Chapter 12
Return, Risk, and the Security
Market Line
12-1
Announcements and News
• Firms make periodic announcements about
events that may significantly impact the profits
of the firm.
• Earnings
• Product development
• Personnel
• The impact of an announcement depends on
how much of the announcement represents
new information.
12-2
Announcements & Surprises
Total return–Expected return = Unexpected return
R
–
E(R)
=
U
Announcement = Expected + Surprise
12-3
Announcements & Surprises
A company announces earnings $1.00 per
share higher than the previous quarter.
Price
Doesn't move
Goes up
Goes down
Indication
No surprise
Market expected lower earnings
Market expected higher earnings
12-4
Systematic & Unsystematic
Components of Return
(12.3)
(12.4)
(12.5)
R – E(R)=Systematic +Unsystematic
R – E(R) = U = m+ε
where m = market risk
ε = unsystematic risk
Total risk=Systematic risk + Unsystematic risk
12-5
Systematic & Unsystematic
Components of Return
(12.5) Total risk = Systematic risk + Unsystematic risk
= Market risk
+ firm-specific risk
If the latest Consumer Price
Index numbers indicate
that inflation has risen
substantially. Will this
impact systematic or
unsystematic risk?
If a company announces
that it will have to restate
its financials for the last 3
years, which risk
component will be
affected?
12-6
Diversification and Risk
• In a large portfolio:
• Some stocks will go up in value because of positive
company-specific events, while
• Others will go down in value because of negative companyspecific events.
• Unsystematic risk is essentially eliminated by
diversification, so a portfolio with many assets has
almost no unsystematic risk.
• Unsystematic risk = diversifiable risk.
• Systematic risk = non-diversifiable risk.
12-7
Systematic Risk
“Unsystematic risk is essentially
eliminated by diversification, so a
portfolio with many assets has
almost no unsystematic risk.”
“The systematic risk principle states
that the reward for bearing risk
depends only on the systematic
risk of an investment.”
“The expected return on an asset
depends only on its systematic
risk.”
12-8
The Systematic Risk Principle
• The systematic risk principle states:
The expected return on an asset depends
only on its systematic risk.
• No matter how much total risk an asset has,
only the systematic portion is relevant in
determining the expected return (and the risk
premium) on that asset.
12-9
Measuring Systematic Risk
• The Beta coefficient (  ) measures the relative
systematic risk of an asset.
• Beta > 1.0  more systematic risk than average.
• Beta < 1.0  less systematic risk than average.
• Assets with larger betas = greater systematic risk
= greater expected returns.
Note that not all Betas are created equally.
12-10
Risk & Beta
Asset 1
Asset 2
Std Dev
25%
45%
Beta
1.30
0.80
• Asset 2 has more total risk because it
has the greater standard deviation.
• Asset 1 has more systematic risk
because it has the larger Beta.
• Asset 1 should have the higher expected
return since it has the larger beta.
12-11
Portfolio Beta
n
P   xi i
i 1
Xi = % of portfolio invested in asset i
βi = Beta of asset i
Asset 1
Asset 2
Wgt
40%
60%
Beta
1.30
0.80
Wgt*B
0.52
0.48
1.00
12-12
Portfolio Beta
Security
Stock W
Stock X
Stock Y
Stock Z
$ Invested
$1,000
$2,500
$3,500
$1,000
E(R)
7.5%
9.0%
12.0%
10.5%
Beta
0.85
0.95
1.20
1.10
What is this portfolio’s expected return and Beta?
12-13
Portfolio Return & Beta Example
Step 1: Calculate each stock’s % or
weight in the portfolio
Security
Stock W
Stock X
Stock Y
Stock Z
$ Invested
$1,000
$2,500
$3,500
$1,000
$8,000
% (wgt)
12.50%
31.25%
43.75%
12.50%
100.00%
12-14
Portfolio Return & Beta
Step 2: Apply the weights to each stock’s
expected return to arrive at the portfolio’s
expected return.
Security
Stock W
Stock X
Stock Y
Stock Z
% (wgt)
12.50%
31.25%
43.75%
12.50%
E(R)
7.5%
9.0%
12.0%
10.5%
0.9%
2.8%
5.3%
1.3%
10.3%
12-15
Portfolio Return & Beta
Step 3: Apply the weights to each stock’s
beta to arrive at the portfolio’s beta.
Security
Stock W
Stock X
Stock Y
Stock Z
% (wgt)
12.50%
31.25%
43.75%
12.50%
Beta
0.85
0.95
1.20
1.10
0.106
0.297
0.525
0.138
1.066
12-16
Beta and the Risk Premium, I.
• Consider a portfolio made up of asset A and a
risk-free asset.
• For asset A: E(RA) = 16% and A = 1.6
• The risk-free rate Rf = 4%. Note that for a risk-free
asset,  = 0 by definition.
• Varying the % invested in each asset will
change the possible portfolio expected
returns and betas.
• Note: if the investor borrows at the risk-free rate and
invests the proceeds in asset A, the investment
in asset A will exceed 100%.
12-17
Beta and the Risk Premium
% in A
0%
25%
50%
75%
100%
125%
150%
% in Rf
100%
75%
50%
25%
0%
-25%
-50%
Portfolio
E( R )
Beta
4.0%
0.0
7.0%
0.4
10.0%
0.8
13.0%
1.2
16.0%
1.6
19.0%
2.0
22.0%
2.4
12-18
12-18
Portfolio Expected Returns
and Betas for Asset A
12-19
Beta and the Risk Premium
% in B
0%
25%
50%
75%
100%
125%
150%
% in Rf
100%
75%
50%
25%
0%
-25%
-50%
Portfolio
E( R )
Beta
4.0%
0.0
6.0%
0.3
8.0%
0.6
10.0%
0.9
12.0%
1.2
14.0%
1.5
16.0%
1.8
12-20
12-20
Portfolio Expected Returns
and Betas for Asset B
12-21
Portfolio Expected Returns
and Betas for Assets A & B
Portfolio Return & Beta
Portfolio E(R)
25.0%
E (RA )  Rf
20.0%
A
 7.5%
15.0%
10.0%
E (RB )  Rf
5.0%
B
 6.67%
0.0%
0.0
0.3
0.6
0.9
1.2
1.5
1.8
Portfolio Beta
12-22
The Fundamental Relationship
between Risk and Return
Reward-to-Risk (A) = 7.50%
Reward-to-Risk (B) = 6.67%
(12.6)
E (RA )  Rf
A

E (RB )  Rf
B
“The reward-to-risk ratio must be the same
for all assets in a competitive market.”
12-23
The Fundamental Result
• The situation we have described for assets A and B
cannot persist in a well-organized, active market
• Investors will be attracted to asset A (and buy A shares)
• Investors will shy away from asset B (and sell B shares)
• This buying and selling will make
• The price of A shares increase
• The price of B shares decrease
• This price adjustment continues until the two assets
plot on exactly the same line.
• That is, until:
ER A   R f ER B   R f

βA
βB
12-24
The Fundamental Result
12-25
Over- and Under-Valued
Security
Stock W
Stock X
Stock Y
Stock Z
E(R)
7.5%
9.0%
12.0%
10.5%
Beta
0.85
0.95
1.20
1.10
If the Risk-free rate is 5%, are these stocks
fairly valued?
12-26
Over- and Under-Valued
Security
Stock W
Stock X
Stock Y
Stock Z
E(R)
7.5%
9.0%
12.0%
10.5%
Beta
0.85
0.95
1.20
1.10
Ratio
2.94%
4.21%
5.83%
5.00%
Stocks W and X offer insufficient returns
for their level of risk compared to
stocks Y and Z.
Stock Y offers the highest return for its
level of risk.
12-27
The Security Market Line (SML)
• The Security market line (SML) = a
graphical representation of the linear
relationship between systematic risk and
expected return in financial markets.
• For a market portfolio,
ER M   R f ER M   R f


βM
1
 ER M   R f
12-28
The Security Market Line
• The term E(RM) – Rf = market risk premium
because it is the risk premium on a market
portfolio. E R   R
i
f
 E RM   Rf
βi
• For any asset i in the market:
 ER i   R f  ER M   R f  βi
• Setting the reward-to-risk ratio for all assets equal to
the market risk premium results in an equation known
as the capital asset pricing model.
12-29
The Security Market Line
• The Capital Asset Pricing Model (CAPM) is
a theory of risk and return for securities in a
competitive capital market.
E Ri   Rf  E RM   Rf  βi
(12.7)
• The CAPM shows that E(Ri) depends on:
• Rf, the pure time value of money.
• E(RM) – Rf, the reward for bearing systematic risk.
• i, the amount of systematic risk.
12-30
The Security Market Line
(12.7)
E( Ri )  Rf  E( RM )  Rf  i
Market Risk Premium
Pure time value of money
Reward for bearing systematic risk
Amount of systematic risk
12-31
The Security Market Line
12-32
Over- and Under-Valued
E ( Ri )  Rf  E ( RM )  Rf   i
Rf  5%
E ( RM )  10%
E ( Ri )  5%  ( 5%)   i
Security
Stock W
Stock X
Stock Y
Stock Z
E(R)
Beta
7.5%
9.0%
12.0%
10.5%
0.85
0.95
1.20
1.10
CAPM
Return
9.25%
9.75%
11.00%
10.50%
Value
Over
Over
Under
Fair
12-33
The Security Market Line
Security Market Line
14.00%
Y
12.00%
10.00%
Z
E(R)
8.00%
X
W
6.00%
RF = 5%
4.00%
2.00%
0.00%
Beta
12-34
Risk and Return Summary, I.
12-35
Risk and Return Summary, II.
12-36
More on Beta
(12.8 and 12.4)
R - E(R)= m + ε
(12.9)
m = [RM –E(RM)] x β
Systematic portion of the unexpected
return on the market M
(12.10)
R-E(R)= [RM –E(RM)] x β + ε
12-37
Decomposition of Total Return
• Suppose the expected return on the market is
10% and the risk-free rate is 5%.
• Asset A has a beta of 0.80.
• The expected return on Asset A is 9%.
• One year the return on the market is actually
8% and the return on Asset A in the same
year is 6.5%. Decompose these returns.
12-38
Decomposition of Total Return
• E(RM) = 10%
• RF = 5%
• E(RA) = 9%
•
•
•
•
Actual RM = 8%
βA = 0.80
Actual RA =6.5%
UNE(RM)= [RM-E(RM)] = 8% - 10% = -2%
UNE(RA) = [RA-E(RA)] = 6.5% - 9% = -2.5%
Systematic UNE = [RM-E(RM)] x β = -2% x .80 = -1.6%
Unsystematic portion = [RA-E(RA)] - [RM-E(RM)] x β
= (-2.5%) – (-1.6%) = -0.90%
12-39
Decomposition of Total Returns
12-40
Unexpected Returns and Beta
12-41
Where Do Betas Come From?
• A security’s Beta depends on:
• How closely correlated the security’s return is with
the overall market’s return, and
• How volatile the security is relative to the market.
• A security’s Beta is equal to the correlation
multiplied by the ratio of the standard
deviations.
σi
β i  CorrR i ,R M  
σm
12-42
Where Do Betas Come From?
12-43
Using a Spreadsheet to Calculate Beta
12-44
Calculating Beta
(12.11)
Year
2004
2005
2006
2007
2008
Totals
Asset H
Market
Covariance =
Correlation=
Beta =
 i  Corr(Ri , RM )   i  M
 im

i
im

 M   M2
Returns
Asset H
Market
(1)
(2)
15.00%
10.00%
11.50%
8.00%
-4.00%
-1.00%
12.50%
7.00%
-2.00%
0.00%
33.00%
24.00%
Average Returns
33% / 5 =
6.60%
24% / 5 =
4.80%
.01751 / 4 =
0044/(.088 x .0497) =
.9914 x (.0888/.0497) =
Return Deviations
Asset H
Market
(3)
(4)
8.40%
5.20%
4.90%
3.20%
-10.60%
-5.80%
5.90%
2.20%
-8.60%
-4.80%
0.00%
0.00%
Variances
.031570 / 4 =
0.007893
.009880 / 4 =
0.002470
0.0044
0.9914
1.77
Squared Deviations
Asset H
Market
(5)
(6)
0.007056
0.002704
0.002401
0.001024
0.011236
0.003364
0.003481
0.000484
0.007396
0.002304
0.031570
0.009880
Standard Deviations
√.007893 =
√.002470 =
Product of
Deviations
(7)
0.0043680
0.0015680
0.0061480
0.0012980
0.0041280
0.0175100
8.88%
4.97%
Beta =
.0044/.00247=1.77
12-45
Calculating Beta
Step 1: Compute average returns for Asset H and the
Market
Year
2004
2005
2006
2007
2008
Totals
Asset H
Market
Returns
Asset H
Market
(1)
(2)
15.00%
10.00%
11.50%
8.00%
-4.00%
-1.00%
12.50%
7.00%
-2.00%
0.00%
33.00%
24.00%
Average Returns
33% / 5 =
6.60%
24% / 5 =
4.80%
12-46
Calculating Beta
Step 2: Compute variance and standard deviations for
Asset H and the Market
Year
2004
2005
2006
2007
2008
Totals
Asset H
Market
Returns
Asset H
Market
(1)
(2)
15.00%
10.00%
11.50%
8.00%
-4.00%
-1.00%
12.50%
7.00%
-2.00%
0.00%
33.00%
24.00%
Average Returns
33% / 5 =
6.60%
24% / 5 =
4.80%
Return Deviations
Asset H
Market
(3)
(4)
8.40%
5.20%
4.90%
3.20%
-10.60%
-5.80%
5.90%
2.20%
-8.60%
-4.80%
0.00%
0.00%
Variances
.031570 / 4 =
0.007893
.009880 / 4 =
0.002470
Squared Deviations
Asset H
Market
(5)
(6)
0.007056
0.002704
0.002401
0.001024
0.011236
0.003364
0.003481
0.000484
0.007396
0.002304
0.031570
0.009880
Standard Deviations
√.007893 =
√.002470 =
8.88%
4.97%
12-47
Calculating Beta
Step 3: Compute the covariance between the Market and
Asset H.
Year
2004
2005
2006
2007
2008
Totals
Asset H
Market
Covariance =
Returns
Asset H
Market
(1)
(2)
15.00%
10.00%
11.50%
8.00%
-4.00%
-1.00%
12.50%
7.00%
-2.00%
0.00%
33.00%
24.00%
Average Returns
33% / 5 =
6.60%
24% / 5 =
4.80%
.01751 / 4 =
Return Deviations
Asset H
Market
(3)
(4)
8.40%
5.20%
4.90%
3.20%
-10.60%
-5.80%
5.90%
2.20%
-8.60%
-4.80%
0.00%
0.00%
Product of
Deviations
(7)
0.0043680
0.0015680
0.0061480
0.0012980
0.0041280
0.0175100
Variances
.031570 / 4 =
0.007893
.009880 / 4 =
0.002470
0.0044
12-48
Calculating Beta
Step 4: Compute the correlation coefficient and the Beta for
Asset H.
Average Returns
33% / 5 =
6.60%
24% / 5 =
4.80%
Asset H
Market
Covariance =
Correlation=
Beta =
(12.11)
Variances
.031570 / 4 =
0.007893
.009880 / 4 =
0.002470
.01751 / 4 =
0044/(.088 x .0497) =
.9914 x (.0888/.0497) =
0.0044
0.9914
1.77
 i  Corr( Ri , RM )   i  M
12-49
Why Do Betas Differ?
• Betas are estimated from actual data.
Different sources estimate differently,
possibly using different data.
• For data, the most common choices are three to
five years of monthly data, or a single year of
weekly data.
• The S&P 500 index is commonly used as a proxy
for the market portfolio.
• Calculated betas may be adjusted for various
statistical and fundamental reasons.
12-50
Beta - β
Beta (β) measures a specific asset’s market
risk relative to an average asset.
Company
Exxon Mobil
General Motors
IBM
Microsoft
Wal-Mart
Value
Line
0.90
1.45
1.10
1.00
0.80
S&P
0.75
1.21
1.62
0.94
0.54
Market Beta = 1.00
Risk-free asset beta = 0.00
12-51
Finding a Beta on the Web
12-52
Company
Beta and Return
General Motors
Wal-Mart
Market
GM
WMT
M
Value
Line
1.21
0.80
1.00
25%
20%
15%
10%
5%
0%
1
GM
2
3
WMT
4
5
MARKET
12-53
Extending CAPM
• The CAPM has a stunning implication:
• What you earn on your portfolio depends only on
the level of systematic risk that you bear
• As a diversified investor, you do not need to worry
about total risk, only systematic risk.
• But, does expected return depend only on
Beta? Or, do other factors come into play?
• The above bullet point is a hotly debated
question.
12-54
Important General Risk-Return
Principles
• Investing has two dimensions: risk and return.
• It is inappropriate to look at the total risk of an
individual security.
• It is appropriate to look at how an individual
security contributes to the risk of the overall
portfolio
• Risk can be decomposed into nonsystematic
and systematic risk.
• Investors will be compensated only for
systematic risk.
12-55
The Fama-French Three-Factor Model
• FF propose two additional factors as useful in
explaining the relationship between risk and
return.
• Size, as measured by market capitalization
• The book value to market value ratio
• Whether these two additional factors are truly
sources of systematic risk is still being
debated.
12-56
Returns from 25 Portfolios Formed
on Size and Book-to-Market
• Note that the portfolio containing the smallest
cap and the highest book-to-market have had
the highest returns.
12-57
Useful Internet Sites
•
earnings.nasdaq.com (to see recent earnings surprises)
•
www.portfolioscience.com (helps you analyze risk)
•
money.cnn.com (a source for betas)
•
finance.yahoo.com (a terrific source of financial information)
•
www.smartmoney.com (another fine source of financial
information)
•
www.moneychimp.com (for a CAPM calculator)
•
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/
(source for data behind the FAMA-French model)
12-58