Risk and Rates of Return

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Risk and Rates of Return
Chapter 11
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Defining and Measuring Risk

• Risk is the chance that an outcome other than
  expected will occur
• 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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Probability Distributions

• It either will rain, or it will not
• only two possible outcomes

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Probability Distributions

• Martin Products and U. S. Electric

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Expected Rate of Return

• The rate of return expected to be realized from
  an investment over a long period of time
• The mean value of the probability distribution of
  possible returns
• The weighted average of the outcomes, where the
  weights are the probabilities

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Expected Rate of Return
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Expected Rate of Return
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Discrete Probability Distributions

• The number of possible outcomes is limited, or
  finite

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Discrete Probability Distributions
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Continuous Probability Distributions

• The number of possible outcomes is unlimited, or
  infinite

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Continuous Probability Distributions
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Measuring Risk The Standard Deviation

• A measure of the tightness, or variability, of a
  set of outcomes

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Calculating Standard Deviation

• Calculate the expected rate of return
• Subtract the expected rate of return from each
  possible outcome to obtain a set of deviations

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Calculating Standard Deviation

• Square each deviation, multiply the result by the
  probability of occurrence for its related
  outcome, and then sum these products to obtain
  the variance of the probability distribution

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Calculating Standard Deviation

• Take the square root of the variance to get the
  standard deviation

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Measuring Risk The Standard Deviation

• Calculating Martin Products Standard Deviation

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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

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Risk Aversion

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

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Risk Aversion and Required Returns

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

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Risk/Return Relationship
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Portfolio Risk and theCapital Asset Pricing Model

• Portfolio
• a collection of investment securities
• CAPM
• a model based on the proposition that any stocks
  required rate of return is equal to the risk-free
  rate of return plus a risk premium, where risk
  reflects diversification

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Portfolio Returns

• Expected return on a portfolio
• the weighted average expected return on the
  stocks held in the portfolio

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Portfolio Returns

• Realized rate of return
• the return that is actually earned
• actual return is generally different from the
  expected return

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Portfolio Risk

• Correlation coefficient
• a measure of the degree of relationship between
  two variables
• positively correlated stocks rates of return move
  in the same direction
• negatively correlated stocks have rates of return
  than move in opposite directions

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Portfolio Risk

• Risk reduction
• combining stocks that are not perfectly
  positively correlated will reduce the portfolio
  risk by diversification
• the riskiness of a portfolio is reduced as the
  number of stocks in the portfolio increases
• the smaller the positive correlation, the greater
  the reduction of risk from adding another
  investment

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Firm-Specific Risk versus Market Risk

• Firm-specific risk
• that part of a securitys risk associated with
  random outcomes generated by events, or
  behaviors, specific to the firm
• it can be eliminated through
  proper diversification

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Firm-Specific Risk versus Market Risk

• Market risk
• that part of a securitys risk that cannot be
  eliminated by diversification because it is
  associated with economic, or market factors that
  systematically affect most firms

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Firm-Specific Risk versus Market Risk

• Relevant risk
• the risk of a security that cannot be diversified
  away--its market risk
• this reflects a securitys contribution to the
  risk of a portfolio

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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 average risk
• ?? 2.0 stock is twice as risky as the average
  stock

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Portfolio Beta Coefficients

• The beta of any set of securities is the weighted
  average of the individual securities betas

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The Relationship between Risk and Rates of Return
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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 5
• Average stock required return 11
• Thus, the market risk premium is 6
• RPM kM - kRF 11 - 5 6

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Risk Premium for a Stock

• Risk premium for stock j

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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

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The Required Rate of Return for Stock j
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Security Market Line
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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, k
• an inflation premium (IP)
• An increase in expected inflation would increase
  the risk-free rate, kRF

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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, which in turn increases the slope

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Changes in a Stocks Beta Coefficient

• The ? 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
  ? or in expected inflation) affects the stock
  price

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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

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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

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Changes in Equilibrium Stock Prices

• Stock prices are not constant due to changes in
• risk-free rate, kRF
• Market risk premium, kM - kRF
• Stock Xs beta coefficient, ?x
• Stock Xs expected growth rate, gX
• Changes in expected dividends, D0(1g)

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SP 500 Index Value and Total Returns
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Physical Assets versus Securities

• Riskiness of a physical asset is only relevant in
  terms of its effect on the stocks risk

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Different Types of Risk

• Systematic Risks
• Interest rate risk
• Inflation risk
• Maturity risk
• Liquidity risk
• Exchange rate risk
• Political risk

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Different Types of Risk

• Unsystematic Risks
• Business risk
• Financial risk
• Default risk
• Combined Risks
• Total risk
• Corporate risk

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End of Chapter 11

• Risk and Rates of Return