Chapter 11 Risk and Rates of Return. Defining and Measuring Risk Risk is the chance that an...
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Transcript of Chapter 11 Risk and Rates of Return. Defining and Measuring Risk Risk is the chance that an...
Chapter 11
Risk and Rates of Return
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.
• Probability must sum to 1.0 (100%)
2
Probability Distributions
3
Either it will rain or it will not.There are only two possible outcomes.Outcome (1) Probability (2)
Rain 0.40 = 40%
No Rain 0.60 = 60%
1.00 100%
Probability Distributions
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Martin Products and U. S. Electric
Martin Products U.S. Electric
Boom 0.2 110% 20%Normal 0.5 22% 16%Recession 0.3 -60% 10%
1.0
Probability of This State Occurring
State of the Economy
Rate of Return on Stock if This State Occurs
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 5
Expected Rate of Return
6
(1) (2) (3) = (4) (5) = (6)Boom 0.2 110% 22% 20% 4%Normal 0.5 22% 11% 16% 8%Recession 0.3 -60% -18% 10% 3%
1.0 km = 15% km = 15%
State of the Economy
Martin Products U. S. Electric
Return if This State Occurs (ki)
Product: (2) x (5)
Probability of This State
Occurring (Pr i)
Return if This State
Occurs (ki)Product: (2) x (3)
^ ^
Continuous versus Discrete Probability Distributions• Discrete Probability Distribution:
Where the number of possible outcomes is limited (or finite).• Continuous Probability Distribution:
Where the number of possible outcomes is unlimited or infinite.
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Discrete Probability DistributionsDiscrete Probability Distributionsa. Martin Products
Probability of Occurrence
b. U. S. ElectricProbability of Occurrence
-60 -45 -30 -15 0 15 22 30 45 60 75 90 110Rate of
Return (%)Expected Rate of Return (15%)
0.5 -
0.4 -
0.3 -
0.2 -
0.1 -
-10 -5 0 5 10 16 20 25Rate of
Return (%)Expected Rate
of Return (15%)
0.5 -
0.4 -
0.3 -
0.2 -
0.1 -
Probability Density
-60 0 15 110Rate of Return
(%)Expected Rate of Return
Martin ProductsMartin Products
U. S. ElectricU. S. Electric
Continuous Probability Distributions
Measuring Risk: The Standard Deviation• Expected rate of return:
The weighted average of the expected returns• Variance:
The weighted average of the squared deviations from the mean expected return
• Standard deviation:The square root of the variance
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Measuring Risk: The Standard Deviation
Calculating Martin Products’ Standard Deviation
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(1) (2) (1) - (2) = (3) (4) (5) (4) x (5) = (6)110% 15% 95 9,025 0.2 1,805.0 22% 15% 7 49 0.5 24.5 -60% 15% -75 5,625 0.3 1,687.5
Payoff
ki(ki - k)
2Pr iProbability
Expected Return
kki - k (ki - k)
2^^
^ ^
%3.59 517,3 Deviation Standard
0.517,3 Variance
2mm
2
^^^^
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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k̂Return
Risk CV Coefficient of variation
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 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
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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
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Portfolio Returns
• Expected return on a portfolio,
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pk̂
The weighted average expected return on the stocks held in the portfolio
Portfolio Returns
• Realized rate of return, k• The return that is actually earned• The actual return usually differs from the expected return.
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Returns Distribution for Two Perfectly Negatively Correlated Stocks (r = -1.0) and for Portfolio WM:
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25
15
0
-10
Stock W
-10
0
15
25
Portfolio WM
-10
0
15
25
Stock M
Returns Distributions for Two Perfectly Positively Correlated Stocks (r = +1.0) and for Portfolio MM’:
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Stock M
0
15
25
-10
0
15
25
-10
Stock M’
0
15
25
-10
Stock MM’
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.
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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.
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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.
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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.
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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 the same risk as the 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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stock j on thereturn of rate k̂ thj expected
The Relationship Between Risk and Rates of Return
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stock j on thereturn of rate k
stock j on thereturn of rate k̂th
j
thj
required
expected
The Relationship Between Risk and Rates of Return
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return of rate k
stock j on thereturn of rate k
stock j on thereturn of rate k̂
RF
thj
thj
freerisk
required
expected
The Relationship Between Risk and Rates of Return
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premiumrisk market k-k RP
return of rate freerisk k
stock j on thereturn of rate required k
stock j on thereturn of rate expected k̂
RFMM
RF
thj
thj
The Relationship Between Risk and Rates of Return
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stock j on the premiumrisk k-k RP
premiumrisk market k-k RP
return of rate k
stock j on thereturn of rate k
stock j on thereturn of rate k̂
thjRFMj
RFMM
RF
thj
thj
freerisk
required
expected
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%.31
Risk Premium for a Stock
• Risk Premium for Stock j = RPj = RPM xj
32
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.33
jstock for return of rate k j required
jRFMRF
jMRFj
kk k
RP k k
Security Market Line
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jRFMRFj kk k k:SML
khigh = 22
kM = kA = 14
kLOW = 10
kRF = 6
Risk, j0 0.5 1.0 1.5 2.0
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%
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• an inflation premium (IP)
• An increase in expected inflation would increase the risk-free rate.
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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 and increases the slope.
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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• expiration of patents
• Any change in the required return (from change in beta or in expected inflation) affects the stock price.
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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 X’s beta coefficient, x,
• Stock X’s expected growth rate, gX, and
• Changes in expected dividends, D0.
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Physical AssetsVersus Securities• Riskiness of corporate assets is only relevant in terms of its
effect on the stock’s risk.
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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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