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

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Chapter 4Risk and Rates of Return

© 2005 Thomson/South-Western

defining and measuring risk
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%).
expected rate of return
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
continuous versus discrete probability distributions
Continuous versus Discrete Probability Distributions
  • Continuous Probability Distribution:number of possible outcomes is unlimited, or infinite.
measuring risk coefficient of variation






Coefficient of variation





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
risk aversion and required returns
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
portfolio risk and the capital asset pricing model
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
portfolio risk and return
Portfolio Risk and Return
  • The goal of finance manager is to create


for a given level of risk or minimizes risk for a

given level of return”.

portfolio returns
Portfolio Returns
  • The weighted average expected return on the stocks held in the portfolio
  • Expected return on a portfolio,
portfolio returns14
Portfolio Returns
  • Realized rate of return, k
    • The return that is actually earned
    • Actual return usually different from expected return
portfolio risk
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.
portfolio size and risk
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.
portfolio risk17
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.
firm specific risk versus market risk
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.
firm specific risk versus market risk19
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.
firm specific risk versus market risk20
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.
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

the concept of beta
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.
steps in deriving beta
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.
portfolio beta coefficients
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)
market risk premium
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%.
the required rate of return for a stock
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.
security market line capm

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
the impact of inflation
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.
changes in risk aversion
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.
changes in a stock s beta coefficient
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.
stock market equilibrium
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
changes in equilibrium stock prices
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.