Download State Occurring

Chapter 11
Risks and
Rates of
Return
1
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved. May
not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Chapter 11 – Learning Objectives
 Explain what it means to take risk when investing.
 Compute the risk and return of an investment, and explain how the risk
and return of an investment are related.
 Identify relevant and irrelevant risk, and explain how irrelevant risk can
be reduced.
 Describe how to determine the appropriate reward—that is, risk
premium—that investors should earn for purchasing a risky
investment.
 Describe actions that investors take when the return they require to
purchase an investment is different from the return they expect the
investment to produce.
 Identify different types of risk and classify each as relevant or irrelevant
with respect to determining an investment’s required rate of return.
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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2
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
 Probabilities must sum to 1.0 (100%)
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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3
Probability Distributions
It either will rain, or it will not
 Only two possible outcomes
Outcome (1)
Probability (2)
Rain
0.40 = 40%
No Rain
0.60 = 60%
1.00 100%
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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4
Probability Distributions
State of the
Economy
Boom
Probability of This
State Occurring
0.2
Rate of Return on Stock if
Economic State Occurs
Martin Products
U.S. Electric
110%
20%
Normal
0.5
22
16
Recession
0.3
-60
10
1.0
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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5
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
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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6
Expected Rate of Return
= r̂ = Pr1r1 + Pr2 r2 + . . . + Prn rn
n
=å Pri ri
i=1
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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7
Discrete Probability Distributions
The number of possible outcomes is
limited, or finite
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8
Discrete Probability Distributions
a. Martin Products
-60
-40
b. U.S. Electric
Probability of
Occurrence
Probability of
Occurrence
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
-20
0
20
40
r̂Martin = 15%
60
80
100 120
Rate of
Return (%)
-10
-5
0
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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5
10
15
20
r̂US = 15%
25
Rate of
Return (%)
9
Continuous Probability Distributions
The number of possible outcomes is
unlimited, or infinite
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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10
Continuous Probability Distributions
Probability Density
U.S.
Electric
Martin Products
-60
0
15
110
Rate of Return (%)
Expected Rate
of Return
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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11
Measuring Risk: The Standard Deviation
A measure of the tightness, or variability,
of a set of outcomes
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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12
Calculating Standard Deviation
1. Calculate the expected rate of return
= r̂ = Pr1r1 + Pr2 r2 + . . . + Prn rn
n
= å Pri ri
i=1
2. Subtract the expected rate of return from
each possible outcome to obtain a set of
deviations
Deviation i = ri - r̂
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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13
Calculating Standard Deviation
3. 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
n
Variance = s = å (ri - r̂) Pri
2
2
i=1
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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14
Calculating Standard Deviation
4. Take the square root of the variance to
get the standard deviation
Standard deviation = s = s 2 =
n
å
(ri - r̂)2 Pri
i=1
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
15
Measuring Risk: The Standard Deviation
 Calculating Martin Products’ Standard
Deviation
Expected
Payoff
Deviation
Return
ri
ri - r
(r i - r)2 Probability (r i - r)2 Pri
r
(1)
(2)
(1) - (2) = (3)
=(4)
(5)
(4) x (5) =
110% 15%
=
95
9,025
0.2 9,025 x 0.2 =
22% 15%
=
7
49
0.5
49 x 0.5 =
-60% 15%
=
-75
5,625
0.3 5,625 x 0.3 =
(6)
1,805.0
24.5
1,687.5
Variance = s 2 = 3,517.0
Standard Deviation = s m = s 2m = 3,517 = 59.3%
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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16
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 s
Coefficient of variation = CV =
=
Return r̂
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
17
Risk Aversion
Risk-averse investors require higher
rates of return to invest in higher-risk
securities
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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18
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
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
19
Risk/Return Relationship
Return, r
rHigh
rAvg
Return = r = rRF + RP
Payment for Risk = Risk Premium = RP
rLow
rRF
Risk-Free Return, rRF = r* + Inflation Premium = r* + IP
0
Risk
Below-Average
Risk
Average
Risk
Above-Average
Risk
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
20
Portfolio Risk and the
Capital Asset Pricing Model
Portfolio
 A collection of investment securities
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 reflects diversification
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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21
Portfolio Returns
Expected return on a portfolio
r̂p
 The weighted average expected return on
the stocks held in the portfolio
r̂p = w1r̂1 + w 2 r̂2 + ...+ w N r̂N
N
= å w jr̂j
j=1
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
22
Portfolio Returns
Realized rate of return
rp
 The return that is actually earned
 Actual return is generally different from the
expected return
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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23
Portfolio Risk
Correlation coefficient
r
 A measure of the degree of relationship
between two variables
 Positively correlated stocks have rates of
return that move in the same direction
 Negatively correlated stocks have rates of
return that move in opposite directions
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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24
Portfolio Risk
Risk reduction
 Combining stocks that are not perfectly
positively 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
greater the reduction of risk from adding
another investment
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
25
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
 It can be eliminated through proper
diversification
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
26
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 most firms
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
27
Firm-Specific Risk versus Market Risk
Relevant risk
 The risk of a security that cannot be
diversified away--its market risk
 This reflects a security’s contribution to the
risk of a portfolio
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
28
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

Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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29
Portfolio Beta Coefficients
The beta of any set of securities is the
weighted average of the individual
securities’ betas
p  w11  w 22  ... w NN
N
  w j j
j1
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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30
The Relationship between Risk
and Rates of Return
r̂j =
rj =
rRF =
bj =
rM =
Expected rate of return on the jth stock
Required rate of return on the jth stock
Risk-free rate of return
Beta coefficient of the jth stock
Required rate of return on a portfolio
consisting of all stocks
RPM = rM -rRF = Market risk premium
th
RPj = rM -rRF b j = Risk premium on the j stock
(
(
)
)
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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31
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 = rM - rRF = 11% - 5% = 6%
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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32
Risk Premium for a Stock
Risk premium for stock j if  = 0.5
 RPM   j
 6%  0.5
 3.0%
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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33
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
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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34
The Required Rate of Return for Stock j
SML: rj  rRF  (RPM ) j
 rRF  (rM  rRF ) j
 5%  (11%  5%)(0.5)
 5%  6%(0.5)
 8%
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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35
Security Market Line
Required Rate
of Return (%)
SML: ri = rRF + (rM – rRF )βi
.
rH = 17
Relatively Risky
Stock’s Risk
Premium: 12%
rM = rA =
rLow = 8
Safe Stock
Risk
Premium: 3%
rRF = 5
Market (Average Stock)
Risk Premium: 6%
Risk-Free
Rate: 5%
0
0.5
Below-Average
Risk
1.0
Average
Risk
1.5
2.0
Risk,
j
Above-Average
Risk
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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36
The Impact of Inflation
rRF is the price of money to a riskless
borrower
The nominal rate consists of
 A real (inflation-free) rate of return, r*
 An inflation premium (IP)
An increase in expected inflation would
increase the risk-free rate, rRF
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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37
Shift in the SML Caused by
a 2% Increase in Inflation
Required Rate
of Return (%)
SML2: ri = 7% + 6%βi
SML1: ri = 5% + 6%βi
rM2 = 13
rM1 = 11
Increase in
Inflation = 2%
rRF2 = 7
rRF1 = 5
Original IP = 2%
Real Risk-Free
Rate: 3%
0
0.5
1.0
1.5
2.0
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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Risk,
j
38
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
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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39
Shift in the SML Caused by
Increased Risk Aversion
Required Rate
of Return (%)
21
SML2: ri2 = 5% + RPM2 βi
= 5% + (8%)βi
17
SML1: ri = rRF + RPM1βi
= 5% + (6%)βi
rM2 = 13
rM1 = 11
New Market Risk
Premium, rM2 – rRF = 8%
9
8
rRF = 5
Original Market Risk
Premium, rM1 – rRF = 6%
0
0.5
1.0
1.5
2.0
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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Risk,
j
40
Changes in a Stock’s Beta Coefficient
 The  risk of a stock is affected by




Composition of its assets
Use of debt financing
Increased competition
Expiration of patents, copyrights, etc.
 Any change in the required return (from
change in  or in expected inflation) affects the
stock price
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
41
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
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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42
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
r̂j = rj
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
43
Changes in Equilibrium Stock Prices
Stock prices are not constant due to
changes in:
 Risk-free rate, rRF
 Market risk premium, rM - rRF
 Stock X’s beta coefficient, X
 Stock X’s expected growth rate, gX
 Changes in expected dividends, D0(1+g)
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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44
Physical Assets versus Securities
Riskiness of a physical asset is only
relevant in terms of its effect on the
stock’s risk
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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45
Different Types of Risk
Systematic Risks
 Interest rate risk
 Inflation risk
 Maturity risk
 Liquidity risk
 Exchange rate risk
 Political risk
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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46
Different Types of Risk
Unsystematic Risks
Business risk
Financial risk
Default risk
Combined Risks
Total risk
Corporate risk
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
47
Chapter Principles
Key Risks and Rates of Return Concepts
 What does it mean to take risk when
investing?
 The chance of receiving a return other than the
one expected
 How are the risk and return of an investment
related?
 Riskier investments must have higher expected
returns than less risky investments; otherwise,
people will not purchase investments with higher
risks.
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
48
Chapter Principles
Key Risks and Rates of Return Concepts
 What are relevant and irrelevant risk?
 Relevant risk is nondiversifiable risk, because it cannot be
eliminated, even in a perfectly diversified portfolio.
 Irrelevant risk can be reduced through diversification.
 How is appropriate reward (risk premium)
determined?
 The effects of nondiversifiable risk can be determined by
computing the beta coefficient (β) of an investment.
 An investment’s required rate of return can be computed as:
ri = rRF + (rRF – rM)βi = rRF + (RPM)βi
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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49
Chapter Principles
Key Risks and Rates of Return Concepts
 What actions do investors take when the
return the require to purchase an investment
is different form the return the investment is
expected to produce?
 When an investment’s expected return is less than
investors’ required return, potential investors will
not purchase it and those who own the investment
will tend to sell it
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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50
Chapter Principles
Key Risks and Rates of Return Concepts
 What are different types of relevant and
irrelevant risks?
 Relevant risks include those types that are related
to economic factors, such as interest rate risk,
inflation risk, and so forth
 Risks that are not relevant because they can be
diversified away includes those types that are
related to a specific firm or industry, such as
business risk, default risk, and so forth.
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
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51
End of Chapter 11
Risks and Rates
of Return
Principles of Finance 5e, Ch. 11 Risks and Rates of Return © 2012 Cengage Learning. All Rights Reserved.
May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
52