Chapter 4 Risk 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 State of the economy Prob.Martin Product RETURNS US Electric RETURNS (1)(2)(3)(4) (2 x 3) (5)(6) (2 x 5) Boom %20% Normal 0.522%16% Recession %10% E(K)

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 Deviation Martin Product KE(K)K – E(K)[K – E(K)] 2 Pr.[K – E(K)] 2 x Pr (1)(2)(3) (1 – 2) (4)(5)(6) (4 x 5) 110%0.2 22% %0.3

8 Measuring Risk: The Standard Deviation

9  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 k ˆReturn Risk CV Coefficient of variation   Measuring Risk: Coefficient of Variation

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 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

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  Expected return on a portfolio,  The weighted average expected return on the stocks held in the 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… sensitivity BETA.. 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 sensitivity is called BETA

22 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.

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  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%.

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 Security Market Line - CAPM k high = 22 k M = k A = 14 k LOW = 10 k RF = 6 Risk,  j 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%

29 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, 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, 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.