Chapter 9, Solutions
Cornett, Adair, and Nofsinger
CHAPTER 9 – CHARACTERIZING RISK AND RETURN
Questions
LG1
1. Why is the percentage return a more useful measure than the dollar return?
The dollar return is most important relative to the amount invested. Thus, a $100 return is
more impressive from a $1,000 investment than a $5,000 investment. The percentage
return incorporates both the dollar return and the amount invested. Therefore, it is easier
to compare percentage return across different investments.
LG2
2. Characterize the historical return, risk, and risk-return relationship of the stock, bond
and cash markets.
Examining Table 9.2, it is clear that the stock market has earned about double the return
since 1950 than bonds. Bonds have earned about 50% higher return than the cash
markets. The risk in the stock market is also higher than the bond and cash markets
according to the standard deviation measurement (Table 9.4). Another illustration of the
high risk is that the stock market frequently losses money and sometimes does not earn
more than the bond and cash markets over short periods of time (Table 9.2). The riskreturn relationship tells us that we should expect higher returns for the riskier market. We
do see higher realized returns over the long term to the higher risk asset classes.
LG3
3. How do we define risk in this chapter and how do we measure it?
Risk is defined as the volatility of an asset’s returns over time. Specifically, the standard
deviation of returns is used to measure risk. This computation measures the deviation
from the average return. The idea is to use standard deviation, a measure of volatility of
past returns to proxy for how variable returns are expected to be in the future.
LG3
4. What are the two components of total risk? Which component is part of the risk-return
relationship? Why?
Total risk includes firm specific risk and market risk. The firm specific risk portion can
be eliminated through diversification by owning many different investments. The portion
of total risk that is left after diversifying, market risk, is the risk that is expected to be
rewarded. Thus, market risk in the risk of the risk-return relationship.
LG3
5. What’s the source of firm-specific risk? What’s the source of market risk?
Firm-specific risk stems from the uncertainty arising from micro-events that primarily
impact the firm or industry. Market risk comes from the macro events that impact all
firms to some extent.
9-1
Chapter 9, Solutions
LG3
Cornett, Adair, and Nofsinger
6. Which company is likely to have lower total risk, General Electric or Coca-Cola? Why?
General Electric is a firm that has diversified business lines. It makes kitchen appliances,
medical devices, and own the TV network NBC. Thus, much of GE’s firm specific risk is
reduced. Coca-Cola does not have such business line diversification. So GE’s total risk is
likely to be lower because its firm specific risk is lower.
LG3
7. Can a company change its total risk level over time? How?
A company can change is risk level over time. The company can change the mix of
business lines it pursues. Some industries are riskier than others. For example, the airline
industry has much risk while the utility industry has much less risk. Companies can also
change their risk by changing the amount of money they have borrowed (more borrowing
is riskier).
LG4
8. What does the coefficient of variation measure? Why is a lower value better for the
investor?
The coefficient of variation measures the amount of risk taken for each one percent of
return achieved. It is computed by dividing the standard deviation of return by the total
return. Investors would prefer to achieve a high return with little risk. In other words, they
would like a high return with little standard deviation. This is realized in the coefficient of
variation measure by a lower number.
LG4
9. You receive an investment newsletter advertisement in the mail. The letter claims that
you should invest in a stock that has doubled the return of the S&P 500 Index over the last
three months. It also claims that this stock is a surefire safe bet for the future. Explain how
these two claims are inconsistent with finance theory.
A stock that can earn a large return quickly versus the market is a very volatile stock.
Thus, it is a high risk stock. The stock may indeed increase in the future. However, high
risk means that it could also decrease much in price in the future. It is not a surefire safe
bet.
LG5
10. What does diversification do to the risk and return characteristics of a portfolio?
Diversifying does little for the return of the portfolio. The portfolio return is the weighted
average of the investment returns in the portfolio. However, diversification can do much
for reducing the total risk of the portfolio as measured by the standard deviation. By
combining assets that perform differently in different economic environments, the overall
level of the risk in the portfolio is reduced. In addition, diversifying reduces the firm
specific portion of each asset’s total risk.
9-2
Chapter 9, Solutions
LG5
Cornett, Adair, and Nofsinger
11. Describe the diversification potential of two assets with a −0.8 correlation. What’s
the potential if the correlation is +0.8?
The diversification potential is very good with two assets that have a −0.8 correlation.
Since these two assets tend to move in opposite directions, the combination will greatly
reduce the risk or volatility an investor would experience with only one of the assets.
There is not much diversification potential for two assets with a correlation close to one,
like +0.8.
LG5
12. You are a risk adverse investor with a low-risk portfolio of bonds. How is it possible
that adding some stocks (which are riskier than bonds) to the portfolio can lower the total
risk of the portfolio?
Bonds and stocks have a low correlation (see Table 9.6). In some economic
environments, stocks do well and bonds do not. During other times, bonds do better.
Adding a small portion of stocks to a bond portfolio can actually decrease the volatility of
the portfolio.
LG5
13. You own only two stocks in your portfolio but want to add more. When you add a
third stock, the total risk of your portfolio declines. When you add a tenth stock to the
portfolio, the total risk declines. Adding which stock, the third or the tenth, likely reduced
the total risk more? Why?
A portfolio of two stocks likely still has much firm specific risk left. Assuming that the
stocks are not highly correlated, a nine stock portfolio should already have much of its
firm specific risk diversified away. Therefore, the third stock added has much more
potential for reducing the risk of the portfolio than the tenth stock added.
LG5
14. Many employees believe that their employer’s stock is less likely to lose half of its
value than a well diversified portfolio of stocks. Explain why this belief is erroneous.
A single firm has a lot of firm specific risk. This means that it has more volatility in its
returns than the overall stock market. Remember, high volatility means large price
changes. Also consider that if a well diversified stock portfolio falls by half, this means
large declines for the overall stock market and all firms, including the employer’s stock
(known as market risk). But a large decline in the employer’s stock does not mean a large
decline occurs in the overall market (firm specific risk).
LG6
15. Explain what we mean when we say that one portfolio dominates another portfolio?
A dominate portfolio has a better risk return relationship. This means that it either has
high return for the level of risk taken or lower risk for the level of return achieved. No
investor should want a dominated portfolio.
LG6
16. Explain what the efficient frontier is and why it is important to investors.
9-3
Chapter 9, Solutions
Cornett, Adair, and Nofsinger
The efficient frontier is the set of efficient, or dominating, portfolios. These portfolios
have the highest return for each level of risk desired. Since all other portfolios are
dominated by the efficient frontier portfolios, all investors should and these efficient
portfolios.
LG6
17. If an investor’s desired risk level changes over time, should the investor change the
composition of his or her portfolio? How?
Yes, investors should modify their portfolios to be consistent with their level of risk. For
example, many people want to reduce their level of risk as they approach their retirement
years. One way to change the level of risk in a portfolio is to change the allocation of
stocks and bonds. An increase in bonds would cause a decrease in the risk of the
portfolio.
LG7
18. Say you own 200 shares of Mattel and 100 shares of RadioShack. Would your
portfolio return be different if you instead owned 100 shares of Mattel and 200 shares of
RadioShack? Why?
The portfolio return would be the weighted average of the Mattel and RadioShack stock
returns. The weights are determined by the proportion of money invested in each firm.
The portfolio’s return in these two cases would be different because the proportions of
money invested in each stock are different.
Problems
Basic
Problems
LG1
9-1 Investment Return FedEx Corp stock ended the previous year at $103.39 per share.
It paid a $0.35 per share dividend last year. It ended last year at $106.69. If you owned
300 shares of FedEx, what was your dollar return and percent return?
Dollar Return  Ending Value  Beginning Value   Income  $106.69  300 - $103.39  300  $0.35  300  $1,095
Percentage Return = $1,095 ÷ ($103.39×300) = 0.0353 = 3.53%
LG1
9-2 Investment Return Sprint Nextel Corp stock ended the previous year at $23.36 per
share. It paid a $2.37 per share dividend last year. It ended last year at $18.89. If you
owned 500 shares of Sprint, what was your dollar return and percent return?
Dollar Return  Ending Value  Beginning Value   Income  $18.89  500 - $23.36  500  $2.37  500  $1,050
Percentage Return = -$1,050 ÷ ($23.36×500) = -0.0899 = -8.99%
LG3
9-3 Total Risk Rank the following three stocks by their level of total risk, highest to
lowest. Rail Haul has an average return of 12 percent and standard deviation of 25
9-4
Chapter 9, Solutions
Cornett, Adair, and Nofsinger
percent. The average return and standard deviation of Idol Staff are 15 percent and 35
percent; and of Poker-R-Us are 9 percent and 20 percent.
Rank by standard deviation: Idol Staff, Rail Haul, and then Poker-R-Us
LG3
9-4 Total Risk Rank the following three stocks by their total risk level, highest to lowest.
Night Ryder has an average return of 13 percent and standard deviation of 29 percent.
The average return and standard deviation of WholeMart are 11 percent and 25 percent;
and of Fruit Fly are 16 percent and 40 percent.
Rank by standard deviation: Fruit Fly, Night Ryder, and then WholeMart
LG4
9-5 Risk versus Return Rank the following three stocks by their risk-return relationship,
best to worst. Rail Haul has an average return of 12 percent and standard deviation of 25
percent. The average return and standard deviation of Idol Staff are 15 percent and 35
percent; and of Poker-R-Us are 9 percent and 20 percent.
Rank by coefficient of variation: Rail Haul
CoV=20/9=2.22, and Idol Staff CoV=35/15=2.33.
LG4
CoV=25/12=2.08,
Poker-R-Us
9-6 Risk versus Return Rank the following three stocks by their risk-return relationship,
best to worst. Night Ryder has an average return of 13 percent and standard deviation of
29 percent. The average return and standard deviation of WholeMart are 11 percent and
25 percent; and of Fruit Fly are 16 percent and 40 percent.
Rank by coefficient of variation: Night Ryder CoV=29/13=2.23, WholeMart
CoV=25/11=2.27, and Fruit Fly CoV=40/16=2.5.
LG6
9-7 Dominant Portfolios Determine which one of these three portfolios dominates
another. Name the dominated portfolio and the portfolio that dominates it. Portfolio Blue
has an expected return of 12 percent and risk of 18 percent. The expected return and risk
of portfolio Yellow are 13 percent and 17 percent, and for the Purple portfolio are 14
percent and 20 percent.
Portfolio Yellow dominates Portfolios Blue and Purple because it has both a higher
expected return and a lower risk level.
LG6
9-8 Dominant Portfolios Determine which one of the three portfolios dominates another.
Name the dominated portfolio and the portfolio that dominates it. Portfolio Green has an
expected return of 15 percent and risk of 21 percent. The expected return and risk of
portfolio Red are 13 percent and 17 percent, and for the Orange portfolio are 13 percent
and 16 percent.
9-5
Chapter 9, Solutions
Cornett, Adair, and Nofsinger
Portfolio Orange dominates Portfolios Red and Green because it has the same or lower
expected return with a lower risk level.
LG7
9-9 Portfolio Weights An investor owns $4,000 of Adobe Systems stock, $5,000 of Dow
Chemical, and $6,000 of Office Depot. What are the portfolio weights of each stock?
Total portfolio is $4,000 + $5,000 + $6,000 = $15,000
Adobe System weight = $4,000 / $15,000 = 0.2667
Dow Chemical weight = $5,000 / 15,000 = 0.3333
Office Depot weight = $6,000 / $15,000 = 0.4
LG7
9-10 Portfolio Weights An investor owns $3,000 of Adobe Systems stock, $6,000 of
Dow Chemical, and $7,000 of Office Depot. What are the portfolio weights of each
stock?
Total portfolio is $3,000 + $6,000 + $7,000 = $16,000
Adobe System weight = $3,000 / $16,000 = 0.1875
Dow Chemical weight = $6,000 / 16,000 = 0.375
Office Depot weight = $7,000 / $16,000 = 0.4375
LG7
9-11 Portfolio Return Year-to-date, Oracle had earned a −1.34 percent return. During
the same time period, Valero Energy earned 7.96 percent and McDonalds earned 0.88
percent. If you have a portfolio made up of 30 percent Oracle, 20 percent Valero Energy,
and 50 percent McDonalds, what is your portfolio return?
Portfolio Return is 0.3×−1.34% + 0.2×7.96% + 0.5×0.88% = 1.63%
LG7
9-12 Portfolio Return Year to date, Yum Brands had earned a 3.80 percent return.
During the same time period, Raytheon earned 4.26 percent and Coca-Cola earned −0.46
percent. If you have a portfolio made up of 30 percent Yum Brands, 30 percent Raytheon,
and 40 percent Coca-Cola, what is your portfolio return?
Portfolio Return is 0.3×3.80% + 0.3×4.26% + 0.4×−0.46% = 2.23%
Intermediate
Problems 9-13 Average Return The past five monthly returns for Kohl’s are 3.54 percent, 3.62
percent, −1.68 percent, −1.42 percent, and 8.75 percent. What is the average monthly
LG1
return?
Average Return = (3.54%+3.62%−1.68%−1.42%+8.75%) / 5 = 2.562%
LG1
9-14 Average Return The past five monthly returns for PG&E are 2.14 percent, −1.37
percent, 3.77 percent, 6.47 percent, and 3.58 percent. What is the average monthly return?
9-6
Chapter 9, Solutions
Cornett, Adair, and Nofsinger
Average Return = (2.14%−1.37%+3.77%+6.47%+3.58%) / 5 = 2.918%
LG3
9-15 Standard Deviation Compute the standard deviation of Kohls’ monthly returns
shown in Problem 9-13.
3.54%  2.562%2  3.62%  2.562%2   1.68%  2.562%2   1.42%  2.562%2  8.75%  2.562%2
5 1
LG3
 4.31%
9-16 Standard Deviation Compute the standard deviation of PG&E’s monthly returns
shown in Problem 9-14.
2.14%  2.918%2   1.37%  2.918%2  3.77%  2.918%2  6.47%  2.918%2  3.58%  2.918%2
5 1
 2.86%
LG2&4 9-17 Risk versus Return in Bonds Assess the risk-return relationship of the bond market
(see Tables 9.2 and 9.4) during each decade since 1950.
Compute the coefficient of variation for each decade using the standard deviation and
average return:
Decade
CoV
1950s
NA
1960s
3.85
1970s
1.19
1980s
1.12
1990s
1.35
2000s
0.77
The lower the coefficient of variation, the better the risk-return relationship. The early two
decades, 1950s and 1960s, have a poor risk return relationship for bonds. The 1950s
coefficient of variation is not defined because the average is zero. The poor relationship in
the 1950s is caused by the very low return in that decade. The three full decades since
1970 have had good risk-return relationship.
LG2&4 9-18 Risk versus Return in T-bills Assess the risk-return relationship in T-bills (see
Tables 9.2 and 9.4) during each decade since 1950.
Compute the coefficient of variation for each decade using the standard deviation and
average return:
Decade
1950s
1960s
1970s
1980s
CoV
0.40
0.33
0.29
0.29
9-7
Chapter 9, Solutions
Cornett, Adair, and Nofsinger
1990s
0.24
2000s
0.55
The lower the coefficient of variation, the better the risk-return relationship. All these
CoVs are very low. While they appear to have great risk-return relationships, it is because
the risk is very low. T-bills are very safe instruments. However, they offer very low
returns.
LG4&5 9-19 Diversifying Consider the characteristics of the following three stocks:
Expected
Standard
Return
Deviation
Thumb
13%
23%
Devices
Air Comfort
10%
19%
Sport Garb
10%
17%
The correlation between Thumb Devices and Air Comfort is −0.12. The correlation
between Thumb Devices and Sport Garb is −0.13. The correlation between Air Comfort
and Sport Garb is 0.85. If you can pick only two stocks for your portfolio, which would
you pick? Why?
Air Comfort and Sport Garb have similar expected returns and standard deviations. Since
their correlation is very high, not much risk will be reduced when combined. Combining
either stock with Thumb Devices has good potential because it has higher return and they
have low (negative) correlation it. Since Sport Garb has both lower risk (standard
deviation) and lower correlation with Thumb Devices than does Air Comfort, combine
Sport Garb and Thumb Devices.
LG4&5 9-20 Diversifying Consider the characteristics of the following three stocks:
Expected
Standard
Return
Deviation
Pic Image
11%
19%
Tax Help
10%
19%
Warm Wear
14%
24%
The correlation between Pic Image and Tax Help is 0.88. The correlation between Pic
Image and Warm Wear is −0.21. The correlation between Tax Help and Warm Wear is
−0.19. If you can pick only two stocks for your portfolio, which would you pick? Why?
Pic Image and Tax Help have similar expected returns and standard deviations. Since
their correlation is very high, not much risk will be reduced when combined. Combining
either stock with Warm Wear has good potential because it has higher return and they
have low (negative) correlation it. Since Pic Image has both higher expected return and
lower correlation with Warm Wear than does Tax Help, combine Pic Image and Warm
Wear.
9-8
Chapter 9, Solutions
LG7
Cornett, Adair, and Nofsinger
9-21 Portfolio Weights If you own 300 shares of Alaska Air at $42.88, 350 shares of Best
Buy at $51.32, and 250 shares of Ford Motor at $8.51, what are the portfolio weights of
each stock?
Total portfolio is 300×$42.88 + 350×$51.32 + 250×$8.51 = $32,953.50
Alaska Air weight = 300×$42.88 / $32,953.50 = 0.390
Best Buy weight = 350×$51.32 / $32,953.50 = 0.545
Ford Motor weight = 250×$8.51 / $32,953.50 = 0.065
LG7
9-22 Portfolio Weights If you own 400 shares of Xerox at $17.34, 500 shares of Qwest at
$8.15, and 350 shares of Liz Claiborne at $44.73, what are the portfolio weights of each
stock?
Total portfolio is 400×$17.34 + 500×$8.15 + 350×$44.73 = $26,666.50
Xerox weight = 400×$17.34 / $26,666.50 = 0.260
Qwest weight = 500×$8.15 / $26,666.50 = 0.153
Liz Claiborne weight = 350×$44.73 / $26,666.50 = 0.587
LG7
9-23 Portfolio Return At the beginning of the month, you owned $5,500 of General
Motors, $7,500 of Starbucks, and $9,000 of Nike. The monthly returns for General
Motors, Starbucks, and Nike were 6.80 percent, −1.36 percent, and −0.22 percent. What
is your portfolio return?
Total portfolio is $5,500 + $7,500 + $9,000 = $22,000
General Motors weight = $5,500 / $22,000 = 0.25
Starbucks weight = $7,500 / $22,000 = 0.341
Nike weight = $9,000 / $22,000 = 0.409
So Portfolio Return is 0.25×6.80% + 0.341×−1.36% + 0.409×−0.22% = 1.15%
LG7
9-24 Portfolio Return At the beginning of the month, you owned $6,000 of News Corp,
$5,000 of First Data, and $8,500 of Whirlpool. The monthly returns for News Corp, First
Data, and Whirlpool were 8.24 percent, −2.59 percent, and 10.13 percent. What’s your
portfolio return?
Total portfolio is $6,000 + $5,000 + $8,500 = $19,500
News Corp weight = $6,000 / $19,500 = 0.308
First Data weight = $5,000 / $19,500 = 0.256
Whirlpool weight = $8,500 / $19,500 = 0.436
So Portfolio Return is 0.308×8.24% + 0.256×−2.59% + 0.436×10.13% = 6.29%
Advanced
Problems
9-25 Asset Allocation You have a portfolio with an asset allocation of 50 percent stocks,
9-9
Chapter 9, Solutions
LG2&5
Cornett, Adair, and Nofsinger
40 percent long-term Treasury Bonds, and 10 percent T-bills. Use these weights and the
returns in Table 9.2 to compute the return of the portfolio in the year 2000 and each year
since. Then compute the average annual return and standard deviation of the portfolio and
compare them with the risk and return profile of each individual asset class.
These answers were computed using a spreadsheet. The portfolio return is computed as:
0.5×-9.1% + 0.4×20.11% +0.1×5.9% = 4.08%
Portfolio
Stocks Bonds T-bills Return
2000
-9.1% 20.11%
5.9%
4.08%
2001 -11.9% 4.56%
3.5%
-3.78%
2002 -22.1% 17.17%
1.6%
-4.02%
2003 28.7% 2.06%
1.0%
15.27%
2004 10.9% 7.70%
1.4%
8.67%
2005
4.9% 6.50%
3.1%
5.37%
2006 15.8% 1.85%
4.7%
9.11%
2007
3.5% 9.81%
3.4%
6.01%
Ave =
2.59%
StdDev= 16.42%
8.72%
6.73%
3.08%
1.70%
5.09%
6.51%
The portfolio has the second highest return with the second lowest risk. Combining these
assets achieved some risk reduction.
LG2&5 9-26 Asset Allocation You have a portfolio with an asset allocation of 60 percent stocks,
30 percent long-term Treasury Bonds, and 10 percent T-bills. Use these weights and the
returns in Table 9.2 to compute the return of the portfolio in the year 2000 and each year
since. Then compute the average annual return and standard deviation of the portfolio and
compare them with the risk and return profile of each individual asset class.
These answers were computed using a spreadsheet. The portfolio return is computed as:
0.6×-9.1% + 0.3×20.11% +0.1×5.9% = 1.16%
Portfolio
Stocks Bonds T-bills Return
2000
-9.1% 20.11%
5.9%
1.16%
2001 -11.9% 4.56%
3.5%
-5.42%
2002 -22.1% 17.17%
1.6%
-7.95%
2003 28.7% 2.06%
1.0%
17.94%
2004 10.9% 7.70%
1.4%
8.99%
2005
4.9% 6.50%
3.1%
5.20%
2006 15.8% 1.85%
4.7%
10.51%
2007
3.5% 9.81%
3.4%
5.38%
Ave =
2.59%
8.72%
3.08%
4.48%
9-10
Chapter 9, Solutions
StdDev= 16.42%
Cornett, Adair, and Nofsinger
6.73%
1.70%
8.47%
The portfolio has the second highest return with the second highest risk. Combining these
assets achieved some risk reduction.
LG7
9-27 Portfolio Weights You have $15,000 to invest. You want to purchase shares of
Alaska Air at $42.88, Best Buy at $51.32, and Ford Motor at $8.51. How many shares of
each company should you purchase so that your portfolio consists of 30 percent Alaska
Air, 40 percent Best Buy, and 30 percent Ford Motor? Report only whole stock shares.
Alaska Air: 0.30×$15,000÷$42.88 = 105 shares
Best Buy: 0.40×$15,000÷$51.32 = 117 shares
Ford Motor: 0.30×$15,000÷$8.51 = 528 shares
Because of rounding up, this adds up to slightly more than $15,000. So, one less share of
one of these stocks should be purchased.
LG7
9-28 Portfolio Weights You have $20,000 to invest. You want to purchase shares of
Xerox at $17.34, Qwest at $8.15, and Liz Claiborne at $44.73. How many shares of each
company should you purchase so that your portfolio consists of 25 percent Xerox, 40
percent Qwest, and 35 percent Liz Claiborne? Report only whole stock shares.
Xerox: 0.25×$20,000÷$17.34 = 288 shares
Qwest: 0.40×$20,000÷$8.15 = 982 shares
Liz Claiborne: 0.35×$20,000÷$44.73 = 156 shares
Excluding commissions paid, you will still have a cash balance of $24.90.
LG7
9-29 Portfolio Return The table below shows your stock positions at the beginning of the
year, the dividends that each stock paid during the year, and the stock prices a the end of
the year. What is your portfolio dollar return and percentage return?
Beginning Dividend
End of
Company
Shares
of Year
per share
Year
Price
Price
Washington Mutual
300
$43.50
$2.06
$43.43
PepsiCo
200
$59.08
$1.16
$62.55
JDS Uniphase
500
$18.88
$16.66
Duke Energy
250
$27.45
$1.26
$33.21
Solution by spreadsheet:
Company
beginning
value
Washington
Mutual
$13,050.00
PepsiCo
$11,816.00
JDS
$9,440.00
portfolio
weight
Capital
Gain
Income
0.31699
($21.00) $618.00
0.287016
$694.00 $232.00
0.229302 ($1,110.00)
$0.00
9-11
Total Return
$597.00
$926.00
($1,110.00)
Percentage
Return
4.57%
7.84%
-11.76%
Chapter 9, Solutions
Uniphase
Duke
Energy
total =
LG7
Cornett, Adair, and Nofsinger
$6,862.50 0.166693
$41,168.50
$1,440.00 $315.00
$1,755.00
25.57%
$2,168.00
Portfolio
Return =
5.27%
9-30 Portfolio Return The table below shows your stock positions at the beginning of the
year, the dividends that each stock paid during the year, and the stock prices a the end of
the year. What is your portfolio dollar return and percentage return?
Beginning Dividend
End of
Company
Shares
of Year
per share
Year
Price
Price
Johnson Controls
300
$72.91
$1.17
$85.92
Medtronic
200
$57.57
$0.41
$53.51
Direct TV
500
$24.94
$24.39
Qualcomm
250
$43.08
$0.45
$37.79
Solution by spreadsheet:
Company beginning
value
Johnson
Controls
$21,873.00
Medtronic $11,514.00
Direct TV $12,470.00
Qualcomm $10,770.00
total =
$56,627.00
portfolio
weight
Capital
Gain
Income
0.386265
$3,903.00 $351.00
0.203331
($812.00) $82.00
0.220213
($275.00)
$0.00
0.190192 ($1,322.50) $112.50
Total Return
Percentage
Return
$4,254.00
19.45%
($730.00)
-6.34%
($275.00)
-2.21%
($1,210.00)
-11.23%
$2,039.00
Portfolio
Return =
3.60%
LG3&4 9-31 Risk, Return, and Their Relationship Consider the following annual returns of
Estee Lauder and Lowe’s Companies:
Estee Lauder
Lowe’s
Companies
2006
23.4%
−6.0%
2005
−26.0%
16.1%
2004
17.6%
4.2%
2003
49.9%
48.0%
2002
−16.8%
−19.0%
Compute each stock’s average return, standard deviation, and coefficient of variation.
Which stock appears better? Why?
9-12
Chapter 9, Solutions
Cornett, Adair, and Nofsinger
Solution by spreadsheet:
Estee
Lowe’s
Lauder Companies
Ave =
30.30%
22.77%
StDev=
17.22%
22.65%
CoV = 0.568318
0.994799
Estee Lauder has experienced a higher average return then Lowe’s with a lower risk
(standard deviation). Thus, it is not a surprise that Estee Lauder has a better (lower)
coefficient of variation. Estee Lauder was better.
LG3&4 9-32 Risk, Return, and Their Relationship Consider the following annual returns of
Molson Coors and International Paper:
Molson Coors
International
Paper
2006
16.3%
4.5%
2005
−9.7%
−17.5%
2004
36.5%
−0.2%
2003
−6.9%
26.6%
2002
16.2%
−11.1%
Compute each stock’s average return, standard deviation, and coefficient of variation.
Which stock appears better? Why?
Solution by spreadsheet:
Molson International
Coors
Paper
Ave =
23.00%
15.55%
StDev=
11.69%
15.63%
CoV = 0.508324
1.004956
Molson Coors has experienced a higher average return then IP with a lower risk (standard
deviation). Thus, it is not a surprise that Molson Coors has a better (lower) coefficient of
variation. Molson Coors was better.
9-33 Excel Problem Below are the monthly returns for May 2002 to June 2007 of three
international stock indices; All Ordinaries of Australia, Nikkei 225 of Japan, and FTSE
100 of England.
9-13
Chapter 9, Solutions
Date
Jun 2007
May
2007
Apr
2007
Mar
2007
Feb 2007
All
Ordinaries
(Australia)
Cornett, Adair, and Nofsinger
Nikkei
225
(Japan)
FTSE
100
(England)
1.82%
0.55%
1.65%
-0.49%
1.47%
-0.20%
2.98%
2.73%
2.67%
3.00%
2.79%
0.65%
-1.80%
2.24%
2.21%
Jan 2007
Dec
2006
Nov
2006
1.02%
1.27%
-0.51%
2.01%
0.91%
-0.28%
3.35%
5.85%
2.84%
Oct 2006
2.03%
-0.76%
-1.31%
Sep 2006
Aug
2006
4.69%
1.69%
2.83%
0.65%
-0.08%
0.93%
Jul 2006
2.48%
4.42%
-0.37%
Jun 2006
May
2006
Apr
2006
Mar
2006
Feb 2006
-1.53%
-0.31%
1.63%
1.24%
0.24%
1.91%
-4.51%
-8.51%
-4.97%
2.35%
4.28%
-0.90%
5.27%
0.98%
2.99%
Jan 2006
Dec
2005
Nov
2005
-0.04%
-2.67%
0.54%
3.64%
3.34%
2.52%
2.73%
8.33%
3.61%
Oct 2005
3.87%
9.30%
1.99%
Sep 2005
Aug
2005
-3.92%
0.24%
-2.93%
4.06%
9.35%
3.41%
Jul 2005
1.54%
4.32%
0.28%
Jun 2005
May
2005
2.76%
2.72%
3.31%
3.92%
2.73%
3.01%
Date
Nov
2004
Oct
2004
Sep
2004
Aug
2004
Jul 2004
Jun
2004
May
2004
Apr
2004
Mar
2004
Feb
2004
Jan
2004
Dec
2003
Nov
2003
Oct
2003
Sep
2003
Aug
2003
Jul 2003
Jun
2003
May
2003
Apr
2003
Mar
2003
Feb
2003
Jan
2003
Dec
2002
Nov
2002
Oct
2002
9-14
All
Ordinaries
(Australia)
Nikkei
225
(Japan)
FTSE
100
(England)
2.80%
5.41%
2.36%
4.13%
1.19%
1.71%
3.04%
-0.48%
1.17%
3.17%
0.45%
-2.33%
-2.15%
2.50%
1.05%
0.45%
-4.50%
-1.14%
2.12%
5.54%
0.75%
1.44%
-4.47%
-1.31%
-0.25%
0.40%
2.37%
1.30%
6.10%
-2.37%
2.71%
2.40%
2.31%
-0.68%
1.00%
-1.93%
3.45%
5.70%
3.09%
-2.64%
-4.35%
1.28%
3.34%
3.33%
4.80%
-0.83%
3.10%
-1.20%
8.16%
-1.68%
0.10%
3.59%
5.29%
3.12%
0.64%
7.82%
-0.42%
0.30%
7.57%
3.11%
4.29%
-1.77%
8.65%
2.53%
-4.67%
-1.16%
-5.35%
0.28%
2.47%
-1.35%
-2.79%
-9.47%
-1.64%
-6.91%
-5.49%
1.01%
6.66%
3.21%
Chapter 9, Solutions
Apr
2005
Mar
2005
Feb 2005
Jan 2005
Dec
2004
Cornett, Adair, and Nofsinger
3.23%
2.43%
3.38%
-3.84%
-1.34%
-5.66%
-0.61%
-1.89%
-1.49%
1.21%
3.10%
2.39%
1.32%
-0.88%
0.79%
Sep
2002
Aug
2002
Jul 2002
Jun
2002
May
2002
2.28%
-7.92%
8.54%
-4.73%
1.36%
-2.45%
-2.62%
-11.96%
-0.45%
-4.13%
-7.00%
-8.81%
-4.87%
-9.71%
-8.43%
A. Compute and compare each indices’ monthly average return and standard deviation.
B. Compute the correlation between i) All Ordinaries and Nikkei 225, ii) All Ordinaries
and FTSE 100, and iii) Nikkei 225 and FTSE 100, and compare them.
C. Form a portfolio consisting of one third of each of the indices and show the portfolio
return each year, and the portfolio’s return and standard deviation.
A.
All
Ordinaries
(Australia)
1.10%
Nikkei
225
(Japan)
0.81%
FTSE 100
(England)
0.52%
Ave =
StDev
=
2.62%
4.53%
3.69%
The All Ordinaries index had the highest monthly return with the lowest risk. The FTSE
100 had the lowest return and had the middle level of risk.
B. Correlations
All
Ordinaries
(Australia)
All Ordinaries
(Australia)
Nikkei 225 (Japan)
FTSE 100 (England)
1
0.559
0.692
Nikkei
225
(Japan)
1
0.442
FTSE 100
(England)
1
The Nikkei and the FTSE are the least correlated. The All Ordinaries and the FTSE have
the highest correlation.
C.
Portfolio
0.81%
3.02%
9-15
Chapter 9, Solutions
Cornett, Adair, and Nofsinger
Research It!
Following a Portfolio
Following stocks in a portfolio is easier than ever. Many financial websites have the
capability to follow the stocks in your portfolio over time. Just enter your stocks, the
number of shares, your purchase price, and your commission cost and you can see how
your portfolio is doing. These portfolio managers will update your portfolio as stock
prices change, minute to minute. Yahoo! Finance has a portfolio management tool. Go to
the site and start a portfolio to watch (which required free registration). Try entering
symbols EBAY, T, LMT, DUK, and GSK. As a start, assume you own 200 shares of
each. You watch the value of the portfolio change and see how each stock is doing every
day.
(http://finance.yahoo.com/)
The portfolio might look something like this:
Integrated Mini Case: Diversifying with Other Asset Classes
Many more types of investments are available besides stocks, bonds, and cash securities.
Many people invest in real estate and in precious metals, primarily gold. What is the risk
and return characteristics of these investments and do they provide diversification
opportunities to the typical stock investor?
You can invest in real estate in many ways. You can build properties, own rental
units, and trade raw land. These activities take enormous time and expertise. One of the
easiest ways to invest in real estate is through real estate investment trusts (REITs) that
trade like stocks on the stock exchanges. A REIT represents ownership in a portfolio
consisting of a pool of real estate assets. An index of all REITs is a good measure of the
performance of the real estate market. The table below shows the annual returns for the
All REITs Index along side the returns of the S&P 500 Index.
9-16
Chapter 9, Solutions
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
S&P 500
Index
37.2%
23.8%
-7.2%
6.6%
18.4%
32.4%
-4.9%
21.4%
22.5%
6.3%
32.2%
18.5%
5.2%
16.8%
31.5%
-3.2%
30.6%
7.7%
10.0%
1.3%
37.4%
23.1%
33.4%
28.6%
21.0%
-9.1%
-11.9%
-22.1%
28.7%
10.9%
4.9%
15.8%
3.5%
Cornett, Adair, and Nofsinger
All
REITs
Index
36.3%
49.0%
19.1%
-1.6%
30.5%
28.0%
8.6%
31.6%
25.5%
14.8%
5.9%
19.2%
-10.7%
11.4%
-1.8%
-17.3%
35.7%
12.2%
18.5%
0.8%
18.3%
35.8%
18.9%
-18.8%
-6.5%
25.9%
15.5%
5.2%
38.5%
30.4%
8.3%
34.4%
-17.8%
Gold
Price
Changes
-19.9%
-4.1%
22.6%
37.0%
126.5%
15.2%
-32.6%
14.9%
-16.3%
-19.2%
5.7%
21.3%
22.2%
-15.3%
-2.8%
-1.5%
-10.1%
-5.7%
17.7%
-2.2%
1.0%
-4.6%
-21.4%
-0.8%
0.9%
-5.4%
0.7%
25.6%
19.9%
4.6%
17.8%
24.0%
31.1%
Gold has been a highly sought-after asset all over the world, and has retained at
least some economic value over thousands of years. The United States has had a very
chaotic history with gold. Americans have sought to “strike it rich” through gold rushes
in North Carolina (early 1800s), California and Nevada (mid-1800s), and Alaska (late
1800s). Struggling in the Great Depression, President Franklin D. Roosevelt ordered U.S.
citizens to hand in all the gold they possessed. The ban on U.S. citizens owning gold was
not lifted until the end of 1974.. The table also shows the return from gold prices.
9-17
Chapter 9, Solutions
Cornett, Adair, and Nofsinger
The returns for stocks, real estate, and gold are all volatile. However, during many
years, the return of one asset is up while the others are down. This looks promising for
diversification opportunities.
A. Using a spreadsheet, compute the average return and standard deviation of each of
the three asset class.
B. Compute the annual returns of a portfolio consisting of 50% stocks / 40% real
estate / 10% gold. What is the average return and standard deviation of this portfolio?
Also compute the average return and standard deviation of the following portfolios:
75%/20%/5% and 80%/5%/15%. How do these portfolios perform compared to
owning just stocks?
C. Plot the average return and standard deviation of the three assets and the three
portfolios on a risk-return graph like Figure 9.3.
SOLUTION:
A.
S&P 500 All REITs Gold
Index
Index
Price
Ave =
14.3%
15.3%
7.5%
Std. Dev.=
15.6%
17.7% 27.2%
B.
50/40/10 75/20/5 80/5/15
Ave =
14.0% 14.1% 13.3%
Std.
Dev.=
12.3% 13.2% 13.0%
The first two portfolios would have had similar returns as the all stock portfolio, but both
would have had lower risk. Thus, these two portfolios performed better than the all stock
portfolio.
9-18
Chapter 9, Solutions
Cornett, Adair, and Nofsinger
C.
18.0%
16.0%
14.0%
Average Return
12.0%
50/40/10
75/20/5
10.0%
80/5/15
S&P 500 Index
8.0%
All REITs Index
Gold Price
6.0%
4.0%
2.0%
0.0%
5.0%
10.0%
15.0%
20.0%
25.0%
Standard Deviation of Annual Returns
9-19
30.0%