Fundamentals of corporate finance 10e ROSS JORDAN chap013

Chapter
13

Return, Risk, and the Security
Market Line

13-1
McGraw-Hill/Irwin

Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved.


Chapter Outline
• Expected Returns and Variances
• Portfolios
• Announcements, Surprises, and Expected Returns
• Risk: Systematic and Unsystematic
• Diversification and Portfolio Risk
• Systematic Risk and Beta
• The Security Market Line
• The SML and the Cost of Capital: A Preview

13-2


Chapter Outline
• Expected Returns and Variances
• Portfolios
• Announcements, Surprises, and Expected Returns
• Risk: Systematic and Unsystematic
• Diversification and Portfolio Risk

• Systematic Risk and Beta
• The Security Market Line
• The SML and the Cost of Capital: A Preview

13-3


Expected Returns
• Expected returns are based on the probabilities
of possible outcomes
• In this context, “expected” means average if
the process is repeated many times
• The “expected” return does not even have to be
a possible return
n

E ( R ) = ∑ pi Ri
i =1

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Example: Expected
Returns
Suppose you have predicted the following returns
for stocks C and T in three possible states of the
economy.
1. What is the probability of “Recession”?

State Probability C T

Boom
0.3
15 25
Normal 0.5
10 20
Recession ???
2 1
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Probabilities add up to 100% (or 1.0) thus 1.0 – 0.3
– 0.5 =0.2 or 20%


Example: Expected
Returns
Suppose you have predicted the following returns
for stocks C and T in three possible states of the
economy.
2. What are the expected returns?

State Probability C T
Boom
0.3
15 25
Normal 0.5
10 20
Recession 0.2
2 1
RC =.3(15) +.5(10) +.2(2) =9.9%
RT =.3(25) +.5(20) +.2(1) =17.7%

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Example: Expected
Returns
The three states of the economy still apply to
stocks C and T.
3. If the risk-free rate (from chapter 12) is 4.15%,
what is the risk premium for C & T?
RC =.3(15) +.5(10) +.2(2) =9.9%
RT =.3(25) +.5(20) +.2(1) =17.7%
Stock C’s risk premium: 9.9 - 4.15 =5.75%
Stock T’s risk premium: 17.7 - 4.15 =13.55%
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Variance and Standard
Deviation
• Variance and standard deviation
measure the volatility of returns
• Using unequal probabilities for the
entire range of possible outcomes
• Weighted average of squared deviations
n

σ = ∑ pi ( Ri − E ( R))
2

13-8

i =1

2


Example: Variance and
Standard Deviation
Considering the previous example of
stocks C and T:

State Probability C T
Boom
0.3
15 25
Normal 0.5
10 20
Recession 0.2
2 1
Expected return
9.9%
13-9

17.7%


Example: Variance and
Standard Deviation
1. What is the variance and standard
deviation for C?

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State Probability C T
Boom
0.3
15 25
Normal 0.5
10 20
Recession 0.2
2 1
Expected return
9.9% 17.7%
Stock C
σ2 = .3(15-9.9)2 + .5(10-9.9)2 + .2(2-9.9)2
= 20.29
σ = 4.50%


Example: Variance and
Standard Deviation
2. What is the variance and standard
deviation for T?

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State Probability C T
Boom
0.3
15 25
Normal 0.5

10 20
Recession 0.2
2 1
Expected return
9.9% 17.7%
Stock T
σ2 = .3(25-17.7)2 + .5(20-17.7)2 + .
2(1-17.7)2 = 74.41
σ = 8.63%


Another Example
Consider the following information:
State
Probability ABC, Inc. (%)
Boom .25
15
Normal
.50
8
Slowdown
.15
4
Recession
.10
-3

1. What is the expected return?
E(R) = .25(15) + .5(8) + .15(4) + .1(-3)
= 8.05%

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Another Example
Consider the following information:
State
Probability ABC, Inc. (%)
Boom .25
15
Normal
.50
8
Slowdown
.15
4
Recession
.10
-3

2. What is the variance?

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Variance = σ2= .25(15-8.05)2 + .5(8-8.05)2 + .
15(4-8.05)2 + .1(-3-8.05)2
= 26.7475


Another Example
Consider the following information:

State
Probability ABC, Inc. (%)
Boom .25
15
Normal
.50
8
Slowdown
.15
4
Recession
.10
-3

3. What is the standard deviation?
Standard Deviation = σ = √ 26.7475
= 5.17%
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Chapter Outline
• Expected Returns and Variances
• Portfolios
• Announcements, Surprises, and Expected Returns
• Risk: Systematic and Unsystematic
• Diversification and Portfolio Risk
• Systematic Risk and Beta
• The Security Market Line
• The SML and the Cost of Capital: A Preview

13-15


Portfolios
• A portfolio is a
collection of assets
• An asset’s risk and
return are important in
how they affect the risk
and return of the
portfolio
13-16


Portfolios
•The risk/return tradeoff for a portfolio is
measured by the
portfolio’s expected
return and standard
deviation, just as with Risk
individual assets

13-17

Return


Example: Portfolio
Weights
Suppose you have $15,000 to

invest and you have purchased
securities in the following
amounts:
$2000 of DCLK
$3000 of KO
$4000 of INTC
$6000 of KEI

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Example: Portfolio
Weights
What are your portfolio weights in
each security?
$2,000 of DCLK
$3,000 of KO
$4,000 of INTC
$6,000 of KEI
$15,000

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DCLK: 2/15 = .133
KO: 3/15 = .200
INTC: 4/15 = .267
KEI: 6/15 = .400
15/15 = 1.000

Portfolio Expected
Returns
The expected return of a portfolio is the weighted
average of the expected returns of the respective
assets in the portfolio
m

E ( RP ) = ∑ w j E ( R j )
j =1

You can also find the expected return by finding
the portfolio return in each possible state and
computing the expected value as we did with
individual securities
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Example: Expected
Portfolio Returns
Consider the portfolio weights computed
previously. The individual stocks have the
following expected returns:

DCLK: 19.69%
KO: 5.25%
INTC: 16.65%
KEI: 18.24%
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Example: Expected
Portfolio Returns
1. What is the expected return on this
portfolio?

Return Weight
DCLK: 19.69% .133
KO: 5.25% .200
INTC: 16.65% .267
KEI: 18.24% .400
E(RP) = .133(19.69) + .2(5.25) + .267(16.65) + .4(18.24)
= 15.41%
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Portfolio Variance
•Compute the expected portfolio return, the
variance, and the standard deviation using the
same formula as for an individual asset
•Compute the portfolio return for each state:
RP = w1R1 + w2R2 + … + wmRm

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Example: Portfolio
Variance
Consider the following information:
State Probability A B
Boom .4

30% -5%
Bust .6
-10% 25%

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Example: Portfolio
Variance
Consider the following information:
State Probability A B
Boom .4
30% -5%
Bust .6
-10% 25%

1. What is the expected return for
asset A?
Asset A: E(RA) = .4(30) + .6(-10) = 6%

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