Chapter 10, Solutions
Cornett, Adair, and Nofsinger
CHAPTER 10 –CALCULATING EXPECTED RETURN AND MARKET RISK
Questions
LG1
1. Consider an asset that provides the same return no matter what economic state occurs.
What would be the standard deviation (or risk) of this asset? Explain.
Since this asset has no variation in its return, it will have no standard deviation. This could
be shown mathematically be demonstrating that each economic state’s return is the same
as it average. Therefore, all terms in the standard deviation summation equation are zero.
This asset would be known as a risk-free asset.
LG1
2. Why is expected return considered “forward-looking”? What are the challenges for
practitioners to utilize expected return?
Expected return is “forward-looking” in the sense that it represents the return investors
expect to receive in the future as compensation for the market risk taken. The challenge is
that practitioners cannot precisely know what the future holds and thus what the expected
return should be. Thus, we create methods to estimate the expected return.
LG2
3. In 2000, the S&P 500 Index earned −9.1 percent while the T-bill yield was 5.9 percent.
Does this mean the market risk premium was negative? Explain.
The market risk premium is a forward-looking tool and should always be positive.
Because the market has risk, it will periodically have a negative return or a small positive
return that is smaller than the T-bill rate. Thus, realized returns over a short period of time
will sometimes show what appears to be a negative risk premium. However, historical
risk premiums should be measured over long periods of time.
LG2
4. How might the magnitude of the market risk premium impact people’s desire to buy
stocks?
Everybody has a different level of risk aversion. People who have a low level of risk
aversion would be willing to buy stocks with high risk . However, people who have a
high level of risk aversion would only be willing to buy stocks with low risk. Therefore,
the magnitude of the risk premium does impact who wants to buy stocks.
LG3
5. Describe how adding a risk-free security to modern portfolio theory allows investors to
do better than the efficient frontier.
The best portfolios investors can hold with only risky assets are the efficient portfolios on
the efficient frontier. If investors can borrow and lend at a risk free rate, then they can do
better. To improve over the efficient frontier, investors should allocate their portfolio to
the risk free rate and to the market portfolio. With the right weights between the two, an
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Chapter 10, Solutions
Cornett, Adair, and Nofsinger
investor can find a portfolio with the same level of risk as an efficient portfolio but has a
higher expected return.
LG3
6. Show on a graph like Figure 10.2 where a stock with a beta of 1.3 would be located on
the Security Market Line. Then show where that stock would be located if it is
undervalued.
Required Return (%)
Figure shown:
Security Market Line
Under valued stock
with 1.3 Beta Depot
RStock
RM
Stock with 1.3 Beta
Depot
M
Rf
1
LG3
1.3
Beta
7. Consider that you have three stocks in your portfolio and wish to add a fourth. You
want to know if the fourth stock will make the portfolio riskier or less risky. Compare and
contrast how this would be assessed using standard deviation versus market risk (beta) as
the measure of risk.
Using standard deviation, you would need to determine how the fourth stock interacts
with the three stocks already owned. To do this you would have to compute the
correlation between the new stock and each of the three already held. Then, the portfolio
standard deviation could be computed. If the new portfolio standard deviation is lower
then the original portfolio standard deviation, then adding the new stock lowers the risk.
Of course, the portions, or weights of all the stocks will matter. Determining whether
adding a stock will increase or lower the risk of the portfolio is much easier using beta. If
the beta of the fourth stock is higher than the beta of the portfolio, then it will increase the
risk when added.
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Chapter 10, Solutions
LG3
Cornett, Adair, and Nofsinger
8. Describe how different allocations between the risk-free security and the market
portfolio can achieve any level of market risk desired. Give examples of a portfolio from a
person who is very risk averse and a portfolio for someone who is not so averse to taking
risk.
An investor can allocate money between a risk-free security that has zero risk (β=0), and
the market portfolio that has market risk (β=1). If 75% of the portfolio is invested in the
market, then the portfolio will have a β=0.75. If only 25% is invested in the market, then
the portfolio will have a market risk of β=0.25. The first example (β=0.75) might be taken
by a less risk averse investor while the second example (β=0.25) illustrates the portfolio of
a more risk averse investor. By allocating the investment money between 0 and 100% into
the market portfolio, an investor can achieve any level of market risk desired.
LG4
9. Cisco Systems has a beta of 1.88. Does this mean that you should expect Cisco to earn
a return 88 percent higher than the S&P 500 Index return? Explain.
Not quite. A beta of 1.88 means that Cisco’s risk premium is 88% higher then the market
risk premium. In other words, we must account for the risk free rate. This relationship is
shown in the CAPM equation.
LG4
10. Note from Table 10.2 that some technology-oriented firms (Intel, and IBM) in the
Dow Jones Industrial Average have high market risk while others (AT&T, Microsoft, and
Verizon) have low market risk. How do you explain this?
Not all technology industries have the same level of risk. Notice from this example that
the more manufacturing (hardware) tech companies have higher risk. The service and
software tech companies have lower risk. This may be an indication of the type of assets
needed by the firms and the amount of debt required.
LG4
11. Find a beta estimate from three different sources for General Electric (GE). Compare
these three values. Why might they be different?
Yahoo! Finance beta was 0.59. MSN Money shows a beta of 0.76. Hoovers lists a beta of
0.8. The beta sources may use (i) different market portfolios, (ii) different time periods, or
(iii) different time increments (annual returns versus months, weeks, etc.).
LG4
12. If you were to compute beta yourself, what choices would you make regarding the
market portfolio, the holding period for the returns (daily, weekly, etc.), and the number of
returns? Justify your choices.
It is common to use the S&P500, monthly returns, and either three to five years of data.
LG5
13. Explain how the concept of a positive risk-return relationship breaks down if you can
systematically find stocks that are over-valued and under-valued.
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Chapter 10, Solutions
Cornett, Adair, and Nofsinger
Consider two stocks: one stock has a beta of 0.9 and is undervalued, the other has a beta
of 1 and is overvalued. If beta perfectly explained expected returns, then the higher beta
stock would offer a higher expected return. However, if you believe the lower beta stock
is undervalued, then you are saying it will achieve a return higher than expected by its
beta. You also believe the overvalued stock will earn a return lower than expected by its
beta. Thus, you might expect the undervalued stock to outperform the overvalued stock
even though the risks of the two stocks suggest otherwise.
LG5
14. Determine what level of market efficiency each event is consistent with:
A. Immediately after an earnings announcement the stock price jumps and then
stays at the new level.
B. The CEO buys 50,000 shares of his company and the stock price does not
change.
C. The stock price immediately jumps when a stock split is announced, but then
retraces half of the gain over the next day.
D. An investor analyzes company quarterly and annual balance sheets and income
statements looking for under-valued stocks. The investor earns about the same
return as the S&P 500 Index.
A. semi-strong form
B. strong form
C. not efficient
D. semi-strong form
LG5
15. Why do most investment scams conducted over the Internet and e-mail involve penny
stocks instead of S&P 500 Index stocks?
There is tremendous liquidity in the large stocks. As such, these scams would not impact
their stocks price and thus not be effective. Penny stocks have very little liquidity. So if a
few investors buy the stocks in the scam, they will push up the price and allow the scam
promoters to sell at a profit.
LG5
16. Describe a stock market bubble. Can a bubble occur in a single stock?
Bubbles are initially started with an increase in price that is typically justified by the
economics and fundamentals. Then many people get irrationally exuberant about the
asset(s) and push prices beyond those that are justified. Eventually, there are no more
buyers for the overvalued asset and prices drop. As people begin to believe that the price
is a bubble, the price free falls. No one buys the stock while it is plummeting. Yes, a
bubble can occur in a single stock.
LG6
17. If stock prices are not strong-form efficient, then what might be the price reaction to a
firm announcing a stock buyback? Explain.
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Cornett, Adair, and Nofsinger
Two different arguments could be made. First, the price could increase with the
realization that this demand for stock will push up the stock price. Alternatively, the price
could decline if investors believe that the company does not have any good product
related investments and thus must buy back its stock.
LG7
18. Compare and contrast the assumptions that need to be made to compute a required
return using CAPM and the constant growth rate model.
When using the CAPM to compute required return, you need to make assumptions about
what the expected market return will be, what the risk free rate will be, and what the
future beta of the firm will be. The future beta is commonly similar to the recent past beta.
The risk free rate is well estimated by T-bill rates and the yield curve. These two are
reasonably estimated. However, the stock market is very volatile and the future market
return is difficult to estimate. The constant growth rate model assumes that the growth of
the firm will remain constant. The growth rate and the dividend must be assumed. Firms
do not change their dividends very much, so that estimation is not difficult. However, the
required rate is very sensitive to the estimated growth rate. Both models require difficult
assumptions.
LG7
19. How should you handle a case where required return computations from CAPM and
the constant growth rate model are very different?
First, examine the assumptions of each model. If no mistakes have been made, then
compute the required return for similar firms in the same industry. Use the CAPM or
constant growth rate estimate that most resembles that of its competitors.
Problems
Basic
Problems
LG1
10-1 Expected Return Compute the expected return given these three economic states,
their likelihoods,
and the potential returns:
Economic
Probability Return
State
Fast Growth
0.3
40%
Slow Growth
0.5
10%
Recession
0.2
−25%
Expected return = 0.3×40% + 0.5×10% + 0.2×-25% = 12%
LG1
10-2 Expected Return Compute the expected return given these three economic states,
their likelihoods, and the potential returns:
Economic
Probability Return
State
10-5
Chapter 10, Solutions
Fast Growth
Slow Growth
Recession
Cornett, Adair, and Nofsinger
0.2
0.6
0.2
35%
10%
−30%
Expected return = 0.2×35% + 0.6×10% + 0.2×-30% = 7%
LG2
10-3 Required Return If the risk-free rate is 6 percent and the risk premium is 5 percent,
what is the required return?
Required return = 6% + 5% = 11%
LG2
10-4 Required Return If the risk-free rate is 3 percent and the risk premium is 7 percent,
what is the required return?
Required return = 3% + 7% = 10%
LG2
10-5 Risk Premium The average annual return on the S&P 500 Index from 1986 to 1995
was 15.8 percent. The average annual T-bill yield during the same period was 5.6 percent.
What was the market risk premium during these ten years?
Average market risk premium = 15.8% − 5.6% = 10.2%
LG2
10-6 Risk Premium The average annual return on the S&P 500 Index from 1996 to 2005
was 10.8 percent. The average annual T-bill yield during the same period was 3.6 percent.
What was the market risk premium during these ten years?
Average market risk premium = 10.8% − 3.6% = 7.2%
LG3
10-7 CAPM Required Return Hastings Entertainment has a beta of 0.24. If the market
return is expected to be 11 percent and the risk-free rate is 4 percent, what is Hastings’
required return?
Hastings’ required return = 4% + 0.24 × (11% − 4%) = 5.68%
LG3
10-8 CAPM Required Return Nanometrics Inc. has a beta of 4.05. If the market return
is expected to be 12 percent and the risk-free rate is 4.5 percent, what is Nanometrics’
required return?
Nanometrics’ required return = 4.5% + 4.05 × (12% − 4.5%) = 34.875%
LG3
10-9 Company Risk Premium Netflicks, Inc. has a beta of 3.61. If the market return is
expected to be 13 percent and the risk-free rate is 6 percent, what is Netflicks’ risk
premium?
10-6
Chapter 10, Solutions
Cornett, Adair, and Nofsinger
Netflicks’ risk premium = 3.61 × (13% − 6%) = 25.27%
LG3
10-10 Company Risk Premium Paycheck Inc. has a beta of 0.94. If the market return is
expected to be 11 percent and the risk-free rate is 3 percent, what is Paycheck’s risk
premium?
Paycheck’s risk premium = 0.94 × (11% − 3%) = 7.52%
LG3
10-11 Portfolio Beta You have a portfolio with a beta of 1.2. What will be the new
portfolio beta if you keep 90 percent of your money in the old portfolio and 10 percent in
a stock with a beta of 1.9?
New portfolio beta = 0.90×1.2 + 0.10×1.9 = 1.27
LG3
10-12 Portfolio Beta You have a portfolio with a beta of 1.1. What will be the new
portfolio beta if you keep 85 percent of your money in the old portfolio and 15 percent in
a stock with a beta of 0.5?
New portfolio beta = 0.85×1.1 + 0.15×0.5 = 1.01
LG5
10-13 Stock Market Bubble The Nasdaq stock market bubble peaked at 4,816 in 2000.
Two and a half years later it had fallen to 1,000. What was the percentage decline?
Market decline = (1,000 − 4,816) ÷ 4,816 = −0.7924 = −79.24%
LG5
10-14 Stock Market Bubble The Japanese stock market bubble peaked at 38,916 in 1989.
Two and a half years later it had fallen to 15,900. What was the percentage decline?
Market decline = (15,900 − 38,916) ÷ 38,916 = −0.5914 = −59.14%
LG7
10-15 Required Return Paccar’s current stock price is $73.10 and it is likely to pay a
$2.69 dividend next year. Since analysts estimate Paccar will have a 11.2% growth rate,
what is its required return?
Use equation 10.6:
LG7
i
D1
$2.69
g
 0.112  0.1488  14.88%
P0
$73.10
10-16 Required Return Universal Forest’s current stock price of Universal Forest is
$54.00 and it is likely to pay a $0.23 dividend next year. Since analysts estimate
Universal Forest will have a 10.0% growth rate, what is its required return?
Use equation 10.6:
i
D1
$0.23
g
 0.10  0.1043  10.43%
P0
$54.00
10-7
Chapter 10, Solutions
Cornett, Adair, and Nofsinger
Intermediate
Problems 10-17 Expected Return Risk For the same economic state probability distribution in
Problem 10.1, determine the standard deviation of the expected return.
LG1
Economic
State
Fast Growth
Slow Growth
Recession
Probability Return
0.3
0.5
0.2
40%
10%
−25%
Use equation 10.2 and expected return from Problem 10.1 of 12%:
Standard Deviation  0.3  40%  12%  0.5  10%  12%  0.2  (25%  12%) 2
2
2
 235.2  2  273.8  22.6%
LG1
10-18 Expected Return Risk For the same economic state probability distribution in
Problem 10.2, determine the standard deviation of the expected return.
Economic
Probability Return
State
Fast Growth
0.2
35%
Slow Growth
0.6
10%
Recession
0.2
−30%
Use equation 10.2 and expected return from problem 10.2 of 7%:
Standard Deviation  0.2  35%  7%  0.6  10%  7%  0.2  (30%  7%) 2
2
2
 156.8  5.4  273.8  20.9%
LG3
10-19 Under/Over Valued Stock A manager believes his firm will earn a 14 percent
return next year. His firm has a beta of 1.5, the expected return on the market is 12
percent, and the risk-free rate is 4 percent. Compute the return the firm should earn given
its level of risk and determine whether the manager is saying the firm is under-valued or
over-valued.
Use CAPM to determine the firm’s required return = 4% + 1.5 × (12% − 4%) = 16%
Since the return required for the level of risk is 16% and the manager believes a 14%
return will be achieved, the manager is saying the firm is over-valued.
LG3
10-20 Under/Over Valued Stock A manager believes his firm will earn a 14 percent
return next year. His firm has a beta of 1.2, the expected return on the market is 11
percent, and the risk-free rate is 5 percent. Compute the return the firm should earn given
its level of risk and determine whether the manager is saying the firm is under-valued or
over-valued.
10-8
Chapter 10, Solutions
Cornett, Adair, and Nofsinger
Use CAPM to determine the firm’s required return = 5% + 1.2 × (11% − 5%) = 12.2%
Since the return required for the level of risk is 12.2% and the manager believes a 14%
return will be achieved, the manager is saying the firm is under-valued.
LG3
10-21 Portfolio Beta You own $5,000 of Olympic Steel stock that has a beta of 2.9. You
also own $7,000 of Rent-a-Center (beta=1.5) and $8,000 of Lincoln Educational
(beta=0.2). What is the beta of your portfolio?
First determine the total value of the portfolio and the weights of each stock in the
portfolio:
Total value = $5,000 + $7,000 + $8,000 = $20,000
Olympic Steel weight = $5,000 / $20,000 = 25%
Rent-a-Center weight = $7,000 / $20,000 = 35%
Lincoln Educational weight = $8,000 / $20,000 = 40%
Now compute the portfolio beta = 0.25×2.9 + 0.35×1.5 + 0.40×0.2 = 1.33
LG3
10-22 Portfolio Beta You own $7,000 of Human Genome stock that has a beta of 3.5.
You also own $8,000 of Frozen Food Express (beta=1.6) and $10,000 of Molecular
Devices (beta=0.4). What is the beta of your portfolio?
First determine the total value of the portfolio and the weights of each stock in the
portfolio:
Total value = $7,000 + $8,000 + $10,000 = $25,000
Human Genome weight = $7,000 / $25,000 = 28%
Frozen Food Express weight = $8,000 / $25,000 = 32%
Molecular Devices weight = $10,000 / $25,000 = 40%
Now compute the portfolio beta = 0.28×3.5 + 0.32×1.6 + 0.40×0.4 = 1.65
Advanced
Problems
10-23 Expected Return and Risk Compute the expected return and standard deviation
given these four economic states, their likelihoods, and the potential returns:
LG1
Economic
State
Fast Growth
Slow Growth
Recession
Depression
Probability Return
0.30
0.50
0.15
0.05
60%
13%
−15%
−45%
Expected return = 0.3×60% + 0.5×13% + 0.15×-15% + 0.05×-45% = 20%
Standard Deviation  0.3  60%  20%  0.5  13%  20%  0.15  (15%  20%) 2  0.05  (45%  20%) 2
2
2
 480  24.5  183.75  211.25  29.99%
10-9
Chapter 10, Solutions
LG1
Cornett, Adair, and Nofsinger
10-24 Expected Return and Risk Compute the expected return and standard deviation
given these four economic states, their likelihoods, and the potential returns:
Economic
State
Fast Growth
Slow Growth
Recession
Depression
Probability Return
0.25
0.55
0.15
0.05
50%
11%
−15%
−50%
Expected return = 0.25×50% + 0.55×11% + 0.15×-15% + 0.05×-50% = 13.8%
Standard Deviation  0.25  50%  13.8%  0.55  11%  13.8%  0.15  (15%  13.8%) 2  0.05  (50%  13.8%) 2
2
2
 327.6  4.3  124.4  203.5  25.69%
LG3
10-25 Risk Premiums You own $10,000 of Denny’s Corp stock that has a beta of 2.9.
You also own $15,000 of Qwest Communications (beta=1.5) and $15,000 of Southwest
Airlines (beta=0.4). Assume that the market return will be 13 percent and the risk-free rate
is 5.5 percent. What is the market risk premium? What is the risk premium of each stock?
What is the risk premium of the portfolio?
Market risk premium = 13% − 5.5% = 7.5%
Denny’s risk premium = 2.9×(13%−5.5%) = 21.75%
Qwest’s risk premium = 1.5×(13%−5.5%) = 11.25%
Southwest Airlines risk premium = 0.4×(13%−5.5%) = 3.0%
For the portfolio, determine the total value of the portfolio and the weights of each stock
in the portfolio:
Total value = $10,000 + $15,000 + $15,000 = $40,000
Denny’s weight = $10,000 / $40,000 = 25%
Qwest’s weight = $15,000 / $40,000 = 37.5%
Southwest Airlines weight = $15,000 / $40,000 = 37.5%
Now compute the portfolio beta = 0.25×2.9 + 0.375×1.5 + 0.375×0.4 = 1.44
So the portfolio’s risk premium = 1.44×(13%−5.5%) = 10.8%
LG3
10-26 Risk Premiums You own $15,000 of Opsware Inc. stock that has a beta of 3.8.
You also own $10,000 of Lowe’s Companies (beta=1.6) and $10,000 of New York Times
(beta=0.8). Assume that the market return will be 12 percent and the risk-free rate is 6
percent. What is the market risk premium? What is the risk premium of each stock? What
is the risk premium of the portfolio?
Market risk premium = 12% − 6% = 6%
Opsware’s risk premium = 3.8×(12%−6%) = 22.8%
Lowe’s risk premium = 1.6×(12%−6%) = 9.6%
10-10
Chapter 10, Solutions
Cornett, Adair, and Nofsinger
New York Times risk premium = 0.8×(12%−6%) = 4.8%
For the portfolio, determine the total value of the portfolio and the weights of each stock
in the portfolio:
Total value = $15,000 + $10,000 + $10,000 = $35,000
Opsware’s weight = $15,000 / $35,000 = 42.9%
Lowe’s weight = $10,000 / $35,000 = 28.55%
New York Times weight = $10,000 / $35,000 = 28.55%
Now compute the portfolio beta = 0.429×3.8 + 0.2855×1.6 + 0.2855×0.8 = 2.32
So the portfolio’s risk premium = 2.32×(12%−6%) = 13.9%
LG3
10-27 Portfolio Beta and Required Return You hold the positions in the table below.
What is the beta of your portfolio? If you expect the market to earn 12 percent and the
risk-free rate is 3.5 percent, what is the required return of the portfolio?
Price
Shares
Beta
Amazon.com
$40.80
100
3.8
Family Dollar Stores
$30.10
150
1.2
McKesson Corp
$57.40
75
0.4
Schering-Plough Corp
$23.80
200
0.5
This problem can be solved two different and equivalent ways. Both ways require the
weights of the stocks in the portfolio. In one method, compute the required return for
each stock and then use the weights to form the portfolio required return. The other
solution uses the weights to compute the portfolio beta. This portfolio beta is used to
compute the portfolio required return. The solution below shows the portfolio beta
approach.
For the portfolio, determine the total value of the portfolio and the weights of each stock
in the portfolio:
Total value = $40.80×100 + $30.10×150 + $57.40×75 + $23.80×200 = $17,660
Amazon.com weight = $40.80×100 / $17,660 = 23.1%
Family Dollar weight = $30.10×150 / $17,660 = 25.6%
McKesson weight = $57.40×75 / $17,660 = 24.4%
Schering-Plough weight = $23.80×200 / $17,660 = 26.9%
Now compute the portfolio beta = 0.231×3.8 + 0.256×1.2 + 0.244×0.4 + 0.269×0.5 = 1.42
So the portfolio’s required return = 3.5%+1.42×(12%−3.5%) = 15.5%
LG3
10-28 Portfolio Beta and Required Return You hold the positions in the table below.
What is the beta of your portfolio? If you expect the market to earn 12 percent and the
risk-free rate is 3.5 percent, what is the required return of the portfolio?
Price
Shares
Beta
Advanced
Micro $14.70
200
4.2
Devices
FedEx Corp
$120.00
50
1.1
Microsoft
$28.90
150
0.7
10-11
Chapter 10, Solutions
Sara Lee Corp
Cornett, Adair, and Nofsinger
$17.25
200
0.5
This problem can be solved two different and equivalent ways. Both ways require the
weights of the stocks in the portfolio. In one method, compute the required return for
each stock and then use the weights to form the portfolio required return. The other
solution uses the weights to compute the portfolio beta. This portfolio beta is used to
compute the portfolio required return. The solution below shows the portfolio beta
approach.
For the portfolio, determine the total value of the portfolio and the weights of each stock
in the portfolio:
Total value = $14.70×200 + $120.00×50 + $28.90×150 + $17.25×200 = $16,725
Advanced Micro Devices weight = $14.70×200 / $16,725 = 17.6%
FedEx Corp weight = $120.00×50 / $16,725 = 35.9%
Microsoft weight = $28.90×150 / $16,725 = 25.9%
Sara Lee Corp weight = $17.25×200 / $16,725 = 20.6%
Now compute the portfolio beta = 0.176×4.2 + 0.359×1.1 + 0.259×0.7 + 0.206×0.5 = 1.42
So the portfolio’s required return = 3.5%+1.42×(12%−3.5%) = 15.5%
LG3&7 10-29 Required Return Using the information in the table, compute the required return
for each company using both CAPM and the constant growth model. Compare and discuss
the results. Assume that the market portfolio will earn 12 percent and the risk-free rate is
3.5 percent.
Price
Upcoming Growth
Beta
Dividend
US Bancorp
$36.55
$1.60
10.0%
0.8
Praxair
$64.75
$1.12
11.0%
0.7
Eastman Kodak
$24.95
$1.00
4.5%
2.0
First use CAPM to determine each firm’s required return:
US Bancorp required return = 3.5% + 0.8 × (12% − 3.5%) = 10.3%
Praxair required return = 3.5% + 0.7 × (12% − 3.5%) = 9.45%
Eastman Kodak required return = 3.5% + 2.0 × (12% − 3.5%) = 20.5%
Now compute the required return using the constant growth rate model:
US Bancorp required return = $1.60  0.10  0.1438  14.38%
Praxair required return =
Eastman Kodak required
$36.55
$1.12
 0.11  0.1273  12.73%
$64.75
return = $1.00  0.045  0.0851  8.51%
$24.95
The US Bancorp CAPM estimate of 10.3% is low compared to the 14.4% constant growth
rate model estimate. The CAPM estimate for Praxair is high compared to the constant
growth rate model estimate. The CAPM estimate for Eastman Kodak is more than double
that of the constant growth rate model.
10-12
Chapter 10, Solutions
Cornett, Adair, and Nofsinger
LG3&7 10-30 Required Return Using the information in the table, compute the required return
for each company using both CAPM and the constant growth model. Compare and discuss
the results. Assume that the market portfolio will earn 11 percent and the risk-free rate is 4
percent.
Price
Upcoming Growth
Beta
Dividend
Estee Lauder
$47.40
$0.60
11.7%
0.75
Kimco Realty
$52.10
$1.54
8.0%
1.3
Nordstrom
$5.25
$0.50
14.6%
2.2
First use CAPM to determine each firm’s required return:
Estee Lauder required return = 4% + 0.75 × (11% − 4%) = 9.25%
Kimco Realty required return = 4% + 1.3 × (11% − 4%) = 13.1%
Nordstrom required return = 4% + 2.2 × (11% − 4%) = 19.4%
Now compute the required return using the constant growth rate model:
Estee Lauder required return = $0.60  0.117  0.1297  12.97%
$47.40
Kimco Realty required return = $1.54  0.08  0.1096  10.96%
$52.10
Nordstrom required return = $0.50  0.146  0.2412  24.12%
$5.25
The Estee Lauder CAPM estimate of 9.25% is low compared to the 13% constant growth
rate model estimate. The CAPM estimate for Kimco Realty is high compared to the
constant growth rate model estimate. The CAPM estimate for Nordstrom is a little lower
than that of the constant growth rate model.
10-13
Chapter 10, Solutions
Cornett, Adair, and Nofsinger
10-31 Excel Problem As discussed in the text, beta estimates for one firm will vary depending on various factors like, the time over which
the estimation is conducted, the market portfolio proxy, and the return intervals. You will demonstrate this variation using
returns for Microsoft.
A. Using all 45 monthly returns for Microsoft and the three stock market indices, compute Microsoft’s beta using the S&P 500
Index as the market proxy. Then compute the beta using the DJIA and the Nasdaq indices as the market portfolio proxy.
Compare the three beta estimates.
B. Now estimate the beta using only the most recent 30 monthly returns and the S&P 500 Index. Compare the beta estimate to
the estimate in part A when using the S&P 500 Index and all 45 monthly returns.
Date
MSFT
S&P500
DJIA
Nasdaq
Date
MSFT
S&P500
DJIA
Nasdaq
Date
MSFT
S&P500
DJIA
Nasdaq
Jun 2007
4.45%
3.07%
4.04%
4.19%
Mar 2006
-11.22%
1.22%
2.32%
-0.74%
Dec 2004
-1.66%
-2.53%
-2.72%
-5.20%
May 2007
-3.98%
-1.78%
-1.61%
-0.05%
Feb 2006
1.25%
1.11%
1.05%
2.56%
Nov 2004
-0.31%
3.25%
3.40%
3.75%
Apr 2007
2.85%
3.25%
4.32%
3.15%
Jan 2006
-4.21%
0.05%
1.18%
-1.06%
Oct 2004
6.80%
3.86%
3.99%
6.17%
Mar 2007
7.42%
4.33%
5.74%
4.27%
Dec 2005
7.61%
2.55%
1.37%
4.56%
Sep 2004
1.17%
1.40%
-0.52%
4.12%
Feb 2007
-1.07%
1.00%
0.70%
0.23%
Nov 2005
-5.50%
-0.10%
-0.82%
-1.23%
Aug 2004
1.31%
0.94%
-0.92%
3.20%
Jan 2007
-8.38%
-2.18%
-2.80%
-1.94%
Oct 2005
8.01%
3.52%
3.50%
5.31%
Jul 2004
-3.89%
0.23%
0.34%
-2.61%
Dec 2006
3.34%
1.41%
1.27%
2.01%
Sep 2005
-0.12%
-1.77%
-1.22%
-1.46%
Jun 2004
-0.28%
-3.43%
-2.83%
-7.83%
Nov 2006
1.71%
1.26%
1.97%
-0.68%
Aug 2005
-6.02%
0.69%
0.83%
-0.02%
May 2004
8.90%
1.80%
2.42%
3.07%
Oct 2006
2.60%
1.65%
1.17%
2.75%
Jul 2005
7.22%
-1.12%
-1.50%
-1.50%
Apr 2004
0.40%
1.21%
-0.36%
3.47%
Sep 2006
4.99%
3.15%
3.44%
4.79%
Jun 2005
3.10%
3.60%
3.56%
6.22%
Mar 2004
4.82%
-1.68%
-1.28%
-3.71%
Aug 2006
6.41%
2.46%
2.62%
3.42%
May 2005
-3.70%
-0.01%
-1.84%
-0.54%
Feb 2004
-6.05%
-1.64%
-2.14%
-1.75%
Jul 2006
7.21%
2.13%
1.75%
4.41%
Apr 2005
2.28%
3.00%
2.70%
7.63%
Jan 2004
-4.05%
1.22%
0.91%
-1.76%
Jun 2006
3.26%
0.51%
0.32%
-3.71%
Mar 2005
4.69%
-2.01%
-2.96%
-3.88%
Dec 2003
1.01%
1.73%
0.33%
3.13%
May 2006
2.86%
0.01%
-0.16%
-0.31%
Feb 2005
-3.93%
-1.91%
-2.44%
-2.56%
Nov 2003
6.47%
5.08%
6.86%
2.20%
Apr 2006
-5.86%
-3.09%
-1.75%
-6.19%
Jan 2005
-3.97%
1.89%
2.63%
-0.52%
Oct 2003
-1.64%
0.71%
-0.19%
1.45%
10-14
Chapter 10, Solutions
Cornett, Adair, and Nofsinger
C. Estimate Microsoft’s beta using the quarterly data returns below. Compare the estimate
to the ones from part A and B.
Date
Q2
2007
Q1
2007
Q4
2006
Q3
2006
Q2
2006
Q1
2006
Q4
2005
Q3
2005
Q2
2005
Q1
2005
Q4
2004
Q3
2004
Q2
2004
Q1
2004
Q4
2003
MSFT
S&P500
3.15%
4.53%
-2.64%
3.07%
7.85%
4.38%
19.76%
7.93%
0.00%
13.90%
-2.59%
9.84%
6.05%
0.64%
-2.20%
1.55%
6.68%
-3.42%
-2.07%
4.70%
4.52%
-1.50%
2.59%
9.02%
-0.50%
-5.52%
-2.11%
5.79%
7.65%
2.39%
A. Beta estimates using different market proxies and 45 months. The estimate is from the
Excel Slope function.
S&P500 DJIA
Nasdaq
Beta =
1.206
0.952
0.716
Microsoft’s beta is high when compared to S&P 500 type companies and low compared to
the tech compares in the Nasdaq.
10-15
Chapter 10, Solutions
Cornett, Adair, and Nofsinger
B. Beta estimate using 30 months.
S&P500
Beta =
1.420
The beta estimate is larger using the most recent 30 months compared to the full 45
months.
C. Beta estimate using quarterly returns.
S&P500
Beta =
1.085
This Microsoft beta estimate is the smallest using the quarterly S&P 500 market portfolio.
Note that the assumptions used can make a large difference in the beta estimate. This
makes beta difficult to use in practice.
Research It!
Find a Beta
Using beta as a risk measure has been fully integrated into corporate finance and the
investment industry. You can obtain a beta for most companies at many financial
websites. Sites that list a beta include: Hoovers (in the Market Data section), MSN
Money (in the Company Report section), Yahoo! Finance (in the Key Statistics section),
and Zacks (follow the Detailed Quote link). Obtain the beta for your favorite company
from several different websites. Are the values you obtain similar? If they are not, why
might they be different?
(hoovers.com, moneycentral.msn.com, finance.yahoo.com, www.zacks.com)
SOLUTION: For General Electric (GE), I found:
Yahoo! Finance beta was 0.59.
MSN Money shows a beta of 0.76.
Hoovers lists a beta of 0.8.
Zacks reports a beta of 0.83.
The beta sources may use (i) different market portfolios, (ii) different time periods, or (iii)
different time increments (annual returns versus months, weeks, etc.).
Integrated Mini Case: AT&T’s Beta
When you go on the Web to find a firm’s beta, you do not know how recently it was
computed, what index was used as a proxy for the market portfolio, or which time series
of returns the calculations used. Earlier in this chapter, it was shown that when we went
on the Web to find a beta for AT&T, we found the following: Hoovers (1.5), MSN Money
(1.52), Yahoo! Finance (0.50), and Zacks (1.52).
10-16
Chapter 10, Solutions
Cornett, Adair, and Nofsinger
An alternative is to compute beta yourself. A common estimation procedure is to use 60
months of return data and to use the S&P500 Index as the market portfolio. You can
obtain price data for a company and for the S&P500 Index for free from websites like
Yahoo! Finance. Using monthly prices, you can compute the monthly returns, as (Pn − Pn1)÷Pn-1. Below are 60 monthly returns for AT&T and the S&P500 Index. You can use
these returns to compute AT&T’s beta. A spreadsheet, like Excel, can run a regression
(go to Tool menu, select Data Analysis, and then Regression). Select AT&T returns as
the Y Variable and S&P500 Index return as the X Variable. The coefficient for the X
Variable is the beta estimate. The regression will provide all the statistical information
you might like. However, if you only want beta, you can simply use the SLOPE function
in Excel. Or, you may have learned to run a regression using statistical software.
Date
Jun 2007
May 2007
Apr 2007
Mar 2007
Feb 2007
Jan 2007
Dec 2006
Nov 2006
Oct 2006
Sep 2006
Aug 2006
Jul 2006
Jun 2006
May 2006
Apr 2006
Mar 2006
Feb 2006
Jan 2006
Dec 2005
Nov 2005
AT&T
-2.26%
0.39%
6.77%
-0.90%
7.14%
-2.22%
6.36%
5.42%
-0.97%
6.27%
4.59%
3.81%
8.82%
7.02%
-0.59%
-1.86%
-1.97%
6.29%
7.40%
-1.66%
S&P500
Index
3.07%
-1.78%
3.25%
4.33%
1.00%
-2.18%
1.41%
1.26%
1.65%
3.15%
2.46%
2.13%
0.51%
0.01%
-3.09%
1.22%
1.11%
0.05%
2.55%
-0.10%
Date
Oct 05
Sep 05
Aug 05
Jul 05
Jun 05
May 05
Apr 05
Mar 05
Feb 05
Jan 05
Dec 04
Nov 04
Oct 04
Sep 04
Aug 04
Jul 04
Jun 04
May 04
Apr 04
Mar 04
AT&T
4.45%
0.85%
-0.45%
-1.54%
4.36%
1.58%
-1.78%
1.82%
-1.51%
1.25%
-6.60%
2.35%
-0.35%
-1.53%
0.61%
1.79%
5.86%
2.32%
-4.79%
2.70%
S&P500
Index
3.52%
-1.77%
0.69%
-1.12%
3.60%
-0.01%
3.00%
-2.01%
-1.91%
1.89%
-2.53%
3.25%
3.86%
1.40%
0.94%
0.23%
-3.43%
1.80%
1.21%
-1.68%
Date
Feb 04
Jan 04
Dec 03
Nov 03
Oct 03
Sep 03
Aug 03
Jul 03
Jun 03
May 03
Apr 03
Mar 03
Feb 03
Jan 03
Dec 02
Nov 02
Oct 02
Sep 02
Aug 02
Jul 02
AT&T
2.22%
-5.83%
-1.04%
11.95%
-2.89%
9.61%
-0.96%
-3.83%
-7.25%
0.38%
8.97%
18.28%
-3.61%
-14.85%
-9.07%
-4.88%
11.08%
29.35%
-18.76%
-10.55%
S&P500
Index
-1.64%
1.22%
1.73%
5.08%
0.71%
5.50%
-1.19%
1.79%
1.62%
1.13%
5.09%
8.10%
0.84%
-1.70%
-2.74%
-6.03%
5.71%
8.64%
-11.00%
0.49%
a. Compute AT&T’s beta using the above returns.
b. Compare your estimate with the ones found on the Web as listed above.
c. How different will be the required returns using these betas? Compute required
return using each beta (assume that the risk free rate is 5 percent and the market
return will be 13 percent).
SOLUTION:
a. Excel Regression output.
10-17
Chapter 10, Solutions
Cornett, Adair, and Nofsinger
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.679405
R Square
0.461591
Adjusted R Square
0.452308
Standard Error
0.053805
Observations
60
ANOVA
df
Regression
Residual
1
58
SS
0.143951
0.167908
Total
59
0.311859
Coefficients
-0.00177
1.568504
Standard
Error
0.007252
0.222433
Intercept
X Variable 1
MS
0.143951
0.002895
F
49.72478
Significance
F
2.4E-09
t Stat
-0.24387
7.05158
P-value
0.808194
2.4E-09
Lower 95%
-0.01629
1.123256
Upper
95%
0.012748
2.013752
Lower
95.0%
-0.01629
1.123256
b. The beta estimate from the regression is 1.57. This estimate is similar to the ones from
Hoovers (1.5), MSN Money (1.52), and Zacks (1.52). The Yahoo! Finance (0.50) estimate
still seems very low.
c. Required returns using these beta estimates:
Excel estimate = 5% + 1.57 × (13% − 5%) = 17.56%
Hoovers estimate = 5% + 1.5 × (13% − 5%) = 17.0%
MSN Money and Zacks estimate = 5% + 1.52 × (13% − 5%) = 17.16%
Yahoo! Finance estimate = 5% + 0.50 × (13% − 5%) = 9.0%
All the required return estimates are very similar except the Yahoo! Estimate.
10-18
Upper
95.0%
0.012748
2.013752