Chapter 4 Risk and Rates of Return

1. Chapter 4Risk and Rates of Return © 2005 Thomson/South-Western

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; • must sum to 1.0 (100%).

3. 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

4. Expected Rate of Return

5. Expected Rate of Return

6. Continuous versus Discrete Probability Distributions • Continuous Probability Distribution:number of possible outcomes is unlimited, or infinite.

7. Measuring Risk: The Standard DeviationMartin Product

8. Measuring Risk: The Standard Deviation

9. s Risk = = = Coefficient of variation CV Return ˆ k 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

10. 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

11. Portfolio Risk and theCapital 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

12. Portfolio Risk and Return • The goal of finance manager is to create AN EFFICIENT PORTFOLIO: “Maximizes return for a given level of risk or minimizes risk for a given level of return”.

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

14. Portfolio Returns • Realized rate of return, k • The return that is actually earned • Actual return usually different from expected return

15. 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.

16. Portfolio size and risk • Inc size of a portfolio  risk dec • Risk dec to a certain point .. (Co. risk = 0) • If we take all sec in the stock mkt as one portfolio (max size)  still some risk exist (Market Risk) = relevant risk = the contribution of a sec’s risk to a portfolio.

17. 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.

18. 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.

19. 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.

20. Firm-Specific Risk versus Market Risk • Relevant Risk: • The risk of a security that cannot be diversified away, or its market risk. • This reflects a security’s contribution to a portfolio’s total risk.

21. NO GOOD… .. of thinking how risky a security is if helf in isolation – you need to measure its market risk … measure how sensitive it is to market … this sensitivityis called BETA

22. The Concept of Beta • Beta Coefficient, b: • A measure of the extent to which the returns on a given stock move with the stock market. • b = 0.5: Stock is only half as volatile, or risky, as the average stock. • b = 1.0: Stock has the same risk as the average risk. • b = 2.0: Stock is twice as risky as the average stock.

23. Steps in deriving Beta • Plot mkt ret (X) and asset ret (Y) at various point in time. • Regression: the slope = beta • The higher the beta the higher the risk • Beta for the market = 1, all other betas are viewed in relation to this value. • Beta may be +ve or –v, +ve is the norm • Majority of betas fall between .5 and 2.

24. Portfolio Beta Coefficients • The beta of any set of securities is the weighted average of the individual securities’ betas • IF mkt ret inc by 10%, a port with a beta of .75 will experience a 7.5% inc in its return (.75 x 10)

25. The Relationship Between Risk and Rates of Return

26. Market Risk Premium • RPM 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: • RPM = kM - kRF = 14% - 6% = 8%.

27. 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.

28. Required Rate of Return (%) khigh = 22 kM = kA = 14 kLOW = 10 kRF = 6 Relatively Risky Stock’s Risk Premium: 16% Market (Average Stock) Risk Premium: 8% Safe Stock Risk Premium: 4% Risk-Free Rate: 6% 0 0.5 1.0 1.5 2.0 Risk, bj Security Market Line - CAPM

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

30. 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.

31. 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, and • expiration of patents. • Any change in the required return (from change in beta or in expected inflation) affects the stock price.

32. 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

33. Changes in Equilibrium Stock Prices • Stock prices are not constant due to changes in: • Risk-free rate, kRF, • Market risk premium, kM – kRF, • Stock X’s beta coefficient, bx, • Stock X’s expected growth rate, gX, and • Changes in expected dividends, D0.