Risk and Rates of Return Chapter 11

Defining and Measuring Risk uRisk is the chance that an outcome other than expected will occur uProbability distribution is a listing of all possible outcomes with a probability assigned to each F must sum to 1.0 (100%)

Probability Distributions uIt either will rain, or it will not F only two possible outcomes

Probability Distributions uMartin Products and U. S. Electric

Expected Rate of Return uThe rate of return expected to be realized from an investment uThe mean value of the probability distribution of possible returns uThe weighted average of the outcomes, where the weights are the probabilities

^^ Expected Rate of Return

^^

Continuous versus Discrete Probability Distributions uDiscrete probability distribution F the number of possible outcomes is limited, or finite

Rate of Return (%) Expected Rate of Return (15%) b. U. S. Electric Probability of Occurrence Discrete Probability Distributions Rate of Return (%) Expected Rate of Return (15%) a. Martin Products Probability of Occurrence

Continuous versus Discrete Probability Distributions uContinuous probability distribution F the number of possible outcomes is unlimited, or infinite

Rate of Return (%) Expected Rate of Return Martin Products Probability Density U. S. Electric Continuous Probability Distributions

uCalculating Martin Products’ Standard Deviation ^ ^ ^^ Measuring Risk: The Standard Deviation

Measuring Risk: Coefficient of Variation uStandardized measure of risk per unit of return uCalculated as the standard deviation divided by the expected return uUseful where investments differ in risk and expected returns

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

Risk Aversion and Required Returns uRisk premium (RP) F the portion of the expected return that can be attributed to the additional risk of an investment F the difference between the expected rate of return on a given risky asset and that on a less risky asset

Portfolio Risk and the Capital Asset Pricing Model uCAPM F 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 uPortfolio F a collection of investment securities

uExpected return on a portfolio, k p F the weighted average expected return on the stocks held in the portfolio Portfolio Returns

uRealized rate of return, k F the return that is actually earned F actual return is generally different from the expected return Portfolio Returns

Portfolio Risk uCorrelation coefficient, r F a measure of the degree of relationship between two variables F positively correlated stocks rates of return move together in the same direction F negatively correlated stocks have rates of return than move in opposite directions

Portfolio Risk uRisk reduction F combining stocks that are not perfectly positively correlated will reduce the portfolio risk by diversification F the riskiness of a portfolio is reduced as the number of stocks in the portfolio increases F the smaller the positive correlation, the lower the risk

Firm-Specific Risk versus Market Risk uFirm-specific risk F that part of a security’s risk associated with random outcomes generated by events, or behaviors, specific to the firm

Firm-Specific Risk versus Market Risk uFirm-specific risk F that part of a security’s risk associated with random outcomes generated by events, or behaviors, specific to the firm F it can be eliminated by proper diversification

Firm-Specific Risk versus Market Risk uMarket risk F that 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

Firm-Specific Risk versus Market Risk uRelevant risk F the risk of a security that cannot be diversified away--its market risk F this reflects a security’s contribution to the risk of a portfolio

The Concept of Beta uBeta coefficient,  F a measure of the extent to which the returns on a given stock move with the stock market F  = 0.5: stock is only half as volatile, or risky, as the average stock F  = 1.0: stock is of average risk F  = 2.0: stock is twice as risky as the average stock

uThe beta of any set of securities is the weighted average of the individual securities’ betas Portfolio Beta Coefficients

The Relationship between Risk and Rates of Return

Market Risk Premium uRPM is the additional return over the risk-free rate needed to compensate investors for assuming an average amount of risk uAssuming: F Treasury bonds yield = 6% F Average stock required return = 14% F Thus, the market risk premium is 8%: uRP M = k M - k RF = 14% - 6% = 8%

Risk Premium for a Stock uRisk premium for stock j = RP j = RP M   j

The Required Rate of Return for a Stock

uSecurity Market Line (SML) F The line that shows the relationship between risk as measured by beta and the required rate of return for individual securities

Required Rate of Return (%) Risk-Free Rate: 6% 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: Risk Premium = 16% Security Market Line

The Impact of Inflation uk RF is the price of money to a riskless borrower uThe nominal rate consists of F a real (inflation-free) rate of return, k* F an inflation premium (IP) uAn increase in expected inflation would increase the risk-free rate, k RF

Changes in Risk Aversion uThe slope of the SML reflects the extent to which investors are averse to risk uAn increase in risk aversion increases the risk premium, which increases the slope

Changes in a Stock’s Beta Coefficient uThe  risk of a stock is affected by F composition of its assets F use of debt financing F increased competition F expiration of patents uAny change in the required return (from change in  or in expected inflation) affects the stock price

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

Changes in Equilibrium Stock Prices uStock prices are not constant due to changes in: F risk-free rate, k RF F Market risk premium, k M - k RF F Stock X’s beta coefficient,  x F Stock X’s expected growth rate, g X F Changes in expected dividends, D 0 (1+g)

uRiskiness of a physical asset is only relevant in terms of its effect on the stock’s risk Physical Assets versus Securities

Word of Caution uCAPM F based on expected conditions F only have historical data F as conditions change, future volatility may differ from past volatility F estimates are subject to error

End of Chapter 11 Risk and Rates of Return