Transcript Chapter 4 - Risk and Rates of Return

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%)
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Probability Distributions
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%
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Probability Distributions
Martin Products and U. S. Electric
State of the
Economy
Boom
Normal
Recession
Probability of This State
Occurring
0.2
0.5
0.3
1.0
Rate of Return on Stock if
This State Occurs
Martin Products
U.S. Electric
110%
22%
-60%
20%
16%
10%
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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
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Expected Rate of Return
Probability of
This State
State of the
Economy Occurring (Pr i)
(1)
Boom
Normal
Recession
(2)
0.2
0.5
0.3
1.0
Martin Products
Return if This State Product:
Occurs (ki)
(2) x (3)
(3)
110%
22%
-60%
^ =
km
= (4)
22%
11%
-18%
15%
U. S. Electric
Return if This Product:
State Occurs (ki) (2) x (5)
(5)
20%
16%
10%
^ =
km
= (6)
4%
8%
3%
15%
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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 Distributions
a. Martin Products
Probability of
Occurrence
b. U. S. Electric
Probability of
Occurrence
0.5 -
0.5 -
0.4 -
0.4 -
0.3 -
0.3 -
0.2 -
0.2 -
0.1 -
0.1 -
-60 -45 -30 -15 0 15 22 30 45 60 75 90 110
Rate of
Expected Rate
Return (%)
of Return (15%)
-10
-5
0
5
10
16 20
Expected Rate
of Return (15%)
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Rate of
Return (%)
Continuous Probability Distributions
Probability Density
U. S. Electric
Martin Products
-60
0
15
110
Rate of Return
(%)
Expected Rate of
Return
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
Expected
Payoff Return
ki
k^
(1)
(2)
110%
15%
22%
15%
-60%
15%
^
^
ki - k
^2
(ki - ^k)
Probability
^^ 2
(ki - k) Pr i
(1) - (2) = (3)
95
7
-75
(4)
9,025
49
5,625
(5)
0.2
0.5
0.3
(4) x (5) = (6)
1,805.0
24.5
1,687.5
Variance  2  3,517.0
Standard Deviation  m  
2
m
 3,517  59.3%
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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
 12
Risk

Coefficient of variation  CV 
Return
kˆ
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 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
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Portfolio Returns
• Expected return on a portfolio,
kˆ p
 The weighted average expected return on
the stocks held in the portfolio
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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:
Stock W
Stock M
Portfolio WM
25
25
25
15
15
15
0
0
0
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-10
-10
-10
Returns Distributions for Two Perfectly Positively
Correlated Stocks (r = +1.0) and for Portfolio MM’:
Stock MM’
Stock M’
Stock M
25
25
25
15
15
15
0
0
0
-10
-10
-10
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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, 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.
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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
ˆk  expected rateof returnon thejth stock
j
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The Relationship Between
Risk and Rates of Return
ˆk  expected rateof returnon thejth stock
j
k j  required rateof returnon thej stock
th
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The Relationship Between
Risk and Rates of Return
ˆk  expected rateof returnon thejth stock
j
k j  required rateof returnon thej stock
th
k RF  risk  free rateof return
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The Relationship Between
Risk and Rates of Return
ˆk  expectedrateof returnon thej th stock
j
k j  required rateof returnon thej stock
th
k RF  risk  free rateof return
RPM  k M - k RF   marketrisk premium
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The Relationship Between
Risk and Rates of Return
ˆk  expected rateof returnon thejth st ock
j
k j  required rateof returnon thej st ock
th
k RF  risk  free rateof return
RPM  k M - k RF   marketrisk premium
RPj  k M - k RF b j  risk premiumon thej st ock
th
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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 = 6%
• Average stock required return = 14%
• Then the market risk premium is 8 percent:
• RPM = kM - kRF = 14% - 6% = 8%.
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Risk Premium for a Stock
•
Risk Premium for Stock j
= RPj = RPM x bj
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The Required Rate of Return for a
Stock
k j  required rateof returnfor stock j
k j  k RF  RPM b j
 k RF  k M  k RF b j
• 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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Security Market Line
SML : k j  k RF  k M  k RF b j
Required Rate
of Return (%)
khigh = 22
kM = kA = 14
kLOW = 10
Safe Stock Risk
Premium: 4%
kRF = 6
Market (Average
Stock) Risk Premium:
8%
Risk-Free
Rate: 6%
0
0.5
Relatively
Risky
Stock’s
Risk
Premium:
16%
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1.0
1.5
2.0 Risk, bj
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, bx,
• Stock X’s expected growth rate, gX, and
• Changes in expected dividends, D0.
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Physical Assets
Versus 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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