1. 5 - 1 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Chapter 5 Risk and Rates of Return Copyright © 2000 by Harcourt, Inc. All rights reserved. Requests for permission to make copies of any part of the work should be mailed to the following address: Permissions Department, Harcourt, Inc., 6277 Sea Harbor Drive, Orlando, Florida 32887- 6777.

2. 5 - 2 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Defining and Measuring Risk 4 Risk is the chance that an outcome other than expected will occur 4 Probability distribution is a listing of all possible outcomes with a probability assigned to each [must sum to 1.0 (100%)]

3. 5 - 3 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Probability Distributions It either will rain, or it will not – only two possible outcomes

4. 5 - 4 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Probability Distributions Martin Products and U. S. Electric

5. 5 - 5 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Expected Rate of Return èThe rate of return expected to be realized from an investment èThe mean value of the probability distribution of possible returns èThe weighted average of the outcomes, where the weights are the probabilities

6. 5 - 6 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Expected Rate of Return (1)(2)(3)= (4)(5)= (6) Boom0.2110%22%20%4% Normal0.522%11%16%8% Recession0.3-60%-18%10%3% 1.0k m = 15%k m = State of the Economy Martin ProductsU. S. Electric Return if This State Occurs (k i ) Product: (2) x (5) Probability of This State Occurring (Pr i ) Return if This State Occurs (k i ) Product: (2) x (3) ^^

7. 5 - 7 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Expected Rate of Return

8. 5 - 8 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Continuous versus Discrete Probability Distributions èDiscrete Probability Distribution: èDiscrete Probability Distribution: the number of possible outcomes is limited, or finite

9. Discrete Probability Distributions -60 -45 -30 -15 0 15 22 30 45 60 75 90 110 Rate of Return (%) Expected Rate of Return (15%) a. Martin Products Probability of Occurrence -10 -5 0 5 10 16 20 25 Rate of Return (%) Expected Rate of Return (15%) b. U. S. Electric Probability of Occurrence 0.5 - 0.4 - 0.3 - 0.2 - 0.1 - 0.5 - 0.4 - 0.3 - 0.2 - 0.1 -

10. 5 - 10 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. èContinuous Probability Distribution: èContinuous Probability Distribution: the number of possible outcomes is unlimited, or infinite Continuous versus Discrete Probability Distributions

11. 5 - 11 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Continuous Probability Distributions -60 0 15 110 Rate of Return (%) Expected Rate of Return Martin Products Probability Density U. S. Electric

12. 5 - 12 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Measuring Risk: The Standard Deviation Calculating Martin Products’ Standard Deviation ^ ^ ^^

13. 5 - 13 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Measuring Risk: The Standard Deviation

14. 5 - 14 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Measuring Risk: Coefficient of Variation k ˆReturn Risk CV Coefficient of variation   èStandardized measure of risk per unit of return èCalculated as the standard deviation divided by the expected return èUseful where investments differ in risk and expected returns

15. 5 - 15 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Risk Aversion èRisk-averse investors require higher rates of return to invest in higher-risk securities

16. 5 - 16 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Risk Aversion and Required Returns lRisk Premium (RP) n The portion of the expected return that can be attributed to the additional risk of an investment n The difference between the expected rate of return on a given risky asset and that on a less risky asset

17. 5 - 17 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Portfolio Risk and the Capital Asset Pricing Model lCAPM A model based on the proposition that any stock’s required rate of return is equal to the risk-free rate of return plus a risk premium, where risk reflects diversification lPortfolio A collection of investment securities

18. 5 - 18 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Portfolio Returns 4 Expected return on a portfolio, k p The weighted average expected return on the stocks held in the portfolio ^

19. 5 - 19 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 4 Realized rate of return, k _ Portfolio Returns The return that is actually earned Actual return is usually different from the expected return

20. 5 - 20 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Returns Distribution for Two Perfectly Negatively Correlated Stocks (r = -1.0) and for Portfolio WM: 25 15 0 -10 0 0 15 25 Stock WStock MPortfolio WM

21. 5 - 21 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Returns Distributions for Two Perfectly Positively Correlated Stocks (r = +1.0) and for Portfolio MM: Stock M 0 15 25 -10 0 15 25 -10 Stock MM’ 0 15 25 -10 Stock MM’

22. 5 - 22 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Portfolio Risk è Correlation Coefficient, r Ù A measure of the degree of relationship between two variables Ù Perfectly correlated stocks rates of return move together in the same direction Ù Negatively correlated stocks have rates of return than move in opposite directions

23. 5 - 23 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. è Risk Reduction Ù Combining stocks that are not perfectly correlated will reduce the portfolio risk by diversification Ù The riskiness of a portfolio is reduced as the number of stocks in the portfolio increases Ù The smaller the positive correlation, the lower the risk Portfolio Risk

24. 5 - 24 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Firm-Specific Risk versus Market Risk lFirm-Specific Risk l That part of a security’s risk associated with random outcomes generated by events, or behaviors, specific to the firm l It can be eliminated by proper diversification

25. 5 - 25 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Firm-Specific Risk versus Market Risk 4 Market Risk 3That part of a security’s risk that cannot be eliminated by diversification because it is associated with economic, or market factors that systematically affect most firms

26. 5 - 26 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. 4 Relevant Risk 3 The risk of a security that cannot be diversified away, or its market risk 3 This reflects a security’s contribution to the risk of a portfolio Firm-Specific Risk versus Market Risk

27. 5 - 27 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. The Concept of Beta Beta Coefficient,  Beta Coefficient,  l A measure of the extent to which the returns on a given stock move with the stock market  = 0.5: stock is only half as volatile, or risky, as the average stock  = 1.0: stock is of average risk  = 2.0: stock is twice as risky as the average stock

28. 5 - 28 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Portfolio Beta Coefficients lThe beta of any set of securities is the weighted average of the individual securities’ betas

29. 5 - 29 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. The Relationship Between Risk and Rates of Return

30. 5 - 30 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. The Relationship Between Risk and Rates of Return

31. 5 - 31 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. The Relationship Between Risk and Rates of Return

32. 5 - 32 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. The Relationship Between Risk and Rates of Return

33. 5 - 33 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. The Relationship Between Risk and Rates of Return

34. 5 - 34 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Market Risk Premium RP M RP M is the additional return over the risk-free rate needed to compensate investors for assuming an average amount of riskAssuming: Treasury bonds yield = 6% Average stock required return = 14% Then the market risk premium is 8 percent: RP M = k M - k RF = 14% - 6% = 8%

35. 5 - 35 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Risk Premium for a Stock Risk Premium for Stock j = RP j = RP M x  j

36. 5 - 36 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. The Required Rate of Return for a Stock Security Market Line (SML) ÙThe line that shows the relationship between risk as measured by beta and the required rate of return for individual securities

37. 5 - 37 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Security Market Line Required Rate of Return (%) Risk-Free Rate: 6% 0 0.5 1.0 1.5 2.0 Risk,  j k high = 22 k M = k A = 14 k LOW = 10 k RF = 6 Safe Stock Risk Premium: 4% Market (Average Stock) Risk Premium: 8% Relatively Risky Stock’s Risk Premium: 16%

38. 5 - 38 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. The Impact of Inflation èk RF is the price of money to a riskless borrower èThe nominal rate consists of Ù a real (inflation-free) rate of return Ù an inflation premium (IP) èAn increase in expected inflation would increase the risk-free rate

39. 5 - 39 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Changes in Risk Aversion 4 The slope of the SML reflects the extent to which investors are averse to risk 4 An increase in risk aversion increases the risk premium and increases the slope

40. 5 - 40 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Changes in a Stock’s Beta Coefficient lThe Beta risk of a stock is affected by l composition of its assets l use of debt financing l increased competition l expiration of patents lAny change in the required return (from change in beta or in expected inflation) affects the stock price

41. 5 - 41 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Stock Market Equilibrium l The condition under which the expected return on a security is just equal to its required return l Actual market price equals its intrinsic value as estimated by the marginal investor, leading to price stability

42. 5 - 42 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Changes in Equilibrium Stock Prices Stock prices are not constant due to changes in: èRisk-free rate, k RF èMarket risk premium, k M - k RF  Stock X’s beta coefficient,  x èStock X’s expected growth rate, g X èChanges in expected dividends, D 0

43. 5 - 43 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Actual Stock Prices and Returns S&P 500 over 10 years

44. 5 - 44 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Physical Assets Versus Securities 4 Riskiness of corporate assets is only relevant in terms of its effect on the stock’s risk

45. 5 - 45 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Word of Caution èCAPM Û Based on expected conditions Û Only have historical data Û As conditions change, future volatility may differ from past volatility Û Estimates are subject to error

46. 5 - 46 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. End of Chapter 5 Risk and Rates of Return