„
P5-1.
Solutions to Problems
LG 1: Rate of return: rt =
( Pt − Pt −1 + Ct )
Pt −1
Basic
a.
Investment X: Return =
($21,000 − $20,000 + $1,500)
= 12.50%
$20,000
Investment Y: Return =
($55,000 − $55,000 + $6,800)
= 12.36%
$55,000
b. Investment X should be selected because it has a higher rate of return for the same level
of risk.
P5-2.
LG 1: Return calculations: rt =
(Pt − Pt −1 + Ct )
Pt −1
Basic
Investment
A
B
C
D
E
P5-3.
Calculation
($1,100 − $800 − $100) ÷ $800
($118,000 − $120,000 + $15,000) ÷ $120,000
($48,000 − $45,000 + $7,000) ÷ $45,000
($500 − $600 + $80) ÷ $600
($12,400 − $12,500 + $1,500) ÷ $12,500
rt(%)
25.00
10.83
22.22
−3.33
11.20
LG 1: Risk preferences
Intermediate
The risk-averse manager would accept Investment X because it provides the highest return and
has the lowest amount of risk. Investment X offers an increase in return for taking on more risk
than what the firm currently earns.
P5-4.
LG 2: Risk analysis
Intermediate
a.
Expansion
A
B
Range
24% − 16% = 8%
30% − 10% = 20%
b. Project A is less risky, since the range of outcomes for A is smaller than the range for
Project B.
c. Since the most likely return for both projects is 20% and the initial investments are equal, the
answer depends on your risk preference.
d. The answer is no longer clear, since it now involves a risk–return tradeoff. Project B has a
slightly higher return but more risk, while A has both lower return and lower risk.
Chapter 5
P5-5.
Risk and Return
LG 2: Risk and probability
Intermediate
a.
Camera
R
S
Range
30% − 20% = 10%
35% − 15% = 20%
b.
c.
P5-6.
Possible
Outcomes
Probability
Pri
Camera R
Pessimistic
Most likely
Optimistic
Camera S
Pessimistic
Most likely
Optimistic
0.25
0.50
0.25
1.00
0.20
0.55
0.25
1.00
Expected Return
ri
20
25
30
Expected return
15
25
35
Expected return
Weighted
Value (%)(ri × Pri)
5.00
12.50
7.50
25.00
3.00
13.75
8.75
25.50
Camera S is considered more risky than Camera R because it has a much broader range of
outcomes. The risk–return tradeoff is present because Camera S is more risky and also
provides a higher return than Camera R.
LG 2: Bar charts and risk
Intermediate
a.
91
92
Gitman • Principles of Managerial Finance, Brief Fifth Edition
b.
Market
Acceptance
c.
P5-7.
Line J
Very Poor
Poor
Average
Good
Excellent
Line K
Very Poor
Poor
Average
Good
Excellent
Probability
Pri
0.05
0.15
0.60
0.15
0.05
1.00
0.05
0.15
0.60
0.15
0.05
1.00
Expected Return
ri
0.0075
0.0125
0.0850
0.1475
0.1625
Expected return
0.010
0.025
0.080
0.135
0.150
Expected return
Weighted Value
(ri × Pri)
0.000375
0.001875
0.051000
0.022125
0.008125
0.083500
0.000500
0.003750
0.048000
0.020250
0.007500
0.080000
Line K appears less risky due to a slightly tighter distribution than Line J, indicating a lower
range of outcomes.
LG 2: Coefficient of variation: CV =
σr
r
Basic
7%
= 0.3500
20%
9.5%
= 0.4318
B CVB =
22%
6%
= 0.3158
C CVC =
19%
5.5%
= 0.3438
D CVD =
16%
b. Asset C has the lowest coefficient of variation and is the least risky relative to the other choices.
a.
A CVA =
Chapter 5
P5-8.
93
LG 2: Personal finance: Rate of return, standard deviation, coefficient of variation
Challenge
a.
Stock Price
Year Beginning
2006
2007
2008
2009
14.36
21.55
64.78
72.38
b.
Average return
c.
Sum of variances
Variance
End
Returns
(Return–Average Return)2
21.55
64.78
72.38
91.80
50.07%
200.60%
11.73%
26.83%
0.0495
1.6459
0.3670
0.2068
2.31%
2.2692
3
0.7564
86.97%
d.
e.
P5-9.
Risk and Return
1.20
Sample divisor (n − 1)
Variance
Standard deviation
Coefficient of variation
The stock price of Apple has definitely gone through some major price changes over this
time period. It would have to be classified as a volatile security having an upward price
trend over the past 4 years. Note how comparing securities on a CV basis allows the investor
to put the stock in proper perspective. The stock is riskier than what Mike normally buys but
if he believes that Apple will continue to rise then he should include it.
LG 2: Assessing return and risk
Challenge
a. Project 257
(1) Range: 1.00 − (−0.10) = 1.10
n
(2) Expected return: r = ∑ ri × Pri
i =1
Expected Return
n
Rate of Return
ri
−0.10
0.10
0.20
0.30
0.40
0.45
0.50
0.60
0.70
0.80
1.00
Probability
Pri
0.01
0.04
0.05
0.10
0.15
0.30
0.15
0.10
0.05
0.04
0.01
1.00
Weighted Value
ri × Pri
r = ∑ ri × Pri
i=1
−0.001
0.004
0.010
0.030
0.060
0.135
0.075
0.060
0.035
0.032
0.010
0.450
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Gitman • Principles of Managerial Finance, Brief Fifth Edition
n
∑ (r − r )
(3) Standard deviation: σ =
i
i =1
2
× Pri
ri
r
ri − r
( ri − r )2 2
Pr i
( ri − r )2 × Pri
−0.10
0.10
0.20
0.30
0.40
0.45
0.50
0.60
0.70
0.80
1.00
0.450
0.450
0.450
0.450
0.450
0.450
0.450
0.450
0.450
0.450
0.450
−0.550
−0.350
−0.250
−0.150
−0.050
0.000
0.050
0.150
0.250
0.350
0.550
0.3025
0.1225
0.0625
0.0225
0.0025
0.0000
0.0025
0.0225
0.0625
0.1225
0.3025
0.01
0.04
0.05
0.10
0.15
0.30
0.15
0.10
0.05
0.04
0.01
0.003025
0.004900
0.003125
0.002250
0.000375
0.000000
0.000375
0.002250
0.003125
0.004900
0.003025
0.027350
σ Project 257 = 0.027350 = 0.165378
(4) CV =
0.165378
= 0.3675
0.450
b. Project 432
(1) Range: 0.50 − 0.10 = 0.40
n
(2) Expected return: r = ∑ ri × Pri
i =1
Expected Return
Rate of Return
ri
Probability
Pri
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.05
0.10
0.10
0.15
0.20
0.15
0.10
0.10
0.05
1.00
Weighted Value
ri × Pri
n
r = ∑ ri × Pri
i =1
0.0050
0.0150
0.0200
0.0375
0.0600
0.0525
0.0400
0.0450
0.0250
0.300
Chapter 5
(3) Standard deviation: σ =
n
∑ (r − r )
i =1
ri
r
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.300
0.300
0.300
0.300
0.300
0.300
0.300
0.300
0.300
σProject 432 =
(4) CV =
c.
2
× Pri
ri − r
( ri − r )2
Pri
−0.20
−0.15
−0.10
−0.05
0.00
0.05
0.10
0.15
0.20
0.0400
0.0225
0.0100
0.0025
0.0000
0.0025
0.0100
0.0225
0.0400
0.05
0.10
0.10
0.15
0.20
0.15
0.10
0.10
0.05
0.011250 = 0.106066
0.106066
= 0.3536
0.300
Bar Charts
i
Risk and Return
( ri − r )2 × Pri
0.002000
0.002250
0.001000
0.000375
0.000000
0.000375
0.001000
0.002250
0.002000
0.011250
95
96
Gitman • Principles of Managerial Finance, Brief Fifth Edition
d. Summary statistics
Project 257
Project 432
Range
Expected return (r )
1.100
0.450
0.400
0.300
Standard deviation (σ r )
0.165
0.106
Coefficient of variation (CV)
0.3675
0.3536
Since Projects 257 and 432 have differing expected values, the coefficient of variation should
be the criterion by which the risk of the asset is judged. Since Project 432 has a smaller CV, it
is the opportunity with lower risk.
P5-10. LG 2: Integrative–expected return, standard deviation, and coefficient of variation
Challenge
a.
n
Expected return: r = ∑ ri × Pri
i =1
Expected Return
Rate of Return
ri
Asset F
0.40
0.10
0.00
−0.05
−0.10
Probability
Pri
0.10
0.20
0.40
0.20
0.10
Weighted Value
ri × Pri
n
r = ∑ ri × Pri
i =1
0.04
0.02
0.00
−0.01
−0.01
0.04
Asset G
0.35
0.10
−0.20
0.40
0.30
0.30
0.14
0.03
−0.06
Asset H
0.40
0.20
0.10
0.00
−0.20
0.10
0.20
0.40
0.20
0.10
0.04
0.04
0.04
0.00
−0.02
0.11
0.10
Asset G provides the largest expected return.
Chapter 5
∑ (r − r )
i =1
i
ri − r
0.40 − 0.04
0.10 − 0.04
0.00 − 0.04
−0.05 − 0.04
−0.10 − 0.04
97
n
b. Standard deviation: σ =
Asset F
Risk and Return
= 0.36
= 0.06
= −0.04
= −0.09
= −0.14
2
xPri
( ri − r ) 2
0.1296
0.0036
0.0016
0.0081
0.0196
Pr i
0.10
0.20
0.40
0.20
0.10
Asset G
0.35 − 0.11 = 0.24
0.10 − 0.11 = −0.01
−0.20 − 0.11 = −0.31
0.0576
0.0001
0.0961
0.40
0.30
0.30
Asset H
0.40 − 0.10
0.20 − 0.10
0.10 − 0.10
0.00 − 0.10
−0.20 − 0.10
0.0900
0.0100
0.0000
0.0100
0.0900
0.10
0.20
−0.40
0.20
0.10
= 0.30
= 0.10
= 0.00
= −0.10
= −0.30
σ2
0.01296
0.00072
0.00064
0.00162
0.00196
0.01790
0.02304
0.00003
0.02883
0.05190
0.009
0.002
0.000
0.002
0.009
0.022
σr
0.1338
0.2278
0.1483
Based on standard deviation, Asset G appears to have the greatest risk, but it must be measured
against its expected return with the statistical measure coefficient of variation, since the three
assets have differing expected values. An incorrect conclusion about the risk of the assets
could be drawn using only the standard deviation.
c.
Coefficient of variation =
standard deviation (σ )
expected value
0.1338
= 3.345
0.04
0.2278
= 2.071
Asset G: CV =
0.11
0.1483
= 1.483
Asset H: CV =
0.10
As measured by the coefficient of variation, Asset F has the largest relative risk.
Asset F:
CV =
98
Gitman • Principles of Managerial Finance, Brief Fifth Edition
P5-11. LG 3: Personal finance: Portfolio return and standard deviation
Challenge
a. Expected portfolio return for each year: rp = (wL × rL) + (wM × rM)
Year
Asset L
(wL × rL)
+
Asset M
(wM × rM)
2010
2011
2012
2013
2014
2015
(14% × 0.40 = 5.6%)
(14% × 0.40 = 5.6%)
(16% × 0.40 = 6.4%)
(17% × 0.40 = 6.8%)
(17% × 0.40 = 6.8%)
(19% × 0.40 = 7.6%)
+
+
+
+
+
+
(20% × 0.60 = 12.0%)
(18% × 0.60 = 10.8%)
(16% × 0.60 = 9.6%)
(14% × 0.60 = 8.4%)
(12% × 0.60 = 7.2%)
(10% × 0.60 = 6.0%)
n
b. Portfolio return: rp =
rp =
c.
∑w
j =1
j
n
Expected
Portfolio Return
rp
=
=
=
=
=
=
17.6%
16.4%
16.0%
15.2%
14.0%
13.6%
× rj
Return
17.6 + 16.4 + 16.0 + 15.2 + 14.0 + 13.6
= 15.467 = 15.5%
6
Standard deviation:
σ rp =
σ rp =
σ rp =
(ri − r )2
i =1 ( n − 1)
n
∑
⎡(17.6% − 15.5%)2 + (16.4% − 15.5%)2 + (16.0% − 15.5%)2 ⎤
⎢
2⎥
2
2
⎣ + (15.2% − 15.5%) + (14.0% − 15.5%) + (13.6% − 15.5%) ⎦
6 −1
⎡(2.1%)2 + (0.9%)2 + (0.5%)2
⎤
⎢
2
2
2⎥
⎣ + (−0.3%) + (−1.5%) + (−1.9%) ⎦
5
(.000441 + 0.000081 + 0.000025 + 0.000009 + 0.000225 + 0.000361)
5
0.001142
σ rp =
= 0.000228% = 0.0151 = 1.51%
5
srp =
d. The assets are negatively correlated.
e. Combining these two negatively correlated assets reduces overall portfolio risk.
Chapter 5
Risk and Return
P5-12. LG 3: Portfolio analysis
Challenge
a. Expected portfolio return:
Alternative 1: 100% Asset F
rp =
16% + 17% + 18% + 19%
= 17.5%
4
Alternative 2: 50% Asset F + 50% Asset G
Year
Asset F
(wF × rF)
+
Asset G
(wG × rG)
2010
2011
2012
2013
(16% × 0.50 = 8.0%)
(17% × 0.50 = 8.5%)
(18% × 0.50 = 9.0%)
(19% × 0.50 = 9.5%)
+
+
+
+
(17% × 0.50 = 8.5%)
(16% × 0.50 = 8.0%)
(15% × 0.50 = 7.5%)
(14% × 0.50 = 7.0%)
rp =
Portfolio Return
rp
=
=
=
=
16.5%
16.5%
16.5%
16.5%
16.5% + 16.5% + 16.5% + 16.5%
= 16.5%
4
Alternative 3: 50% Asset F + 50% Asset H
Year
Asset F
(wF × rF)
+
Asset H
(wH × rH)
Portfolio Return
rp
2010
2011
2012
2013
(16% × 0.50 = 8.0%)
(17% × 0.50 = 8.5%)
(18% × 0.50 = 9.0%)
(19% × 0.50 = 9.5%)
+
+
+
+
(14% × 0.50 = 7.0%)
(15% × 0.50 = 7.5%)
(16% × 0.50 = 8.0%)
(17% × 0.50 = 8.5%)
15.0%
16.0%
17.0%
18.0%
rp =
15.0% + 16.0% + 17.0% + 18.0%
= 16.5%
4
b. Standard deviation:
(1) σ rp =
(ri − r )2
i =1 ( n − 1)
n
∑
σF =
[(16.0% − 17.5%)2 + (17.0% − 17.5%)2 + (18.0% − 17.5%)2 + (19.0% − 17.5%)2 ]
4 −1
σF =
[(−1.5%)2 + (−0.5%)2 + (0.5%)2 + (1.5%)2 ]
3
σF =
(0.000225 + 0.000025 + 0.000025 + 0.000225)
3
σF =
0.0005
= .000167 = 0.01291 = 1.291%
3
99
100
Gitman • Principles of Managerial Finance, Brief Fifth Edition
(2) σ FG =
σ FG =
[(16.5% − 16.5%)2 + (16.5% − 16.5%)2 + (16.5% − 16.5%)2 + (16.5% − 16.5%)2 ]
4 −1
[(0)2 + (0)2 + (0)2 + (0)2 ]
3
σ FG = 0
(3) σ FH =
[(15.0% − 16.5%)2 + (16.0% − 16.5%)2 + (17.0% − 16.5%)2 + (18.0% − 16.5%)2 ]
4 −1
σ FH =
[(−1.5%)2 + (−0.5%)2 + (0.5%)2 + (1.5%)2 ]
3
σ FH =
[(0.000225 + 0.000025 + 0.000025 + 0.000225)]
3
0.0005
= 0.000167 = 0.012910 = 1.291%
3
Coefficient of variation:
σ FH =
c.
CV = σ r ÷ r
1.291%
= 0.0738
17.5%
0
=
=0
16.5%
1.291%
=
= 0.0782
16.5%
CVF =
CVFG
CVFH
d. Summary:
Alternative 1 (F)
Alternative 2 (FG)
Alternative 3 (FH)
rp: Expected Value
of Portfolio
σrp
17.5%
16.5%
16.5%
1.291%
0
1.291%
CVp
0.0738
0.0
0.0782
Since the assets have different expected returns, the coefficient of variation should be used to
determine the best portfolio. Alternative 3, with positively correlated assets, has the highest
coefficient of variation and therefore is the riskiest. Alternative 2 is the best choice; it is
perfectly negatively correlated and therefore has the lowest coefficient of variation.
Chapter 5
Risk and Return
101
P5-13. LG 4: Correlation, risk, and return
Intermediate
a. (1) Range of expected return: between 8% and 13%
(2) Range of the risk: between 5% and 10%
b. (1) Range of expected return: between 8% and 13%
(2) Range of the risk: 0 < risk < 10%
c. (1) Range of expected return: between 8% and 13%
(2) Range of the risk: 0 < risk < 10%
P5-14. LG 1, 4: Personal finance: International investment returns
Intermediate
24,750 − 20,500 4,250
a. Returnpesos =
=
= 0.20732 = 20.73%
20,500
20,500
b.
Purchase price
Sales price
c.
Price in pesos
20.50
=
= $2.22584 × 1,000 shares = $2,225.84
Pesos per dollar 9.21
Price in pesos
24.75
=
= $2.51269 × 1,000 shares = $2,512.69
Pesos per dollar 9.85
Returnpesos =
2,512.69 − 2,225.84
286.85
=
= 0.12887 = 12.89%
2,225.84
2,225.84
d. The two returns differ due to the change in the exchange rate between the peso and the dollar.
The peso had depreciation (and thus the dollar appreciated) between the purchase date and the
sale date, causing a decrease in total return. The answer in Part (c) is the more important of
the two returns for Joe. An investor in foreign securities will carry exchange-rate risk.
P5-15. LG 5: Total, nondiversifiable, and diversifiable risk
Intermediate
a. and b.
c.
Only nondiversifiable risk is relevant because, as shown by the graph, diversifiable risk can
be virtually eliminated through holding a portfolio of at least 20 securities that are not positively
correlated. David Talbot’s portfolio, assuming diversifiable risk could no longer be reduced
by additions to the portfolio, has 6.47% relevant risk.
102
Gitman • Principles of Managerial Finance, Brief Fifth Edition
P5-16. LG 5: Graphic derivation of beta
Intermediate
a.
b. To estimate beta, the “rise over run” method can be used:
Rise ΔY
=
Beta =
Run ΔX
Taking the points shown on the graph:
Beta A =
ΔY 12 − 9 3
=
= = 0.75
ΔX 8 − 4 4
Beta B =
ΔY 26 − 22 4
=
= = 1.33
ΔX 13 − 10 3
A financial calculator with statistical functions can be used to perform linear regression
analysis. The beta (slope) of Line A is 0.79; of Line B, 1.379.
c.
With a higher beta of 1.33, Asset B is more risky. Its return will move 1.33 times for each one
point the market moves. Asset A’s return will move at a lower rate, as indicated by its beta
coefficient of 0.75.
P5-17. LG 5: Interpreting beta
Basic
Effect of change in market return on asset with beta of 1.20:
a. 1.20 × (15%) = 18.0% increase
b. 1.20 × (−8%) = 9.6% decrease
c. 1.20 × ( 0%) = no change
d. The asset is more risky than the market portfolio, which has a beta of 1. The higher beta
makes the return move more than the market.
Chapter 5
Risk and Return
103
P5-18. LG 5: Betas
Basic
a. and b.
Asset
A
B
C
D
Beta
Increase in
Market Return
Expected Impact
on Asset Return
Decrease in
Market Return
Impact on
Asset Return
0.10
0.10
0.10
0.10
0.05
0.16
−0.02
0.09
−0.10
−0.10
−0.10
−0.10
−0.05
−0.16
0.02
−0.09
0.50
1.60
−0.20
0.90
c. Asset B should be chosen because it will have the highest increase in return.
d. Asset C would be the appropriate choice because it is a defensive asset, moving in opposition
to the market. In an economic downturn, Asset C’s return is increasing.
P5-19. LG 5: Personal finance: Betas and risk rankings
Intermediate
a.
Stock
Most risky
Least risky
B
A
C
Beta
1.40
0.80
−0.30
b. and c.
Asset
A
B
C
Beta
0.80
1.40
−0.30
Increase in
Market Return
0.12
0.12
0.12
Expected Impact
on Asset Return
0.096
0.168
−0.036
Decrease in
Market Return
Impact on
Asset Return
−0.05
−0.05
−0.05
−0.04
−0.07
0.015
d. In a declining market, an investor would choose the defensive stock, Stock C. While the
market declines, the return on C increases.
e. In a rising market, an investor would choose Stock B, the aggressive stock. As the market
rises one point, Stock B rises 1.40 points.
104
Gitman • Principles of Managerial Finance, Brief Fifth Edition
P5-20. LG 5: Portfolio betas: bp =
n
∑w
j =1
j
× bj
Intermediate
a.
Portfolio A
Asset
Beta
wA
1
2
3
4
5
1.30
0.70
1.25
1.10
0.90
0.10
0.30
0.10
0.10
0.40
bA
wA × bA
0.130
0.210
0.125
0.110
0.360
= 0.935
Portfolio B
wB
0.30
0.10
0.20
0.20
0.20
bB
wB × bB
0.39
0.07
0.25
0.22
0.18
= 1.11
b. Portfolio A is slightly less risky than the market (average risk), while Portfolio B is more
risky than the market. Portfolio B’s return will move more than Portfolio A’s for a given
increase or decrease in market return. Portfolio B is the more risky.
P5-21. LG 6: Capital asset pricing model (CAPM): rj = RF + [bj × (rm − RF)]
Basic
Case
rj
=
A
B
C
D
E
8.9%
12.5%
8.4%
15.0%
8.4%
=
=
=
=
=
RF + [bj × (rm − RF)]
5% + [1.30 × (8% − 5%)]
8% + [0.90 × (13% − 8%)]
9% + [−0.20 × (12% − 9%)]
10% + [1.00 × (15% − 10%)]
6% + [0.60 × (10% − 6%)]
P5-22. LG 5, 6: Personal finance: Beta coefficients and the capital asset pricing model
Intermediate
To solve this problem you must take the CAPM and solve for beta. The resulting model is:
r − RF
Beta =
rm − RF
10% − 5% 5%
=
= 0.4545
16% − 5% 11%
15% − 5% 10%
=
= 0.9091
b. Beta =
16% − 5% 11%
18% − 5% 13%
=
= 1.1818
c. Beta =
16% − 5% 11%
20% − 5% 15%
=
= 1.3636
d. Beta =
16% − 5% 11%
e. If Katherine is willing to take a maximum of average risk then she will be able to have an
expected return of only 16%. (r = 5% + 1.0(16% − 5%) = 16%.)
a.
Beta =
Chapter 5
Risk and Return
105
P5-23. LG 6: Manipulating CAPM: rj = RF + [bj × (rm − RF)]
Intermediate
a.
rj = 8% + [0.90 × (12% − 8%)]
rj = 11.6%
b. 15% = RF + [1.25 × (14% − RF)]
RF = 10%
c. 16% = 9% + [1.10 × (km − 9%)]
rm = 15.36%
d. 15% = 10% + [bj × (12.5% − 10%)
bj
= 2
P5-24. LG 1, 3, 5, 6: Personal finance: Portfolio return and beta
Challenge
a. bp = (0.20)(0.80) + (0.35)(0.95) + (0.30)(1.50) + (0.15)(1.25)
= 0.16 + 0.3325 + 0.45 + 0.1875 = 1.13
b. rA =
c.
($20,000 − $20,000) + $1,600 $1,600
=
= 8%
$20,000
$20,000
rB =
($36,000 − $35,000) + $1,400 $2,400
=
= 6.86%
$35,000
$35,000
rC =
($34,500 − $30,000) + 0 $4,500
=
= 15%
$30,000
$30,000
rD =
($16,500 − $15,000) + $375 $1,875
=
= 12.5%
$15,000
$15,000
rP =
($107,000 − $100,000) + $3,375 $10,375
=
= 10.375%
$100,000
$100,000
d. rA = 4% + [0.80 × (10% − 4%)] = 8.8%
rB = 4% + [0.95 × (10% − 4%)] = 9.7%
rC = 4% + [1.50 × (10% − 4%)] = 13.0%
rD = 4% + [1.25 × (10% − 4%)] = 11.5%
e.
Of the four investments, only C (15% versus 13%) and D (12.5% versus 11.5%) had actual
returns that exceeded the CAPM expected return (15% versus 13%). The underperformance
could be due to any unsystematic factor that would have caused the firm not do as well as
expected. Another possibility is that the firm’s characteristics may have changed such that the
beta at the time of the purchase overstated the true value of beta that existed during that year.
A third explanation is that beta, as a single measure, may not capture all of the systematic
factors that cause the expected return. In other words, there is error in the beta estimate.
106
Gitman • Principles of Managerial Finance, Brief Fifth Edition
P5-25. LG 6: Security market line, SML
Intermediate
a. b. and d.
rj = RF + [bj × (rm − RF)]
Asset A
rj = 0.09 + [0.80 × (0.13 − 0.09)]
rj = 0.122
Asset B
rj = 0.09 + [1.30 × (0.13 − 0.09)]
rj = 0.142
d. Asset A has a smaller required return than Asset B because it is less risky, based on the beta
of 0.80 for Asset A versus 1.30 for Asset B. The market risk premium for Asset A is 3.2%
(12.2% − 9%), which is lower than Asset B’s market risk premium (14.2% − 9% = 5.2%).
c.
P5-26. LG 6: Integrative-risk, return, and CAPM
Challenge
a.
Project
rj
=
RF + [bj × (rm − RF)]
A
B
C
D
E
rj
rj
rj
rj
rj
=
=
=
=
=
9% + [1.5 × (14% − 9%)]
9% + [0.75 × (14% − 9%)]
9% + [2.0 × (14% − 9%)]
9% + [0 × (14% − 9%)]
9% + [(−0.5) × (14% − 9%)]
=
=
=
=
=
16.5%
12.75%
19.0%
9.0%
6.5%
Chapter 5
Risk and Return
107
b. and d.
c.
Project A is 150% as responsive as the market.
Project B is 75% as responsive as the market.
Project C is twice as responsive as the market.
Project D is unaffected by market movement.
Project E is only half as responsive as the market, but moves in the opposite direction as the
market.
P5-27. Ethics problem
Intermediate
One way is to ask how the candidate would handle a hypothetical situation. One may gain insight
into the moral/ethical framework within which decisions are made. Another approach is to use a
pencil-and-paper honesty test—these are surprisingly accurate, despite the obvious notion that the
job candidate may attempt to game the exam by giving the “right” versus the individually accurate
responses. Before even administering the situational interview question or the test, ask the candidate
to list the preferred attributes of the type of company he or she aspires to work for, and see if
character and ethics terms emerge in the description. Some companies do credit history checks, after
gaining the candidates approval to do so. Using all four of these techniques allows one to “triangulate”
toward a valid and defensible appraisal of a candidate’s honesty and integrity.
108
„
Gitman • Principles of Managerial Finance, Brief Fifth Edition
Case
Analyzing Risk and Return on Chargers Products’ Investments
This case requires students to review and apply the concept of the risk–return tradeoff by analyzing two
possible asset investments using standard deviation, coefficient of variation, and CAPM.
( P − Pt −1 + Ct )
1. Expected rate of return: rt = t
Pt −1
Asset X:
Year
Cash
Flow (Ct)
Ending
Value (Pt)
Beginning
Value (Pt – 1)
Gain/
Loss
Annual Rate
of Return
2000
2001
2002
2003
$1,000
1,500
1,400
1,700
$22,000
21,000
24,000
22,000
$20,000
22,000
21,000
24,000
2004
2005
2006
2007
2008
2009
1,900
1,600
1,700
2,000
2,100
2,200
23,000
26,000
25,000
24,000
27,000
30,000
22,000
23,000
26,000
25,000
24,000
27,000
$2,000
−1,000
3,000
−2,000
1,000
3,000
−1,000
−1,000
3,000
3,000
15.00%
2.27
20.95
−1.25
13.18
20.00
2.69
4.00
21.25
19.26
Average expected return for Asset X = 11.74%
Asset Y:
Year
Cash
Flow (Ct)
Ending
Value (Pt)
Beginning
Value (Pt – 1)
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
$1,500
1,600
1,700
1,800
1,900
2,000
2,100
2,200
2,300
2,400
$20,000
20,000
21,000
21,000
22,000
23,000
23,000
24,000
25,000
25,000
$20,000
20,000
20,000
21,000
21,000
22,000
23,000
23,000
24,000
25,000
Average expected return for Asset Y = 11.14%
Gain/
Loss
$
0
0
1,000
0
1,000
1,000
0
1,000
1,000
0
Annual Rate
of Return
7.50%
8.00
13.50
8.57
13.81
13.64
9.13
13.91
13.75
9.60
Chapter 5
2.
σr =
n
∑ (r − r )
i =1
i
2
÷ (n − 1)
Asset X:
Year
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
Return
ri
15.00%
2.27
20.95
1.25
13.18
20.00
2.69
4.00
21.25
19.26
σx =
Average
Return, r
( ri − r )
11.74%
11.74
11.74
11.74
11.74
11.74
11.74
11.74
11.74
11.74
3.26%
9.47
9.21
12.99
1.44
8.26
9.05
7.74
9.51
7.52
( ri − r ) 2
0.001063
0.008968
0.008482
0.016874
0.000207
0.006823
0.008190
0.005991
0.009044
0.005655
0.071297
0.071297
= 0.07922 = .0890 = 8.90%
10 − 1
8.90%
= 0.76
CV =
11.74%
Asset Y:
Year
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
Return ri
7.50%
8.00
13.50
8.57
13.81
13.64
9.13
13.91
13.75
9.60
Average
Return, r
11.14%
11.14
11.14
11.14
11.14
11.14
11.14
11.14
11.14
11.14
(ri − r )
−3.64%
−3.14
2.36
−2.57
2.67
2.50
−2.01
2.77
2.61
−1.54
(ri − r ) 2
0.001325
0.000986
0.000557
0.000660
0.000713
0.000625
0.000404
0.000767
0.000681
0.000237
0.006955
Risk and Return
109
110
Gitman • Principles of Managerial Finance, Brief Fifth Edition
σY =
3.
0.006955
= 0.0773 = 0.0278 = 2.78%
10 − 1
2.78%
= 0.25
CV =
11.14%
Summary statistics:
Expected return
Standard deviation
Coefficient of variation
Asset X
11.74%
8.90%
0.76
Asset Y
11.14%
2.78%
0.25
Comparing the expected returns calculated in Part (a), Asset X provides a return of 11.74%, only
slightly above the return of 11.14% expected from Asset Y. The higher standard deviation and
coefficient of variation of Investment X indicates greater risk. With just this information, it is difficult
to determine whether the 0.60% difference in return is adequate compensation for the difference in
risk. Based on this information, however, Asset Y appears to be the better choice.
4.
Using the capital asset pricing model, the required return on each asset is as follows:
Capital asset pricing model: rj = RF + [bj× (rm − RF)]
Asset
X
Y
RF + [bj × (rm − RF)]
=
rj
7% + [1.6 × (10% − 7%)]
7% + [1.1 × (10% − 7%)]
=
=
11.8%
10.3%
From the calculations in Part (a), the expected return for Asset X is 11.74%, compared to its required
return of 11.8%. On the other hand, Asset Y has an expected return of 11.14% and a required return
of only 10.8%. This makes Asset Y the better choice.
5.
In Part c, we concluded that it would be difficult to make a choice between X and Y because the
additional return on X may or may not provide the needed compensation for the extra risk. In
Part (d), by calculating a required rate of return, it was easy to reject X and select Y. The required
return on Asset X is 11.8%, but its expected return (11.74%) is lower; therefore Asset X is
unattractive. For Asset Y the reverse is true, and it is a good investment vehicle.
Clearly, Charger Products is better off using the standard deviation and coefficient of variation, rather
than a strictly subjective approach, to assess investment risk. Beta and CAPM, however, provide a
link between risk and return. They quantify risk and convert it into a required return that can be
compared to the expected return to draw a definitive conclusion about investment acceptability.
Contrasting the conclusions in the responses to Questions c and d above should clearly demonstrate
why Junior is better off using beta to assess risk.
Chapter 5
6.
Risk and Return
111
a. Increase in risk-free rate to 8% and market return to 11%:
Asset
X
Y
RF + [bj × (rm − RF)]
=
8% + [1.6 × (11% − 8%)]
8% + [1.1 × (11% − 8%)]
= 12.8%
= 11.3%
rj
b. Decrease in market return to 9%:
Asset
X
Y
RF + [bj × (rm − RF)]
= rj
7% + [1.6 × (9% − 7%)]
7% + [1.1 × (9% − 7%)]
= 10.2%
= 9.2%
In Situation 1, the required return rises for both assets, and neither has an expected return above the
firm’s required return.
With Situation 2, the drop in market rate causes the required return to decrease so that the expected
returns of both assets are above the required return. However, Asset Y provides a larger return
compared to its required return (11.14 − 9.20 = 1.94), and it does so with less risk than Asset X.
„
Spreadsheet Exercise
The answer to Chapter 5’s stock portfolio analysis spreadsheet problem is located in the Instructor’s
Resource Center at www.prenhall.com/irc.
„
A Note on Web Exercises
A series of chapter-relevant assignments requiring Internet access can be found at the book’s Companion
Website at http://www.prenhall.com/gitman. In the course of completing the assignments students access
information about a firm, its industry, and the macro economy, and conduct analyses consistent with those
found in each respective chapter.