1. Chapter 11 Risk and Rates of Return

2. Defining and Measuring Risk Risk is the chance that an unexpected outcome will occur A probability distribution is a listing of all possible outcomes with a probability assigned to each. Probability must sum to 1.0 (100%) 2

3. Probability Distributions 3 Either it will rain or it will not. There are only two possible outcomes.

4. Probability Distributions 4 Martin Products and U. S. Electric Martin ProductsU.S. Electric Boom0.2110%20% Normal0.522%16% Recession0.3-60%10% 1.0 Probability of This State Occurring State of the Economy Rate of Return on Stock if This State Occurs

5. Expected Rate of Return Rate of return expected to be realized from an investment during its life Mean value of the probability distribution of possible returns Weighted average of the outcomes, where the weights are the probabilities 5

6. Expected Rate of Return 6 (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. Continuous versus Discrete Probability Distributions Discrete Probability Distribution: Where the number of possible outcomes is limited (or finite). Continuous Probability Distribution: Where the number of possible outcomes is unlimited or infinite. 7

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

9. Probability Density -60 0 15 110 Rate of Return (%) Expected Rate of Return Martin Products U. S. Electric Continuous Probability Distributions

10. Measuring Risk: The Standard Deviation Expected rate of return: The weighted average of the expected returns Variance: The weighted average of the squared deviations from the mean expected return Standard deviation: The square root of the variance 10

11. Measuring Risk: The Standard Deviation Calculating Martin Products’ Standard Deviation 11 (1)(2)(1) - (2) = (3)(4)(5)(4) x (5) = (6) 110%15%959,025 0.2 1,805.0 22%15%749 0.5 24.5 -60%15%-755,625 0.3 1,687.5 Payoff k i (k i - k) 2 Pr i Probability Expected Return k k i - k (k i - k) 2 ^ ^ ^^ ^ ^ ^ ^

12. Measuring Risk: Coefficient of Variation Standardized measure of risk per unit of return Calculated as the standard deviation divided by the expected return Useful where investments differ in risk and expected returns 12 k ˆReturn Risk CV Coefficient of variation  

13. Risk Aversion Risk-averse investors require higher rates of return to invest in higher-risk securities 13

14. Risk Aversion and Required Returns Risk Premium (RP): The portion of the expected return that can be attributed to an investment’s risk beyond a riskless investment The difference between the expected rate of return on a given risky asset and that on a less risky asset 14

15. Portfolio Risk and the Capital Asset Pricing Model CAPM: 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 is based on diversification. Portfolio A collection of investment securities 15

16. Portfolio Returns Expected return on a portfolio, 16  The weighted average expected return on the stocks held in the portfolio

17. Portfolio Returns Realized rate of return, k The return that is actually earned The actual return usually differs from the expected return. 17

18. Returns Distribution for Two Perfectly Negatively Correlated Stocks (r = -1.0) and for Portfolio WM: 18 25 15 0 -10 Stock W -10 0 15 25 Portfolio WM -10 0 15 25 Stock M

19. Returns Distributions for Two Perfectly Positively Correlated Stocks (r = +1.0) and for Portfolio MM’: 19 Stock M 0 15 25 -10 0 15 25 -10 Stock M’ 0 15 25 -10 Stock MM’

20. Portfolio Risk Correlation Coefficient, r Measures the degree of relationship between two variables. Perfectly correlated stocks have rates of return that move in the same direction. Negatively correlated stocks have rates of return that move in opposite directions. 20

21. Portfolio Risk Risk Reduction Combining stocks that are not perfectly correlated will reduce the portfolio risk through diversification. The riskiness of a portfolio is reduced as the number of stocks in the portfolio increases. The smaller the positive correlation, the lower the risk. 21

22. Firm-Specific Risk versus Market Risk Firm-Specific Risk: That part of a security’s risk associated with random outcomes generated by events, or behaviors, specific to the firm. Firm-specific risk can be eliminated through proper diversification. 22

23. Firm-Specific Risk versus Market Risk Market Risk: That part of a security’s risk that cannot be eliminated through diversification because it is associated with economic, or market, factors that systematically affect all firms. 23

24. The Concept of Beta Beta Coefficient,  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 has the same risk as the average risk.  = 2.0: Stock is twice as risky as the average stock. 24

25. Portfolio Beta Coefficients The beta of any set of securities is the weighted average of the individual securities’ betas 25

26. The Relationship Between Risk and Rates of Return 26

27. The Relationship Between Risk and Rates of Return 27

28. The Relationship Between Risk and Rates of Return 28

29. The Relationship Between Risk and Rates of Return 29

30. The Relationship Between Risk and Rates of Return 30

31. Market Risk Premium RP M is the additional return over the risk-free rate needed to compensate investors for assuming an average amount of risk. Assuming: 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%. 31

32. Risk Premium for a Stock Risk Premium for Stock j = RP j = RP M x  j 32

33. The Required Rate of Return for a Stock Security Market Line (SML): The line that shows the relationship between risk as measured by beta and the required rate of return for individual securities. 33

34. Security Market Line 34 k high = 22 k M = k A = 14 k LOW = 10 k RF = 6 Risk,  j 0 0.5 1.0 1.5 2.0 Required Rate of Return (%) Risk-Free Rate: 6% Safe Stock Risk Premium: 4% Market (Average Stock) Risk Premium: 8% Relatively Risky Stock’s Risk Premium: 16%

35. The Impact of Inflation k RF is the price of money to a riskless borrower. The nominal rate consists of: a real (inflation-free) rate of return an inflation premium (IP) An increase in expected inflation would increase the risk-free rate. 35

36. Changes in Risk Aversion The slope of the SML reflects the extent to which investors are averse to risk. An increase in risk aversion increases the risk premium and increases the slope. 36

37. Changes in a Stock’s Beta Coefficient The Beta risk of a stock is affected by: composition of its assets use of debt financing increased competition expiration of patents Any change in the required return (from change in beta or in expected inflation) affects the stock price. 37

38. Stock Market Equilibrium The condition under which the expected return on a security is just equal to its required return Actual market price equals its intrinsic value as estimated by the marginal investor, leading to price stability 38

39. Changes in Equilibrium Stock Prices Stock prices are not constant due to changes in: Risk-free rate, k RF, Market risk premium, k M – k RF, Stock X’s beta coefficient,  x, Stock X’s expected growth rate, g X, and Changes in expected dividends, D 0. 39

40. Physical Assets Versus Securities Riskiness of corporate assets is only relevant in terms of its effect on the stock’s risk. 40

41. Word of Caution CAPM Based on expected conditions Only have historical data As conditions change, future volatility may differ from past volatility Estimates are subject to error 41