1. 1 B280F Introduction to Financial Management Lecture 5 Risk and Rates of Return

2. 2Objectives n Inflation and rates of return n How to measure risk (variance, standard deviation, beta) (variance, standard deviation, beta) n How to reduce risk (diversification) (diversification) n How to price risk (security market line, Capital Asset Pricing Model) (security market line, Capital Asset Pricing Model)

3. 3 Conceptually: Nominal risk-free Interest Rate k rf = Real risk-free Interest Rate k* + Inflation risk premium IRP Mathematically: (1 + k rf ) = (1 + k*) (1 + IRP) This is known as the “Fisher Effect” Interest Rates

4. 4 n Suppose the real rate is 3%, and the nominal rate is 8%. What is the inflation risk premium? (1 + k rf ) = (1 + k*) (1 + IRP) (1.08) = (1.03) (1 + IRP) (1 + IRP) = (1.0485), so IRP = 4.85% Interest Rates

5. 5 Term Structure of Interest Rates n The pattern of rates of return for debt securities that differ only in the length of time to maturity. yield to maturity (YTM) time to maturity (years)

6. 6 Term Structure of Interest Rates yield to Maturity (YTM) time to maturity (years) n The yield curve may be downward sloping or “inverted” if rates are expected to fall.

7. 7 For a Treasury security, what is the required rate of return? Since Treasuries are essentially free of default risk, the rate of return on a Treasury security is considered the “risk-free” rate of return. Required rate of return = Risk-free return

8. 8 For a corporate stock or bond, what is the required rate of return? How large of a risk premium should we require to buy a corporate security? Required rate of return = += += += + Risk-free returnRiskpremium

9. 9 Returns n Expected Rate of Return - the return that an investor expects to earn on an asset, given its price, growth potential, etc. n Required Rate of Return - the return that an investor requires on an asset given its risk and market interest rates.

10. 10 State of Probability Return Economy (P) Orl. Utility Orl. Tech Recession.20 4% -10% Normal.50 10% 14% Boom.30 14% 30% For each firm, the expected return on the stock is just a weighted average: k = P(k 1 )*k 1 + P(k 2 )*k 2 +...+ P(k n )*k n k = P(k 1 )*k 1 + P(k 2 )*k 2 +...+ P(k n )*k n Expected Return

11. 11 Expected Return State of Probability Return Economy (P) Orl. Utility Orl. Tech Recession.20 4% -10% Normal.50 10% 14% Boom.30 14% 30% k = P(k 1 )*k 1 + P(k 2 )*k 2 +...+ P(k n )*k n k (OU) =.2 (4%) +.5 (10%) +.3 (14%) = 10%

12. 12 Expected Return State of Probability Return Economy (P) Orl. Utility Orl. Tech Recession.20 4% -10% Normal.50 10% 14% Boom.30 14% 30% k = P(k 1 )*k 1 + P(k 2 )*k 2 +...+ P(k n )*k n k (OT) =.2 (-10%)+.5 (14%) +.3 (30%) = 14%

13. 13 Portfolio Expected Returns n n Weighted average of the expected return of each individual stock with the weights being equal to the proportion of the portfolio invested in each security

14. 14 Portfolio Expected Returns n 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 an expected return of 18%. The risk-free rate is 7%. Asset A weights: 0%, 25%, 50%, 75%, 100%, and 125%.

15. 15 Proportion ProportionPortfolio Invested in Invested in Expected Asset A Riskless Asset Return 0 0%100%7.00% 25%75%9.75% 50%50%12.50% 75%25%15.25% 100%0%18.00% 125%-25%20.75%

16. 16 P t+1 60 P t 50 P t 50 Holding Period Return Calculations = = 20% P t+1 - P t 60 - 50 P t 50 P t 50 - 1 = -1 = 20% tt+1 $50$60

17. 17 (a)(b) monthlyexpected monthpricereturn (a - b) 2 Dec$50.00 Jan$58.000.1600.0490.012321 Feb$63.800.1000.0490.002601 Mar$59.00-0.0750.0490.015376 Apr$62.000.0510.0490.000004 May$64.500.0400.0490.000081 Jun$69.000.0700.0490.000441 Jul$69.000.0000.0490.002401 Aug$75.000.0870.0490.001444 Sep$82.500.1000.0490.002601 Oct$73.00-0.1150.0490.028960 Nov$80.000.0960.0490.002090 Dec$86.000.0750.0490.000676 0.0781 St. Dev: sum, divided by (n-1), and take sq root:

18. 18 What is Risk? n The possibility that an actual return will differ from our expected return. n Uncertainty in the distribution of possible outcomes.

19. 19 What is Risk? n Uncertainty in the distribution of possible outcomes. return Company B Company A return

20. 20 How do We Measure Risk? n To get a general idea of a stock’s price variability, we could look at the stock’s price range over the past year. 52 weeks Yld Vol Net Hi Lo Sym Div % PE 100s Hi Lo Close Chg 134 80 IBM.52.5 21 143402 98 95 95 49 -3 115 40 MSFT … 29 558918 55 52 51 94 -4 75

21. 21 How do We Measure Risk? n A more scientific approach is to examine the stock’s standard deviation of returns. n Standard deviation is a measure of the dispersion of possible outcomes. n The greater the standard deviation, the greater the uncertainty, and, therefore, the greater the risk.

22. 22 Standard Deviation = (k i - k) 2 P(k i )  n i=1 

23. 23 Orlando Utility, Inc. ( 4% - 10%) 2 (.2) = 7.2 (10% - 10%) 2 (.5) = 0 (14% - 10%) 2 (.3) = 4.8 Variance = 12 Stand. dev. = 12 = 3.46% Orlando Utility, Inc. ( 4% - 10%) 2 (.2) = 7.2 (10% - 10%) 2 (.5) = 0 (14% - 10%) 2 (.3) = 4.8 Variance = 12 Stand. dev. = 12 = 3.46% ii = (k i - k) 2 P(k i )  n i=1 

24. 24 Orlando Technology, Inc. (-10% - 14%) 2 (.2) = 115.2 (14% - 14%) 2 (.5) = 0 (30% - 14%) 2 (.3) = 76.8 Variance = 192 Stand. dev. = 192 = 13.86% ii = (k i - k) 2 P(k i )  n i=1 

25. 25 Which stock would you prefer? How would you decide?

26. 26 Orlando Orlando Orlando Orlando UtilityTechnology UtilityTechnology Expected Return 10% 14% Standard Deviation 3.46% 13.86% Summary

27. 27 It depends on your tolerance for risk! Remember, there’s a tradeoff between risk and return. Return Risk

28. 28 Portfolios n Combining several securities in a portfolio can actually reduce overall risk. n How does this work?

29. 29 Suppose we have stock A and stock B. The returns on these stocks do not tend to move together over time (they are not perfectly correlated). rate of return time kAkA kBkB

30. 30 rate of return time kpkp kAkA kBkB What has happened to the variability of returns for the portfolio?

31. 31 Diversification Diversification n Investing in more than one security to reduce risk. n If two stocks are perfectly positively correlated, diversification has no effect on risk. n If two stocks are perfectly negatively correlated, the portfolio is perfectly diversified.

32. 32 n If you owned a share of every stock traded on the NYSE and NASDAQ, would you be diversified? YES! YES! n Would you have eliminated all of your risk? NO! Common stock portfolios still have risk. NO! Common stock portfolios still have risk.

33. 33 Some risk can be diversified away and some cannot. n Market risk (systematic risk) is nondiversifiable. This type of risk cannot be diversified away. n Company-unique risk (unsystematic risk) is diversifiable. This type of risk can be reduced through diversification.

34. 34 Market Risk n Unexpected changes in interest rates. n Unexpected changes in cash flows due to tax rate changes, foreign competition, and the overall business cycle.

35. 35 Company-unique Risk n A company’s labor force goes on strike. n A company’s top management dies in a plane crash. n A huge oil tank bursts and floods a company’s production area.

36. 36 As you add stocks to your portfolio, company-unique risk is reduced. portfolio risk number of stocks Market risk company- unique risk

37. 37 Do some firms have more market risk than others? Yes. For example: Interest rate changes affect all firms, but which of the following would be more affected? a) Retail food chain b) Commercial bank

38. 38 n Note As we know, the market compensates investors for accepting risk - but only for market risk. Company- unique risk can and should be diversified away. So - we need to be able to measure market risk.

39. 39 This is why we have Beta. Beta: a measure of market risk. n Specifically, beta is a measure of how an individual stock’s returns vary with market returns. n It’s a measure of the “sensitivity” of an individual stock’s returns to changes in the market.

40. 40 n A firm that has a beta = 1 has average market risk. The stock is as volatile as the market. n A firm with a beta > 1 is more volatile than the market. – (ex: technology firms) n A firm with a beta < 1 is less volatile than the market. – (ex: utilities) The market’s beta is 1

41. 41 Calculating Beta -5 -15 5 10 15 -15 -10 -5 5 10 15 XYZ Co. returns S&P 500 returns....... Beta = slope = 1.20

42. 42 Summary: n We know how to measure risk, using standard deviation for overall risk and beta for market risk. n We know how to reduce overall risk to only market risk through diversification. n We need to know how to price risk so we will know how much extra return we should require for accepting extra risk.

43. 43 What is the Required Rate of Return? n The return on an investment required by an investor given market interest rates and the investment’s risk.

44. 44 market risk company- unique risk can be diversified away Required rate of return = + Risk-free rate of return Risk premium

45. 45 This linear relationship between risk and required return is known as the Capital Asset Pricing Model (CAPM).

46. 46 r j = r rf + j (r m - r rf ) r j = r rf + j (r m - r rf ) where: where: r j = the required return on security j, r rf = the risk-free rate of interest, j = the beta of security j, and j = the beta of security j, and r m = the return on the market index. The CAPM equation:  

47. 47 Required rate of return Beta 12% 0 Is there a riskless (zero beta) security? Treasury securities are as close to riskless as possible. Risk-free rate of return (6%).

48. 48 Required rate of return Beta 12% 1 0 How to find the return of the market portfolio? Stock market index could be used to approximate the market portfolio. Risk-free rate of return (6%)..

49. 49 Required rate of return. Risk-free rate of return (6%) Beta 12% 1 Security Market Line (SML)

50. 50 What does beta tell us? n A beta of 1 implies the asset has the same systematic risk as the overall market n A beta < 1 implies the asset has less systematic risk than the overall market n A beta > 1 implies the asset has more systematic risk than the overall market

51. 51 (I)(I) Estimates of  for Selected Stocks

52. 52 Required rate of return. Beta 12% 1 SML Utility Stocks Risk-free rate of return (6%) 0

53. 53 Required rate of return. Beta 12% 1 SML High-tech stocks Risk-free rate of return (6%) 0

54. 54 Example: n Suppose the Treasury bond rate is 6%, the average return on the S&P 500 index is 12%, and Walt Disney has a beta of 1.2. n According to the CAPM, what should be the required rate of return on Disney stock?

55. 55 r j = r rf + (r m - r rf ) r j =.06 + 1.2 (.12 -.06) r j =.132 = 13.2% According to the CAPM, Disney stock should be priced to give a 13.2% return. 

56. 56 Required rate of return Beta 12% 1 SML 0 Theoretically, every security should lie on the SML If every stock is on the SML, investors are being fully compensated for risk. Risk-free rate of return (6%)

57. 57 Required rate of return. Beta 12% 1 SML 0 If a security is above the SML, it is underpriced. If a security is below the SML, it is overpriced. Risk-free rate of return (6%).

58. 58 Total versus Systematic Risk n Consider the following information: Standard DeviationBeta Standard DeviationBeta – Security C20%1.25 – Security K30%0.95 n Which security has more total risk? n Which security has more systematic risk? n Which security should have the higher expected return?

59. 59 Question for Discussion 1   n n Consider the following stocks. If the risk-free rate is 6.15% and the market risk premium is 9.5%, what is the required rate of return for each? StockBetaRequired Return – – DCLK4.03? – – KO0.84? – – INTC1.05? – – KEI0.59?

60. 60 Portfolio Beta n n Weighted average of the individual stock betas with the weights being equal to the proportion of the portfolio invested in each security n n Portfolio beta indicates the percentage change on average of the portfolio for every 1 percent change in the general market

61. 61 Question for Discussion 2   n Consider the a portfolio consisting of the following four securities SecurityWeightBeta SecurityWeightBeta – DCLK0.1334.03 – KO0.20.84 – INTC0.2671.05 – KEI0.40.59 What are the portfolio beta and portfolio required rate of return? What are the portfolio beta and portfolio required rate of return?

62. 62 Diversification and Beta n Beta measures systematic risk n Diversification does not mean to reduce beta n Investors differ in the extent to which they will take risk, so they choose securities with different betas – E.g., an aggressive investor could choose a portfolio with a beta of 2.0 – E.g., a conservative investor could choose a portfolio with a beta of 0.5

63. 63

64. 64 Answer 1 Answer 1 Security Required Rate of Return – DCLK6.15% + 4.03(9.5%) = 44.435% – KO6.15% + 0.84(9.5%) = 14.130% – INTC6.15% + 1.05(9.5%) = 16.125% – KEI6.15% + 0.59(9.5%) = 11.755%

65. 65 Answer 2 Answer 2 n Portfolio beta = 0.133(4.03)+0.2(0.84)+0.267(1.05)+0.4(0.59) = 0.133(4.03)+0.2(0.84)+0.267(1.05)+0.4(0.59) = 1.22 = 1.22 n Portfolio required rate of return =6.15%+1.22(9.5%) =6.15%+1.22(9.5%) =17.74% =17.74%