. © 2013 McGraw-Hill Ryerson Limited

61. © 2014 Dr. William F. Rentz & Associates Additions, deletions, and corrections to these transparencies were performed by Dr. William F. Rentz solely for use at the University of Ottawa. The above copyright notice applies to all changes made herein. 13-60