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Chapter 11 - Introduction to Risk, Return, and the Opportunity Cost of Capital
Solutions to Chapter 11
Introduction to Risk, Return, and the Opportunity Cost of Capital
1.
Rate of return 
capital gain  dividend
($44  $40)  $2

 0.15  15.0%
initial share price
$40
Dividend yield = dividend/initial share price = $2/$40 = 0.05 = 5%
Capital gains yield = capital gain/initial share price = $4/$40 = 0.10 = 10%
Est time: 01–05
2.
Dividend yield = $2/$40 = 0.05 = 5%
The dividend yield is unaffected; it is based on the initial price, not the final price.
Capital gain = $36 – $40 = $4
Capital gains yield = –$4/$40 = –0.10 = –10%
Est time: 01–05
3.
a.
Rate of return 
capital gain  dividend
($38  $40)  $2

 0%
initial share price
$40
Real rate of return 
b.
Rate of return 
($40  $40)  $2
 0.05  5%
$40
Real rate of return 
c.
Rate of return 
1  nominal rate of return
1 0
1 
 1  0.0385  3.85%
1  inflation rate
1  0.04
1  nominal rate of return
1.05
1 
 1  0.0096  0.96%
1  inflation rate
1.04
($42  $40)  $2
 0.10  10%
$40
Real rate of return 
1  nominal rate of return
1.10
1 
 1  0.0577  5.77%
1  inflation rate
1.04
Est time: 01–05
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Chapter 11 - Introduction to Risk, Return, and the Opportunity Cost of Capital
4.
Real rate of return 
1  nominal rate of return
1
1  inflation rate
Costaguana: Real return 
1.95
 1  0.0833  8.33%
1.80
United States: Real return 
1.12
 1  0.0980  9.80%
1.02
The United States provides the higher real rate of return despite the lower nominal rate
of return.
Notice that the approximate relationship between real and nominal rates of return is
valid only for low rates:
Real rate of return  nominal rate of return – inflation rate
This approximation incorrectly suggests that the Costaguanan real rate was higher than
the U.S. real rate.
Est time: 01–05
5.
We use the following relationship:
Real rate of return 
Asset Class
Treasury bills
Treasury bonds
Common stocks
1  nominal rate of return
1
1  inflation rate
Nominal Rate
of Return
4.0%
5.2%
11.4%
Inflation Rate
3.1%
3.1%
3.1%
Real Rate
of Return
0.87%
2.04%
8.05%
Est time: 01–05
6.
The nominal interest rate cannot be negative. If it were, investors would choose to hold
cash (which pays a rate of return equal to zero) rather than buy a Treasury bill providing
a negative return. On the other hand, the real expected rate of return is negative if the
inflation rate exceeds the nominal return.
Est time: 01–05
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Chapter 11 - Introduction to Risk, Return, and the Opportunity Cost of Capital
7.
Year
Average Price of
Stocks in Market
Index (using
DJIA method)
Total Market
Value of Stocks
Index (using
S&P method)
2005
74.810
100.00
20,166.20
100.00
2006
98.710
131.95
25,121.48
124.57
2007
105.360
140.84
26,111.82
129.48
2008
84.202
112.55
21,276.14
105.50
2009
102.372
136.84
24,359.74
120.79
2010
97.304
130.07
24,015.40
119.09
Est time: 06–10
8.
a.
For the period 1900–2010, average rate of return = 11.4% (see Table 11-1).
b.
For the period 1900–2010, average risk premium = 7.4% (see Table 11-1).
c.
For the period 1900–2010, standard deviation of returns = 20% (see Table 11-4).
Est time: 01–05
9.
a.
Year
Stock
Market
Return
2006
2007
2008
2009
2010
15.77
5.61
–37.23
28.30
17.16
Total
Average
T-Bill
Return
4.80
4.66
1.60
0.10
0.12
Risk
Premium
Deviation
from Mean
10.97
0.95
–38.83
28.20
17.04
18.33
3.67
7.30
–2.72
–42.50
24.53
13.37
Squared
Deviation
53.35
7.38
1,805.91
601.92
178.86
2,647.42
529.48
b.
The average risk premium was 3.67%.
c.
The variance (the average squared deviation from the mean) was 529.48.
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Chapter 11 - Introduction to Risk, Return, and the Opportunity Cost of Capital
Therefore: Standard deviation =
529.48  23.01%
Est time: 11–15
10. In 2010, the Dow was nearly four times its 1990 level. Therefore, in 2010, a 40-point
movement was far less significant in percentage terms than it was in 1990. We would
expect to see more 40-point days in 2010 even if market risk as measured by percentage
returns is no higher than it was in 1990.
Est time: 01–05
11.
Investors would not have invested in bonds during the period 1977–1981 if they had
expected to earn negative average returns. Unanticipated events must have led to these
results. For example, inflation and nominal interest rates during this period rose to
levels not seen for decades. These increases, which resulted in large capital losses on
long-term bonds, were almost certainly unanticipated by investors who bought those
bonds in prior years.
The results for this period demonstrate the perils of attempting to measure “normal”
maturity (or risk) premiums from historical data. While experience over long periods
may be a reasonable guide to normal premiums, the realized premium over short
periods may contain little information about expectations of future premiums.
Est time: 06–10
12. If investors become less willing to bear investment risk, they will require a higher risk
premium to compensate them for holding risky assets. Security prices of risky
investments will fall until the expected rates of return on those securities rise to the
now-higher required rates of return.
Est time: 01–05
13.
Based on the historical risk premium of the S&P 500 (7.6%) and the current level of
the risk-free rate (about 3.5%), one would predict an expected rate of return of 11.1%.
If the stock has the same systematic risk, it also should provide this expected return.
Therefore, the stock price equals the present value of cash flows for a 1-year horizon.
P0 
$2  $50
 $46.80
1.111
Est time: 01–05
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Chapter 11 - Introduction to Risk, Return, and the Opportunity Cost of Capital
14.
Boom:
$8  ($240  $80)
 210%
$80
Normal:
$4  ($90  $80)
 18%
$80
Recession:
r
$0  ($0  $80)
 100%
$80
210  18  (100)
 42.5%
3
Variance =
1
1
1
 (210  42.5) 2   (18  42.5) 2   (100  42.5) 2  16,320.92
3
3
3
Standard deviation = variance = 127.75%
Est time: 06–10
15. The bankruptcy lawyer does well when the rest of the economy is floundering but does
poorly when the rest of the economy is flourishing and the number of bankruptcies is
down. Therefore, the Leaning Tower of Pita is a risk-reducing investment. When the
economy does well and the lawyer’s bankruptcy business suffers, the stock return is
excellent, thereby stabilizing total income.
Est time: 01–05
16.
Escapist Films:
Boom:
$0  ($18  $25)
 28%
$25
Normal:
$1  ($26  $25)
 8%
$25
Recession:
r
$3  ($34  $25)
 48%
$25
( 28)  8  48
 9.33%
3
Variance =
1
1
1
 (28  9.33) 2   (8  9.33) 2   (48  9.33) 2  963.56
3
3
3
Standard deviation = variance = 31.04%
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Chapter 11 - Introduction to Risk, Return, and the Opportunity Cost of Capital
Portfolio rate of return:
Boom: (28 + 210)/2 = 91%
Normal: (8 + 18)/2 = 13%
Recession: (48 –100)/2 = –26%
Expected return = 26%
1
1
1
 (91  26) 2   (13  26) 2   (26  26) 2  2,366
3
3
3
Standard deviation = variance = 48.64%
Variance =
Est time: 11–15
17. a.
b.
Interest rates tend to fall at the outset of a recession and rise during boom periods.
Because bond prices move inversely with interest rates, bonds provide higher
returns during recessions when interest rates fall.
rstock = [0.2  (5%)] + (0.6  15%) + (0.2  25%) = 13.0%
rbonds = (0.2  14%) + (0.6  8%) + (0.2  4%) = 8.4%
Variance (stocks) = [0.2  (5  13)2] + [0.6  (15  13)2] + [0.2  (25 – 13)2] = 96
Standard deviation = 96  9.80%
Variance (bonds) = [0.2  (14  8.4)2] + [0.6  (8  8.4)2] + [0.2  (4  8.4)2] = 10.24
Standard deviation = 10.24  3.20%
c.
Stocks have both higher expected return and higher volatility. More riskaverse investors will choose bonds, while those who are less risk-averse
might choose stocks.
Est time: 06–10
18. a.
b.
Recession:
(5%  0.6) + (14%  0.4) = 2.6%
Normal economy:
(15%  0.6) + (8%  0.4) = 12.2%
Boom:
(25%  0.6) + (4%  0.4) = 16.6%
Expected return = (0.2  2.6%) + (0.6  12.2%) + (0.2  16.6%) = 11.16%
Variance = [0.2  (2.6 – 11.16)2] + [0.6  (12.2 – 11.16)2] + [0.2  (16.6 – 11.16)2]
= 21.22
Standard deviation =
21.22 = 4.61%
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Chapter 11 - Introduction to Risk, Return, and the Opportunity Cost of Capital
c.
The investment opportunities have these characteristics:
Mean Return
13.00%
8.40%
11.16%
Stocks
Bonds
Portfolio
Standard Deviation
9.80%
3.20%
4.61%
The best choice depends on the degree of your aversion to risk. Nevertheless,
we suspect most people would choose the portfolio over stocks since the
portfolio has almost the same return with much lower volatility. This is the
advantage of diversification.
Est time: 06–10
19. If we use historical averages to compute the “normal” risk premium, then our
estimate of normal returns and normal risk premiums will fall when we include a
year with a negative market return. This makes sense if we believe that each
additional year of data reveals new information about the normal behavior of the
market portfolio. We should update our beliefs as additional observations about the
market become available.
Est time: 01–05
20. Risk reduction is most pronounced when the stock returns vary against each other.
When one firm does poorly, the other will tend to do well, thereby stabilizing the
return of the overall portfolio.
Est time: 01–05
21. a.
b.
General Steel ought to have greater sensitivity to broad market movements. Steel
production is more sensitive to changes in the economy than is food consumption.
Club Med sells a luxury good (expensive vacations), while General Cinema sells
movies, which are less sensitive to changes in the economy. Club Med will have
greater market risk.
Est time: 01–05
22. a.
The expected rate of return on the stock is 4%. The standard deviation is
22%.
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Chapter 11 - Introduction to Risk, Return, and the Opportunity Cost of Capital
b.
Because the stock offers a risk premium of zero (its expected return is the
same as the expected return for Treasury bills), it must have no market risk.
All the risk must be diversifiable, and therefore of no concern to investors.
Est time: 01–05
23. Sassafras is not a risky investment for a diversified investor. Its return is better when
the economy enters a recession. Therefore, the company risk offsets the risk of the
rest of the portfolio. Sassafras is a portfolio stabilizer despite the fact that there is a
90% chance of loss.
Compare Sassafras to purchasing an insurance policy. Most of the time, you lose
money on your insurance policy. But the policy pays off big if you suffer losses
elsewhere—for example, if your house burns down. For this reason, we view
insurance as a risk-reducing hedge, not as speculation. Similarly, Sassafras may be
viewed as analogous to an insurance policy on the rest of your portfolio since it tends
to yield higher returns when the rest of the economy fares poorly.
In contrast, the Leaning Tower of Pita has returns that are positively correlated with
the rest of the economy. It does best in a boom and goes out of business in a
recession. For this reason, Leaning Tower would be a risky investment for a
diversified investor since it increases exposure to the macroeconomic or market risk
to which the investor is already exposed.
Est time: 06–10
24. a. Using Excel’s AVERAGE and STDEV functions gives:
XOM
Average
Standard
deviation
BP
WMT
0.83%
0.38%
0.29%
5.76%
8.96%
4.66%
b. Using Excel’s CORREL function gives:
XOM
XOM
BP
WMT
1
BP
0.575497
1
WMT
–0.03348
0.211748
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Chapter 11 - Introduction to Risk, Return, and the Opportunity Cost of Capital
Not surprisingly, two firms from the same industry, ExxonMobil and British
Petroleum, have the highest correlation, at 0.58.
c.
Using Excel, the standard deviation for an equally weighted portfolio of Walmart
and Shell is 3.64. Using the values from part (a), the average standard deviation for
the two stocks is 5.21% = (5.76% + 4.66%)/2.
d.
Using Excel, the standard deviation for an equally weighted portfolio of BP and
ExxonMobil is 6.57%. Using the values from part (a), the average standard
deviation for the two stocks is 7.36% = (8.96% + 5.76%)/2. Pairing Walmart with
ExxonMobil provides greater benefits from diversification because the correlation
in their returns is the lowest (–0.03348).
Est time: 11–15
11-9