FINANCE 384: Corporate Valuation, Investment
Decisions and Risk Management
STUDENT LECTURE NOTE 1 Sp14CR
I. Systematic Risk, Beta and the Capital Asset Pricing
Model
A. Systematic and Unsystematic Risk
1. Types of Information and Its Relevancy
(Consider the headlines of some stories from the
WSJ Online edition of November 2, 2013)
 “GOP Gives Health Law Stumbling Room”
 “What's Next for Gold? The Precious Metal has
Lost its Luster as Stocks Have Regained Center
Stage”
 “Amazon Mines Its Data Trove to Bet on TV's
Next Hit”
 “Pakistani Taliban Picks New Leader to
Succeed Hakimullah Mehsud, Killed Friday in
U.S. Drone Strike, Roiling Washington’s
Relations with Islamabad”
 “Currency Probe Widens as Major Banks
Suspend Traders Over Investigation of Chatroom Transcripts”
Which headlines are most likely to affect ___
firms in the U.S. market? Which are ________ to
just one firm or perhaps a certain industry?
2. Total (Stand-Alone) Risk = Systematic Risk +
Unsystematic Risk.
1
3. Systematic Risk: Risk from factors that affect ___
marketable assets because they are traded in
financial markets. Also called market risk,
common risk or undiversifiable risk.
4. Unsystematic Risk: Risk that affects only an
individual firm. It is typically due to the firm’s
__________ (business risk) or how it is ________
capital structure/financial risk). To a certain extent
it will also be affected by industry risk and
possibly international risk. It is also called nonmarket risk, specific risk or diversifiable risk.
Can Total Risk be eliminated?  Of course not,
the only risk that can be eliminated is __________
(unsystematic) risk (through diversification).
B. The Principle of Diversification
1. Spreading your investment portfolio over many
different investments, different types of assets,
and/or across different markets is the practice of
investment diversification.
2. How it works: As more and more assets are added
to a portfolio, the ____________ risk of each
individual asset becomes a smaller (and smaller)
component of the portfolio’s overall risk.
3. In fact, the individual risks of some assets will
actually tend to offset those of other assets as the
number of securities grows. (cf. The currency risk
of an importer may be offset by adding an
exporter’s stock to the portfolio. The elastic
demand curve of an automaker could be offset by
the inelastic demand for an electricity producer.)
2
4. Although the non-market (diversifiable) risk may
be reduced through diversification, the ______
risk of each asset will still be a relevant
consideration. Thus, the market risk is
UNDIVERSIFIABLE. While DIVERSIFIABLE
RISK is reduced towards zero through the
addition of additional assets.
p(%)
Diversifiable Risk
Stand-Alone Risk (p)
Market Risk
10
20
30
40
# Stocks in Portfolio
2,000+
5. Given this line of reasoning, in determining
portfolio risk, the only relevant risk to be
considered when adding a particular asset to a
portfolio, is how much ______ (undiversifiable)
risk it adds?
6. This (the previous question) leads to the next
major issue. How much extra ______ do we
require from adding a certain asset, (or
equivalently how large is the risk premium for this
asset) due to the amount of market risk it would
add to a well-diversified portfolio?
3
7. The Capital Asset Pricing Model was developed to
answer that question.
C. The Capital Asset Pricing Model
1. Model: Determines the ________ return on an
asset in relation to the systematic risk which that
asset contributes to the risk of the total portfolio of
marketable securities.
2. This individual asset’s contribution to portfolio
market risk is the ________ risk in the model
because investors are assumed to have diversified
all non-market risk away through portfolio
diversification.
3. Under the Efficient Market Hypothesis, since
markets are (assumed to be) efficient this Required
rate of return (CAPM-ROR) is also the average
investor’s Expected Return.
D. Intuitive Formulation of the CAPM
1. Required Return on any security (CAPM ROR) is
found as follows:
CAPM ROR = Rf + Risk Premium;
(1.1)
where:
Risk Premium = (Beta * Market Risk Premium.)
2. Risk-free Rate is simply the minimum return
required on a risk-free (default-free) security, i.e.
T-Bill rate.
3. Market Risk Premium = Rm – Rf; the added
required return which the Market Portfolio must
earn because it is riskier than the riskless asset
4
(i.e., any non-riskless asset it has added default
risk).
4. It turns out that the risk of an individual security
may be reflected by multiplying the Market Risk
Premium by the "Beta Coefficient".
E. Beta (Term "Beta Coefficient" comes from fact it is
the regression coefficient for the independent variable, i.e. beta.)
1. An index of ___________ between the return on
an asset i and the return on the "Market Portfolio".
a. Specifically it measures the expected change in
the return on asset i for a 1% change in the
market's return.
b. As a practical matter, beta is calculated using
past price data—by regressing the percentage
change in asset i's prices (y-variable) on the
percentage change in the representative market
index (x-variable). Illustrated in later example.
c. It turns out that βeta is equal to:
 Cov(R i , R m )   %Chg(Stock i) 
βi,m = 
 =  %Chg(Market)  .
Var(R
)


 
m
(1.2)
Please understand very clearly, Cov(Ri,Rm) refers to
a particular number, and means specifically, the
__________ between the return on asset i and the
market (m). It is not two numbers multiplied
together, or any other such misconception.
2. Different Ranges for Beta
5
a. Beta(Rf)=__.
 Cov(R f , R m )    (R f , R m ) * (R f ) * (R m ) 
βRf,m = 
=
 = __.
Var(R
)
Var(R
)

 

m
m
By definition, the variance of a risk-free asset is
zero. From statistics, the covariance between
asset Rf and the market return, Rm, equals the
numerator in the formula above. Since σ(Rf) = 0,
Cov(Rf,Rm) also = 0.
b. Beta(Rm)=__. Again by definition:
 Cov(R m , R m )   Var(R m ) 
βm,m = 
 =  Var(R )  = __.
Var(R
)

 
m
m 
Recall from statistics that the covariance of
anything with itself is its variance, this clearly
shows that βm,m equals 1.
c. Betaim > 1. __________ stocks: the expected
change in asset i is greater than the change in
the market. Ex.=Growth, Hi-Tech, Emerging
Industry, etc.
d. 0 < Betajm < 1. _________ stocks: the
expected change in asset j is less than change
in the market. Examples: Utility stocks, stock
of firms with inelastic demand curves.
6
e. Betakm < 0. Counter-cyclical stocks, eg. stocks
of gold mining firms and short-stock positions
(negative of their long position beta).
Figure 1.1: Sample Betas (as of November 2, 2013)
Source
Yahoo.finance
ABT
0.58
ARNA*
-0.32
IBM
0.65
PIR**
1.35
VC***
2.02
*Arena Pharmaceuticals; **Pier 1 Imports; ***Visteon Corporation
In Conclusion:
If Betaim > 1, Asset i is required to earn a ______ return
than the market.
If Betajm < 1, Asset j is required to earn a ______ return
than the market.
If Betakm < 0, Asset k is required to earn ______ than the
risk-free rate.
F. Expectational Version of the CAPM
E(Ri) = Rf + [βi * (E(Rm) – Rf)].
(1.3)
G. Operational Version of the CAPM
Because expected returns are unobservable, past
returns are typically employed in the model. To
make this (admittedly technical) distinction, the
CAPM is restated to focus on the CAPM Required
Rate of Return (ki) as in equation (1.4) below, where
the risk-free rate (kRf) and required market return
(km) are similarly restated.
ki = kRf + βi * (km – kRf).
7
(1.4)
Note: Need to make CLEAR distinction between
the Market Risk Premium (MRP) and km. MRP is
the required return on the market above the riskfree rate.
Market Risk Premium = [km – kRf].
Ex. 1.1
Amy DiGangi (F382 Fa’12) is estimating the CAPM
Required Returns for the five stocks given below, as of
November 6, 2013. She has chosen these stocks using
yahoo.finance and their stock screener. The criteria she
used to choose these stocks is that Market Cap must be
at least $1B, Dividend Yield must be at least 3.0% and
the P/E ratio must be between 15 and 20. Information
on the stocks follows:
Ticker
AHGP
ATO
GIS
HMC
WSTC
Company
Mkt Cap
Alliance Holdings GP
$3.60B
Atmos Energy Corp.
$4.04B
General Mills Inc.
$31.92B
Honda Motor Company $72.27B
West Corporation
$1.85B
P/E
15.77
16.79
18.85
15.89
16.05
DivYld
5.40%
3.10%
3.00%
5.00%
4.10%
Beta
1.48
0.55
0.22
1.17
-0.27
Mkt Price
$57.55
$44.80
$50.40
$39.11
$22.13
Amy has also determined that the current five-year
Treasury rate (kRf) equals 1.288%. Further, she will use
the HPR calculated from the dividend-adjusted S&P
500 Index (Nov ’08 = 896.24 to Nov ’13 = 1770.49) to
represent the Required Return on the Market (km)
assuming the time interval for the annualisation is five
years. Given this information answer the following
questions.
a) Calculate the Annualized HPR that Amy will use to
represent the return on the market.
8
b) What is the Market Risk Premium in this example?
c) Which of these stocks are considered aggressive
(and will have a required return that is greater than
the required return on the market, km)?
d) What stocks are considered to be defensive stocks
(i.e., have a CAPM return less than km)?
e) Do any of these stocks appear to be counter-cyclical
(and will have a CAPM-required return less than the
risk-free rate)?
f) Determine the CAPM required returns for each
stock.
 $1770.49 
A1.1a) HPRS&P500 = km = 
 $896.24 
1
5
 1 = _______%.
A1.1b) MRP = km – kRf = 0.14587 – 0.01288 = ______%.
A1.1c) Assets with betas greater than 1.0 are considered
aggressive stocks and will have CAPM required
returns _______ than km, here these would be
AHGP and HMC.
A1.1d) Assets with betas less than 1.0 are termed
defensive stocks and will have CAPM RORs
_____ than km. ATO and GIS (and also WSTC)
fit into this category.
A1.1e) Stocks with negative betas are counter-cyclical
assets and they will have CAPM required returns
that are _____ than the risk-free rate, here that
would be WSTC.
9
A1.1f) Individual Stock CAPM Required Returns:
kAHGP = 0.01288+[1.48*(0.14587–0.01288)] = ______%.
kATO = 0.01288+[0.55*(0.14587–0.01288)] = ______%.
kGIS = 0.01288+[0.22*(0.14587–0.01288)] = ______%.
kHMC = 0.01288+[1.17*(0.14587–0.01288)] = ______%.
kWSTC = 0.01288+[-0.27*(0.14587–0.01288)] = ______%.
Ex. 1.2
Assume that for every 1% increase in Apple
Computer's (AAPL) common stock price we expect
the market index to rise by 1.6393%. If the Market
Risk Premium is 12.80%, and the Risk-free rate =
2.50%, answer the following questions:
a) What is the required return on the market?
b) What is AAPL's beta equal to?
c) Again, w/o calculation, should we expect the CAPM
ROR for Apple to be greater or less than the
required return on the market?
d) What is the required return on AAPL's stock?
A1.2a) Since MRP=km-kRf, then km = MRP + kRf.
Here: km = 0.1280 + .0250 = 0.1530 = ______%.
 %Chg(Stock AAPL)   1.00 
A1.2b) βAAPL = 
=

 %Chg(Market)  1.6393 
10
= _______.
A1.2c) Since βAAPL < 1.0, CAPM RORAAPL < km.
A1.2d) kAAPL = .0250 + (0.610 * 0.128) = ______%.
II. Estimation of Stock and Portfolio Betas
A. Beta (from the Capital Asset Pricing Model)
measures the stock’s volatility relative to the
market (systematic risk).
B. How are betas calculated?
1. Numerical Formula for beta given above in (1.2).
2. Regression Approach:
 Run a regression with returns on the stock (Yvariable) regressed on the market portfolio (Xvariable).
 Remember, always regress Y (the stock =
dependent variable) on X (the market =
independent variable)!
 The slope of the regression line (the
characteristic line) is the stock’s ______
coefficient, or β.
 Analysts typically use at least 36 monthly returns
or one year of weekly returns.
3. The form of this regression is as follows:
%Chg Stocki = αimt + (βimt* %ChgMarket) + εt,
(1.5)
where:
%ChgStocki = (Monthly) % change in stock i's price,
%ChgMarket = (Monthly) % change in market's price,
11
αim = Unexpected Excess Return on stock i, and
βim = Index of Comovement between stock i rate
of return and market's rate of return.
C. How does the LINEST Excel function work and
how are the Regression Output Results interpreted?
1. LINEST calculates the statistics for a linear
regression line by using the "least squares"
method to calculate a straight line that best fits
your data, and returns an array that describes the
line. Because this function returns an array of
values, it must be entered as an array formula.
The syntax for calculating the least squares
regression statistics function (LINEST) is:
LINEST(known_y’s,known_x’s,const,stats).
To generate all of the available statistics, which
include the slope (m), the intercept (b), coefficient
of determination (R2), the F-test statistic (F) as
well as the standard errors for the slope coefficient
(sem), the intercept (seb), the y-estimate (sey), the
“stats” logical value should be set to ______.
This function will produce results (in this
univariate (one x-variable) example) in the form of
a 5 x 2 matrix (5 rows with 2 columns). So the
target range (highlight it with the cursor),
 Press F2, Enter the function, then hold down
CTRL + SHIFT, then hit ENTER.
2. The F-test is used to determine if the observed
relationship between the dependent and independent variables is likely to be spurious (by
12
chance). High observed F values provide evidence
to reject the null hypothesis of no systematic
relationship. For values of the F-test that are
higher than the critical value the null hypothesis
would be rejected.
3. The coefficient of determination (R2) is used to
describe the regression model’s “goodness of fit”
and ranges from 0 (no fit) to 1.0 (perfect fit).
4. To assess whether the parameter estimates are
significantly different from their hypothesized
values (i.e., H0: Slope = 1 and H0: Intercept = 0)
the t-test statistics may be calculated. The form of
this test (for Slope) is given in (1.6) below.
 Estimated Slope Coefficient   m 
t-test = 
. (1.6)



 Standard Error of Slope Est.   se m 
If the observed t-stat < critical t-value, the null
hypothesis cannot be rejected. If testing the
slope, this means the slope is not significantly
different from 1.0. If testing the intercept, this
finding would suggest the intercept is not
significantly different from 0.
Ex. 1.3
Use the following historical stock returns to calculate
the beta for KWE in F384_LN01_SS_Sp14CR
employing the three approaches described below.
Year
1
Market
25.7
KWE
40.0
Year
6
13
Market
13.7
KWE
30.0
2
3
4
5
8.0
-11.0
15.0
32.5
-15.0
-15.0
35.0
10.0
7
8
9
10
40.0
10.0
-10.8
-13.1
42.0
-10.0
-25.0
25.0
a) Employ the numerical approach in (1.2) using the
covariance (COVAR) and variance (VARP)
functions.
b) Use the SLOPE function to find beta.
c) Use the Excel Regression Data Analysis Tool, i.e.,
[Tools]  [Data Analysis]  [Regression]
(assuming this has been installed on your computer).
A1.3. Spreadsheet Solutions
FIGURE 3
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.5955
R Square
0.3546
Adjusted R Sq
0.2739
Stand Error
0.2204
Observations
10
A1.3a)
A1.3b)
Covariance Function
Variance Function
Calculated Beta
BETA Function
0.025695
0.030927
0.830833
0.830833
ANOVA
df
Regression
Residual
Total
A1.3c)
Intercept
X Variable 1
1
8
9
SS
0.21348
0.38853
0.60201
Coefficients
0.0256
0.8308
Standard
Error
0.08220
0.39628
MS
0.213483
0.048566
F
4.395725
Significan. F
0.069303
t Stat
0.311540
2.096598
P-value
0.76335
0.06930
Lower 95%
-0.16394
-0.08298
Upper 95%
0.21516
1.74465
Obtaining Stock Beta with Regression: Depiction of
the Least-Squares Characteristic Regression Line is
shown below.
14
D. How are beta and regression results interpreted?
1. From the slope of KWE’s characteristic line, the
beta of KWE turns out to be _____. Thus,
40%
kKWE
20%
kM
0%
-40%
-20%
0%
20%
40%
-20%
-40%
kKWE = 0.83kM + 0.03
R2 = 0.36
2. R2 (coefficient of determination) measures the
percent of a stock’s variance that is explained by
the market. Here, _______ of the variation in
KWE is due to changes in the market index.
3. The 95% confidence interval shows the range in
which you should be sure that the true value of
beta lies. From the KWE beta regression the 95%
confidence interval is -0.08298 to 1.74465. This
range is quite wide as the regression is based on
only 10 observations.
15
Ex. 1.4
Brittani Wester (F382, Fa’07) has been provided with
F384_LN01_SS_Sp14CR that contains (beginning-ofthe-month) monthly prices for Southwest Airlines
(LUV), the S&P 500 Index (^GSPC) and for the
period of January 1997 to October 2013. She will use
the LINEST Excel function in conducting the
following analysis.
a) Estimate the beta and all of the other available
statistics by regressing the monthly return for LUV
versus the S&P index, using the Market Model, for:
 The entire overall period, i.e., Jan ’97 to Oct ’13,
 The five-year period from Nov ’08 to Oct ’13,
 The five-year period from Nov ’03 to Oct ’08,
and
 The five-year period from Nov ’98 to Oct ’03.
b) Does the observed relationship between the
dependent and independent variables seem to occur
by chance? (Critical F-test value = 1.88.) Does the
regression model appear to be helpful in predicting
the y-value?
c) Calculate the t-test statistics and use them to
determine if the slope coefficient is significantly
different from one and if the intercept coefficient is
significantly different from zero? (Critical t-test
value = 2.012.) Type “YES” in the cell below the tstat if the null can be rejected. Otherwise, type
“NO” below the observed t-stat if it is not significant
and the null hypothesis cannot be rejected.
Alternatively, use the IF (/Then) Function to
generate the same answers.
16
d) Using the Market Model results, how stable does the
beta estimate appear over the three sub-periods?
A1.4a) As an example, in the spreadsheet, the first set of
calculations (LUV vs. SPX, Whole Period –
Market Model), will have the range W226:X230
as the destination. So select this range (highlight
it with the cursor), Press F2, Enter the formula
(in W226), Then holding down CTRL & SHIFT
together, press ENTER.
The results of running the market model for the
overall period and the three sub-periods are
shown in Figure 3 below.
Summary Statistics
Nov 08 to Oct 13
SPX
Nov98-Oct13
m
sem
R2
F
SSreg
tm
Reject H0?
Nov03-Oct08
m
sem
R2
F
SSreg
tm
Reject H0?
LUV
12.32%
16.24%
1.32
1.00000
60
Arith Annlzd Avg
Arith Annlzd SD
Coef Variation
Corr Coef
Count
10.26%
33.47%
3.26
0.65154
60
Whole Period - Market Model
1.15072
-0.00155
b
0.13830
0.00640
seb
sey
df
SSresid
tb
Reject H0?
0.25809
69.226
0.56412
8.32020
Nov08-Oct13
M
sem
0.09027
199
1.62165
-0.24193
R2
F
SSreg
tm
Reject H0?
LUV vs. SPX
5-Year Period - Market Model
0.40988
-0.00559
b
0.24571
0.00891
seb
sey
df
SSresid
tb
Reject H0?
0.04578
2.78282
0.01324
1.66818
Nov98-Oct03
M
sem
0.06898
58
0.27598
-0.62706
R2
F
SSreg
tm
Reject H0?
17
5-Year Period - Market Model
1.34258
-0.00523
b
0.20526
0.00977
seb
sey
df
SSresid
tb
Reject H0?
0.42450
42.782
0.23374
6.54078
0.07392
58
0.31689
-0.53532
LUV vs. SPX
5-Year Period - Market Model
1.14732
0.00638
b
0.28457
0.01415
seb
sey
df
SSresid
tb
Reject H0?
0.21891
16.25537
0.19532
4.03180
0.10961
58
0.6968947
0.45050
A1.4b) Since most of the F-values are quite high, and
range from 2.7828 to 69.226 (in comparison to
the critical value of 1.88 @ alpha=5%, with 40
degrees of freedom), the null hypothesis of no
systematic relation would be ________.
The coefficient of determination (R2) is used to
describe the regression model’s “goodness of
fit”. The fact that the R2s range from 0.04578 to
0.42450 indicate that the regression model has
fairly poor power for predicting the y-value
(although the best R2 is in the most recent subperiod).
A1.4c) An example of the t-test testing whether the slope
is significantly different from zero is provided
below for the Market model, in the five-year
period of Nov ’08 to Oct ’13.
1.34258 
Observed t-stat = 
= _______.

 0.20526 
From t-test table (Source: M. DeGroot,
Probability and Statistics, (1975), AddisonWesley Publishers), the critical value @ alpha =
5%, n=40, is 2.021.
Since the observed t-stat > critical t-value, the
null hypothesis ____ be rejected, in this case.
[The student needs to make the remaining deter-
18
minations as part of F384_LN01_SS_Sp14CR
using the critical value supplied above].
A1.4f) Although three beta estimates are insufficient to
conduct any formal statistical tests, some general
comments about beta stability are possible. In the
earliest sub-period, βNov98-Oct03 = 1.1473. In the
middle sub-period, βNov03-Oct08 = 0.4099. In the
most recent sub-period, βNov08-Oct13 = 1.3426.
Betas above one suggest greater volatility than
the market (1998-2003 and 2008-2013). Whereas
the middle period (2003-2008) beta suggests less
volatility than the market. Altogether these
results suggest that this firm’s beta has not been
_______. Thus, the period chosen to estimate
beta is an important consideration.
E. Expected Return, Market Risk and Required Return
1. Use the SML to calculate each alternative’s
required return.
2. The Security Market Line (SML) is part of the
Capital Asset Pricing Model (CAPM).
3. The Expected (Probability-Weighted) Return
(EPWR) (as in F382 LN #3: Equation (3.2)) and
the SML Required Return can be compared to
determine whether or not assets are fairly priced.
If EPWR > Required Return  Asset Underpriced.
If EPWR = Required Return  Asset Fairly Priced.
If EPWR < Required Return  Asset Overpriced.
Ex. 1.5
19
Refer back to the five assets in F382 Fa13CR Ex. 3.2.
Use the F384_LN01_SS_Sp14CR to calculate the
betas (numerically) and the SML required returns.
Determine if the assets are fairly priced. Note: The
COVAR function will NOT work since the
probabilities are NOT equi-likely.
Graphical Depiction of the SML
And How the Five Securities Plot
CAPM Required vs. Expected Returns
18%
16%
14%
12%
Return
10%
Sec Mkt Line (SML)
8%
Expected Returns
6%
4%
2%
Beta
0%
-1.00
-0.50
0.00
0.50
20
1.00
1.50
A1.5. The equation approach must be used since the
probabilities are not equal. To correctly calculate
the covariance, you need to multiply the asset’s
de-meaned return times the market’s de-meaned
return in each state, times the probability and then
sum these. This calculation is shown below for the
covariance between Hi-Tech (HT) and the Market
(m).
HT,m = [(-0.22 - 0.174)*(-0.13 - 0.15)* 0.10]
+ [(-0.02 - 0.174)*(0.01 - 0.15)*0.20]
+ [(0.20 - 0.174)*(0.15 - 0.15)*0.40]
+ [(0.35 - 0.174)*(0.29 - 0.15)*0.20]
+ [(0.50 - 0.174)*(0.43 - 0.15)*0.10]
= ________.
 σ HT, m   0.03052 
βHT,m =  2  = 
= _______.

0
.
02352

 σ m  
The SML required return on HT (for example) is:
kHT = .08 + (1.2976)*(.15 - .08) = ______%.
Security
Hi-Tech
Market
USR
T-bills
Collections
Expected
Return
17.4%
15.0%
13.8%
8.0%
1.74%
Market
Risk, β
1.2976
1.0000
0.8929
0.0000
-0.8655
Required
Return
17.08%
15.00%
14.25%
8.00%
1.94%
Conclude
Underpriced
Fairly Priced
Overpriced
Fairly Priced
Overpriced
Additional results are shown at the end of this
lecture note.
F. Calculating Portfolio Betas
21
1. Portfolio beta may be calculated just like the
expected return on a portfolio. The approach used
is to weight each asset’s individual beta, by the
market value (MV) proportion of the portfolio for
which it accounts.
N
βp =  (wi * βi) = (β1*w1) + (β2 * w2) +...+ (βN * wN). (1.7)
i 1
2. The CAPM may then be used to find the
required/expected return on a portfolio of assets,
where the portfolio’s beta is employed and
everything else is the same.
Ex. 1.6
Tiffany Mizell (F382, Sp’08) has decided to make the
following investments to form a starting portfolio on the
basis of information obtained from finance.yahoo.com
as of Monday, 10 November 2013. a) Calculate the
market-value portfolio weights and b) the portfolio beta.
c) If the relevant risk-free rate equals 2.35% and the
market’s required return equals 13.67%, determine the
CAPM required return for this portfolio.
Stock
Abbott Lab
IBM
Visteon Corp
Mkt. Price
$ 38.12
$ 179.99
$ 75.16
#Shares
96
49
100
Beta
0.66
0.65
2.02
A1.6a) She needs to calculate the MV of each stock
investment first. Second, add together all market
values to find MV of her portfolio. Third, divide
22
each stock’s MV by the MV of the portfolio.
Stock
ABT
IBM
VC
Mkt Price #Shares MP*#Sh
$38.12
96
$3,659.52
$179.99
49
$8,819.51
$75.16
100
$7,516.00
$19,995.03
Sum
Weight
0.1830
0.4411
0.3759
1.0000
A1.6b)
βp = (0.1830*0.66) + (0.4411*0.65) + (0.3759*2.02)
= __________.
A1.6c) E(Rp) = 0.0235 + [1.1668 * (0.1367 – 0.0235)]
= _______%.
6
7
8
9
10
11
12
13
14
15
16
17
B
C
D
E
F
G
H
Calculating Beta and CAPM Required Returns for Individual Assets
Ex. 1.5
Economy
Recession
Below Avg.
Average
Above Avg.
Boom
Sum
Prob
0.10
0.20
0.40
0.20
0.10
1.00
Hi-Tech
-22.0%
-2.0%
20.0%
35.0%
50.0%
Colls
28.0%
14.7%
0.0%
-10.0%
-20.0%
USR
10.0%
-10.0%
7.0%
45.0%
30.0%
kRf
(R)
(Exp Return)
18
19
20
21
2(R)
(R)
(Variance)
(Std Devn)
22
i,m
23
24
T-Bill
8.0%
8.0%
8.0%
8.0%
8.0%
Mkt Port
-13.0%
1.0%
15.0%
29.0%
43.0%
km
8.00%
17.40%
1.74%
13.80%
15.00%
0.00000
0.00%
0.04014
20.03%
0.01786
13.36%
0.03542
18.82%
0.02352
15.34%
0
0.03052
-0.02036
0.021
0.02352
0
8.00%
1.2976
17.08%
-0.8655
1.94%
0.8929
14.25%
1.0000
15.00%
(Covariance)
 i,m
(Beta)
SML Req'd. Return
I
23