Lecture Essentials of corporate finance (2/e) – Chapter 11: Risk and return

Risk and return
Chapter 11


Key concepts and skills
• Know how to calculate expected
returns
• Understand the impact of diversification
• Understand the systematic risk
principle
• Understand the security market line
• Understand the risk–return trade-off
Copyright ©2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

11-2


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 (SML)
• The SML and the cost of capital: A
preview
Copyright ©2011 McGraw-Hill Australia Pty Ltd

PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

11-3


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.

E ( R)

n

pi Ri

i 1

• Where:
–

pi = the probability of state ‘I’ occurring

–

Ri = the expected return on an asset in state i

Copyright ©2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

11-4


Expected returns—Example
• Suppose you have predicted the following
returns for shares A and B in three possible
states of nature. What are the expected
returns?
E(R)
State (i)
Recession
Neutral
Boom
E(R)

Stock A
E(Ra)
-20%
15%
35%
25%

p(i)
0.25
0.50

0.25
1.00

Stock B
E(Rb)
30%
15%
-10%
20%

n

E( R )

pi Ri
i

1

Copyright ©2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

11-5


Expected returns—
Example (cont.)
E(R)
State (i)

Recession
Neutral
Boom
E(R)

p(i)
0.25
0.50
0.25
1.00

Stock A
E(Ra) p(i) x E(Ra)
-20%
-5.0%
15%
7.5%
35%
8.8%
11.3%

Copyright ©2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

Stock B
E(Rb) p(i) x E(Rb)
30%
7.5%
15%

7.5%
-10%
-2.5%
12.5%

11-6


Variance and standard
deviation
• Variance and standard deviation still
measure the volatility of returns.
• Using unequal probabilities for the entire
range of possibilities.
• Weighted average of squared deviations.
• Standard deviation = square root of
variance.
σ2

n

pi ( Ri E ( R)) 2

i 1

Copyright ©2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

11-7

Variance and standard
deviation (cont.)
State (i)
Recession
Neutral
Boom

p(i)
0.25
0.50
0.25
1.00
Expected Return
Variance
Standard Deviation

State (i)
Recession
Neutral
Boom

p(i)
0.25
0.50
0.25
1.00
Expected Return
Variance

Standard Deviation

E(R)
-20%
15%
35%

Stock A
DEV^2
10%
0%
6%

x p(i)
0.0244141
0.0007031
0.0141016

11.3%
0.0392188
19.8%

E(R)
30%
15%
-10%

Stock B
DEV^2
3%

0%
5%

x p(i)
0.0076563
0.0003125
0.0126563

12.5%

Copyright ©2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

0.0206
14.4%

11-8


Variance and standard
deviation—Another example
• Consider the following information:
State
– Boom
– Normal
– Slow down
– Recession

Probability

.25
.50
.15
.10

KBC Ltd
.15
.08
.04
-.03

• What is the expected return?
• What is the variance?
• What is the standard deviation?
Copyright ©2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

11-9


Variance and standard
deviation—Another example:
Solution
KBC Ltd

State (i)
p(i)
Boom
0.25

Normal
0.50
Slowdown
0.15
Recession
0.1
E(R)
1.00
Expected Return
Variance
Standard Deviation

E(Ra) p(i) x E(Ra)
15%
3.8%
8%
4.0%
4%
0.6%
-3%
-0.3%
8.050%
8.05%

Copyright ©2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

DEV^2
0.483%

0.000%
0.164%
1.221%

p(i)xDEV^2
0.001207563
0.000000125
0.000246038
0.001221025
0.00267475
0.00267475
0.051717985

11-10


Portfolios
• A portfolio is a collection of assets.
• An asset’s risk and return is important
in how it affects the risk and return of
the portfolio.
• The risk–return trade-off for a portfolio
is measured by the portfolio expected
return and standard deviation, just as
with individual assets.
Copyright ©2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

11-11

Portfolio expected returns
• The expected return of a portfolio is the weighted
average of the expected returns for each asset in the
portfolio.
• Weights (wj) = percentage of portfolio invested in
each asset.
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.
Copyright ©2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

11-12


Portfolio weights: Example
• Suppose you have $15 000 to invest
and you have purchased securities in

the following amounts. What are your
portfolio weights in each security?
Portfolio Weights
Dollars
Asset
Invested
Double Click
$2,000
Coca Cola
$3,000
Intel
$4,000
Keithley Industries
$6,000
$15,000

Copyright ©2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

% of Pf
w(j)
13.3%
20.0%
26.7%
40.0%
100.0%

11-13

Expected portfolio returns:
Example
• Consider the portfolio weights computed
previously. If the individual shares have the
following expected returns, what is the
expected return for the portfolio?
Portfolio Weights
Dollars
Asset
Invested
Double Click
$2,000
Coca Cola
$3,000
Intel
$4,000
Keithley Industries
$6,000
$15,000

% of Pf
w(j)
13.3%
20.0%
26.7%
40.0%
100.0%

Copyright ©2011 McGraw-Hill Australia Pty Ltd

PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

E( Rj )
19.650%
8.960%
9.670%
8.130%

w(j) x
E( Rj )
2.62%
1.79%
2.58%
3.25%
10.24%

11-14


Expected portfolio return
Alternative method
A
1
2
3
4
5
6
7

State (i)
Recession
Neutral
Boom
E(R)

B

C
Stock V
w(j)
30%
p(i)
0.25
-20.0%
0.50
17.5%
0.25
35.0%
1.00
12.5%

D
Stock W
17%
18.0%
15.0%
-10.0%
9.5%

E
F
Stock X Stock Y
22%
20%
Expected Return
5.0%
-8.0%
10.0%
11.0%
15.0%
16.0%
10.0%
7.5%

G
Stock Z
12%

H
Portfolio
100%

4.0%
9.0%
12.0%
8.5%

-3%

13%
17%
10%

Steps:
1. Calculate expected portfolio return in each
state:
2. Apply the probabilities of each state to the
expected return of the portfolio in that
state.

5

E ( R P ,i )

w j E( R j )
j 1

3

E ( RP )

p i E ( R P ,i )
i 1

3. Sum the result of step 2.
Copyright ©2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

11-15


Portfolio risk
Variance and standard
deviation

• Portfolio standard deviation is NOT
a weighted average of the standard
deviation of the component
securities’ risk.
– If it were, there would be no benefit
to diversification.

Copyright ©2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

11-16


Portfolio variance
ompute portfolio return for each state:
RP,i = w1R1,i + w2R2,i + … + wmRm,i
ompute the overall expected portfolio
return using the same formula as for
an individual asset.
ompute the portfolio variance and
standard deviation using the same

Copyright ©2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

11-17


Portfolio risk
Portfolio
State (i)
Recession
Neutral
Boom
E(R)

p(i)
0.25
0.50
0.25
1.00

E( R )
-3%
13%
17%
10%

Dev

Dev^2

x p(i)

-13%
3%
7%

0.01663
0.00101
0.00428
VAR(Pf)
Std(Pf)

0.00416
0.00050
0.00107
0.00573259
7.6%

1. Calculate expected portfolio return in each state of the economy and
overall.
2. Compute deviation (DEV) of expected portfolio return in each state
from total expected portfolio return.
3. Square deviations (DEV^2) found in step 2.
4. Multiply squared deviations from step 3 times the probability of each
state occurring (x p(i)).
5. The sum of the results from step 4 = portfolio variance.
Copyright ©2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

11-18


Expected vs unexpected
returns
• Realised returns are generally not
equal to expected returns.
• There is the expected component and
the unexpected component.
– At any point in time, the unexpected return
can be either positive or negative.
– Over time, the average of the unexpected
component is zero.
Copyright ©2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

11-19


Announcements and news
• Announcements and news contain both
an expected component and a surprise
component.
• It is the surprise component that affects
a share’s price and therefore its return.
• This is very obvious when we watch
how share prices move when an
unexpected announcement is made or

earnings differ from what is anticipated.
Copyright ©2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

11-20


Efficient markets
• Efficient markets are a result of
investors trading on the unexpected
portion of announcements.
• The easier it is to trade on surprises,
the more efficient markets should be.
• Efficient markets involve random price
changes because we cannot predict
surprises.
Copyright ©2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

11-21


Systematic risk
• Factors that affect a large number of
assets.
• ‘Non-diversifiable risk’.
• ‘Market risk’.
• Examples: changes in GDP, inflation

and interest rates.

Copyright ©2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

11-22


Unsystematic risk
• = diversifiable risk
• Risk factors that affect a limited number
of assets.
• Risk that can be eliminated by
combining assets into portfolios.
• ‘Unique risk’.
• ‘Asset-specific risk’.
• Examples: labour strikes, part
shortages.
Copyright ©2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

11-23


Returns
• Total return = Expected return +
Unexpected return
R = E(R) + U

• Unexpected return (U) = Systematic
portion (m) + Unsystematic portion (ε)
• Total return = Expected return E(R)
+ Systematic portion
m
+ Unsystematic portion ε
= E(R) + m + ε
Copyright ©2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

11-24


Diversification
• Portfolio diversification is investment in
several different asset classes or
sectors.
• Diversification is not just holding a lot of
assets.
• For example, if you own 50 internet
company shares, you are not
diversified.
• However, if you own 50 shares that
11-25
span 20 different industries, you are
Copyright ©2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh