Solutions for Appendix A: CFA Questions and Problems

160

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APPENDIX A
CFA SOLUTIONS
Chapter 1
Level
I
1.
A.
Investment
2 is identical to Investment 1 except that Investment 2 has low liquidity. The
difference between the interest rate on Investment 2 and Investment 1 is 0.5 percentage point. This amount
represents the liquidity premium, which represents compensation for the risk of loss relative to an investment
’
s fair
value if the investment needs to be converted to cash quickly.
B.
To estimate the default risk premium, find the two investments that have
the same maturity but different
levels of default risk. Both Investments 4 and 5 have a maturity of eight years. Investment 5, however, has low
liquidity and thus bears a liquidity premium. The difference between the interest rates of Investments 5 and 4
is 2.5
percentage points. The liquidity premium is 0.5 percentage point (from Part A). This leaves 2.5 − 0.5 = 2.0
percentage points that must represent a default risk premium reflecting Investment 5
’
s high default risk.
C.
Investment 3 has liquidity risk
and default risk comparable to Investment 2, but with its longer time to
maturity, Investment 3 should have a higher maturity premium. The interest rate on Investment 3,
r
3
, should thus be
above 2.5 percent (the interest rate on Investment 2). If the liqui
dity of Investment 3 were high, Investment 3 would
match Investment 4 except for investment 3
’
s shorter maturity. We would then conclude that Investment 3
’
s interest
rate should be less than the interest rate on Investment 4, which is 4 percent. In contras
t to Investment 4, however,
Investment 3 has low liquidity. It is possible that the interest rate on Investment 3 exceeds that of Investment 4
despite 3
’
s shorter maturity, depending on the relative size of the liquidity and maturity premiums. However, we
expect
r
3
to be less than 4.5 percent, the expected interest rate on Investment 4 if it had low liquidity. Thus 2.5
percent <
r
3
< 4.5 percent
.
2.
The geometric mean requires that all the numbers be greater than or equal to 0. To ensure that the returns sati
sfy
this requirement, after converting
the returns to decimal form we add 1 to each return.
F
or the geometric mean
return,
R
G
:
(1/10)
10
1
1
(1 ) 1
G
t
R R
which can also be written as
Solutions to 1

3 taken from
Quantitative Methods for Investment Analysis
, Second Edition by Richard A. DeFusco,
CFA, Dennis W. McLeavey, CFA, Jerald E. Pinto, CFA, and
David E. Runkle, CFA. Copyright © 2004 by CFA
Institute. Reprinted with permission. All other solutions copyright © CFA Institute.
Solutions for Appendix A: CFA Questions and Problems

161

Copyright
© 2010 by Nelson Education Ltd.
10
1 2 10
(1 )(1 ) (1 ) 1
G
R R R R
To find the geometric mean in
this
example, we
take the following five steps:
i.
Divide each figure in the table by 100 to put the returns into decimal representation.
ii.
Add 1 to each return to obtain the terms 1 +
R
t
.
Return
Return in Decimal Form
1 + Return
46.21%
0.4621
1.4621
−
6.18%
=
−
0.0618
=
0.9P82
=
8.04%
=
0.0804
=
1.0
8
〴
=
22.8T%
=
0.228T
=
1.228T
=
45.90%
=
0.4590
=
1.4590
=
20.P2%
=
0.20
㌲
=
1.20P2
=
41.20%
=
0.4120
=
1.4120
=
−
9.5P%
=
−
0.095P
=
0.904T
=
−
1T.T5%
=
−
0.1TT5
=
0.8225
=
−
4P.06%
=
−
0.4P06
=
0.5694
=
楩椮
=
䵵汴楰ly=瑯g整h敲=慬氠瑨攠numb敲s=楮=瑨攠th楲d=捯汵mn=瑯=g整e
1.9124.
=
楶.
=
q慫攠瑨攠10瑨=roo琠tf=1.9124=瑯=g整e
10
1.9124 1.0670
.=佮=mos琠
捡汣l污瑯rs,=
w攠敶慬a慴攠
10
1.9124
=
using=
瑨攠
y
x
key. Enter 1.9124 with the
y
x
key. Next, enter 1/10 = 0.10. Then press the = key to get 1.0670.
v.
Subtract 1 to get 0.0670, or 6.70 percent a year. The geometric mean return is
6.7
0
percent. This result
means that the compound annual
rate
of growth of the MSCI Germany Index was 6.7 percent annually during the
1993
–
2002 period.
3.
A.
So
l
ong
as a return s
eries has any variability, the geometric mean return must be less than the arithmetic
mean return.
In the s
olution to Problem 2, we computed the geometric mean annual return as
6.7 percent. In
general, th
e difference between the geometric and
arithmetic me
ans increases with the variability of the period

by

period observations.
B.
The geometric mean return is more meaningful than the arithmetic mean return for an investor concerned
with the terminal value of an investment. The geometric mean return is the co
mpound rate of growth, so it
direc
tl
y relates to the terminal value of an investment. By
contrast, a higher arithmetic mean return does not
necessarily imply a
higher terminal value for an investment
.
C.
The arithmetic mean return is more meaningful than
the geometric mean
return for an investor concerned
with the average one

period performance
of an investment. The arithmetic mean return is a direct representation
of
the average one

period return. In contrast, the geometric mean return, as a
compound rate
of
gro
w
th
,
aims to
summarize what a return
series
means
for the growth rate of an investment over many periods.
Solutions for Appendix A: CFA Questions and Problems

162

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4.
A.
Sec
uri
ty
Market
Line
i.
Fair

value plot.
The following template shows, using the CAPM, the expected return,
ER,
of Stock A and
Stock B on
the SML. The points are consistent with the following equations:
ER on stock Riskfree rate Beta (Market re
turn
Riskfree rate)
ER for A 4.5% 1.2(14.5% 4.5%)
16.5%
ER for B 4.5% 0.8(14.5% 4.5%)
12.5%
ii.
Analyst estimate plot.
Using the analyst
’
s estimates, Stock A plots below the SML and Stock B, above the
SML.
B.
Over versus Underv
alue
Stock A is overvalued
because it should provide a 16.5% return according to the CAPM whereas the analyst
has estimated only a 16.0% return.
Stock B is undervalued
because it should provide a 12.5% return according to the CAPM whereas the analyst
has e
stimated a 14% return.
Level III
5.
A.
Real
risk

free
rate
(%)
+
Expected
inflation
(%)
+
Spreads
or
premiums
(%)
=
Expected annual
fixed

income
return
(%)
1

year U.S.
T

note
1.2
+
2.6
+
0
=
3.8
10

year corp.
bond
1.2
+
2.6
+
1.0 + 0.8 +
0.9
=
6.5
Solution to 4 taken from
Solutions Manual
to accompany
Investment Analysis and Portfolio Management
, Eighth
Edition, by Frank
K. Reilly, CFA and Keith C. Brown, CFA. Copyright
©
2005 by Thomson
S
outh

Western.
Reprinted with permission of South

Western, a division of Thomson Learning.
All other solutions copyright © CFA
Institute.
Managing Investment Portfolios: A Dynamic Proces
s
, Third Edition, John L. Maginn, CFA, Donald L. Tuttle, CFA,
Jerald E. Pinto, CFA, and Dennis W. McLeavey, CFA, editors. Copyright © 2007 by CFA Institute. Reprinted with
permission.
Solutions for Appendix A: CFA Questions and Problems

163

Copyright
© 2010 by Nelson Education Ltd.
10

0
year
MBS
1.2
+
2.6
+
0.95
=
4.75
Note
:
We assign the 10

year corporate a 1% maturity premium based on the 10

year over 1

year government spread.
Estimate of the expected return of an equal

weighted investment in the
three securities: (3.8% + 6.5% +
4.75%)/3 =
5.02%
B.
The average spread at issue is [0 + (1.0% + 0.8% + 0.9%) + 0.95%]/3 = 1.22%
.
As 1.22%
−
1% = 0.22% is
less than 0.5 percent, the investor will not make the
investment
.
6
.
A.
For Swennson, the annualized rate of return is
:
1/5
[(1 0.275)(1 0.189)(1 0.146)(1 0.324)
(1 0.123)] 1
0.0209 2.09%
a
r
For Mattsson, the annualized rate of return is:
1/5
[(1 0.057)(1 0.049)(1 0.078)(1 0.067)
(1 0.053)] 1
0.0327 or 3.27%
a
r
B.
Mattsson
’
s annualized rate of return of 3.27% was higher than Swennson
’
s at
−
2.09%.
Managing Investment Portfolios: A Dynamic Process
, Third Edition, John
L. Maginn, CFA, Donald L. Tuttle, CFA,
Jerald E. Pinto, CFA, and Dennis W. McLeavey, CFA , editors. Copyright © 2007 by CFA Institute. Reprinted with
permission.
Solutions for Appendix A: CFA Questions and Problems

164

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© 2010 by Nelson Education Ltd.
Chapter 1 Appendix
Level I
A
1.
The following table shows the
calculation of the portfolio
’
s annual returns,
and the mean annual return.
Year
Weighted Mean Calculation
Portfolio Return
1993
0.60(4
6
.21) + 0.40(15.74) =
34.02%
1994
0.60(
−
6.18F=+
=
0.40E
−
P,40F==
=
−
5.0T%
=
ㄹ㤵
=
0.60E8.04F=⬠0.40E1
8
.P0F==
=
12.14%
=
ㄹ㤶
=
0.60E22.8TF=⬠0.40E8.P5F==
=
1T.06%
=
ㄹ㤷
=
0.60E45.90F=⬠0.40E6.65F==
=
P0.20%
=
ㄹ㤸
=
0.60E20.P2F=⬠0.40E12.45F==
=
1T.1T%
=
ㄹ㤹
=
0.60E41.20F=⬠0.40E
−
2.19F==
=
2P.84%
=
㈰〰
=
0.60E
−
9.5PF=⬠0.40ET.44F==
=
−
2.T4%
=
2
〰0
=
0.60E
−
1T.T5F=+
=
0.40E5.55F=
=
=
−
8.4P%
=
㈰2
2
=
0.60E
−
4P.06F=
⬠0.40E10.2TF==
=
−
21.TP%
=
=
卵m==
=
96.46%
=
=
䵥慮=Annu慬ao整urn=
=
=
9.65%
=
Note
:
The sum of the portfolio returns carried without rounding is 96.4
8
.
A2.
A.
i.
For the 60/40 equity/bond portfolio, the mean return (as computed in Problem 1) was
9.65 percent
.
We can compute the sample standard deviation of returns as
s
= 18.31 percent The coefficient of
variation for the 60/40 portfolio was
CV/18.31/9.65 1.90
s R
.
ii.
For the MSCI Germany Index,
CV/29.95/10.80 2.77
s R
.
iii.
For the JPM Germany 5
–
7 Year
GBl,
CV/6.94/7.92 0.88
s R
.
B.
The coefficient of variation is a measure of relative dispersion. For returns, it measures the amount of risk
per unit of mean return. The MSCI Germany Index portfolio, the JPM Germany GBI, and the 60/40 equity/bond
portfolio, were respectively most risky, least risky, and intermediate in risk, based on their values of CV.
Portfolio
CV
Risk
MSCI Germany Index
2.77
Highest
60/40 Equity/bond portfolio
1.90
JPM Germany GBI
0.88
Lowest
A3.
The
cova
ria
nce
is 25,
computed as follows. First, we calculate expected values:
B
Z
( ) (0.25 30%) (0.50 15%) (0.25 10%) 17.5%
( ) (0.25 15%) (0.50 10%) (0.25 5%) 10%
E R
E R
Solutions for Appendix A: CFA Questions and Problems

165

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© 2010 by Nelson Education Ltd.
Then we find the covariance as follows:
B Z
Cov (,) (30,15) [(30 17.5) (15 10)] (15,10)
[(15 17.5) (10 10)] (10,5) [(10 17.5)
(5 10)]
(0.25 12.5 5) [0.50 ( 2.5) 0] [0.25
( 7.5) ( 5)]
15.625 0 9.375 25
R R P P
P
L
evel II
A4
.
For
AOL
Time Warner, the required return is
β[ ( ) ] 4.35% 2.50(8.04%) 4.35%
20.10% 24.45%
F M F
r R E R R
For J.P. Morgan
Chase, the required return is
β[ ( ) ] 4.35% 1.50(8.04%) 4.35%
12.06% 16.41%
F M F
r R E R R
For Boeing, the required return is
β[ ( ) ] 4.35% 0.80(8.04%) 4.35%
6.43% 10.78%
F M F
r R E R R
Level III
A
5
.
A.
If
th
e
correla
tion
between
bond market returns and exchange rate movements were equal to zero,
the dollar volatility
of the German bond market would be
2 2 2 2 2
σ σ σ 2ρσσ (5.5) (11.7) 2(0)(5.5)(11.7)
167.14
σ 12.93%
f s s
f
B.
Because the actual dollar volatility is 13.6 percent, we conclude that the co
rr
elation between bond market
returns and exchange rate movements is positive. When the euro gets weaker, U.S. inv
estors lose
on the exchange
rate and also on bond market returns measured in
euros. This can be explained by the idea that a weak currency
usually goes with rising interest rates (and negative bond market return).
A6.
The best diversification vehicle is
an asset whose value gets significantly higher when the rest of the
portfolio
’
s value is low, and thereby partially offsets the loss of other assets. The best vehicle is an asset with a
Solutions to A5 and A6 taken from
Solutions Manual
to accompany
Global Investments,
Sixth Edi
tion, by Bruno
Solnik and Dennis McLeavey, CFA. Copyright © 2008 by Pearson Education. Reprinted with permission of Pearson
Education, publishing as Pearson Addison Wesley.
All other solutions copyright © CFA Institute.
Solutions for Appendix A: CFA Questions and Problems

166

Copyright
© 2010 by Nelson Education Ltd.
negative co
rre
lation
(so it goes up when the portfolio goes down) and
high volatility (large upswings when the
portfolio goes down). Thus the statement is correct.
Chapter 2
Level II
1
.
C
is correct.
Th
e
comments about investment policy statements made by Stephenson
’
s patients are
incorrect. The IPS should identify pertinent investment objectives and constraints for a
particul
a
r
investor. Clearly
identified objectives and constraints ensure that the policy statement is accurate and relevant to the investor
’
s
specific
situation and desires. The result should be an optimal balance between return and risk for that investor. The
IPS provides a long

term plan for an investor and a basis for making disciplined investment decisions over time. The
absence of an investment poli
cy statement reduces decision making to an individual

event
basis and often leads to
pursuing short

term opportunities that may not contribute to, or may even detract from, reaching long

term goals.
2.
B is correct. An investor
’
s ability to take risk puts
an upper limit on a reasonable return objective.
3.
C is correct. Even though Stephenson describes his risk tolerance as
“
average,
”
his present investment
portfolio and his desire for large returns indicate an above

average willingness to take risk. His
financial situation
(large asset base, ample income to cover expenses, lack of need for liquidity, and long time horizon) indicates an
above

average ability to accept risk.
4.
B is correct. Stephenson has adequate income to cover his living expenses and
has no major outlays for
which he needs cash, so his liquidity needs are minimal. He is not a tax

exempt investor (both income and capital
gains are taxed at 30%), so taxes should play a considerable role in his investment decisions.
5.
C is correct. Step
henson
’
s time horizon is long
—
he is currently only 55 years old. The time horizon
consists of two stages: the first stage extends to his retirement in 15 years; the second stage may last for 20 years or
more and extends from retirement until his death.
6.
C is correct.
Risk
:
Stephenson has an above

average risk tolerance based on both his ability and willingness to assume risk. His
large asset base, long time horizon, ample income to cover expenses, and lack of need for liquidity or cash flow
indicate an a
bove

average ability to assume risk. His concentration in U.S. small

capitalization stocks and his desire
for high returns indicate substantial willingness to assume risk.
Return
:
Stephenson
’
s financial circumstances (long time horizon, sizable asset base,
ample income, and low
liquidity needs) and his risk tolerance warrant an above

average total return objective. His expressed desire for a
continued return of 20 percent, however, is unrealistic. Coppa should counsel Stephenson on what level of returns to
Solutions for Appendix A: CFA Questions and Problems

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Copyright
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reasonably expect from the financial markets over long periods of time and to define an achievable return objective.
Level III
7.
A.
i.
The
Maclins
’
overall
risk
objective
must consider both willingness and ability to take
risk:
Willingness.
The Maclins h
ave a below

average willingness to take risk, based on their unhappiness with the
portfolio volatility they have experienced in recent years and their desire not to experience a loss in portfolio value
in excess of 12 percent in any one year.
Ability.
The
Maclins have an average ability to take risk. Although their fairly large asset base and long time horizon
in isolation would suggest an above

average ability to take risk, their living expenses of £74,000 are significantly
higher than Christopher
’
s after

tax
salar
y
of £80,000(1
−
0.40) = £48,000, causing them to be very dependent on
projected portfolio returns to cover the difference
Overall.
The Maclins
’
overall risk tolerance is below average, as
their below

average willingness to take risk dominates the
ir average ability to take risk in determining their overall
risk tolerance.
ii
.
The Maclins
’
return objective is to grow the portfolio to meet their educational and retirement needs as well
as to provide for ongoing net expenses. The Maclins will require annual after

tax cash flows of £26,000 (calculated
below) to cover ongoing net expenses and w
i
ll need £2 million in 18 years to fund their children
’
s education and
their retirement. To meet this objective, the Maclins
’
pretax required return is 7.38 percent, which is determined
below.
The after

tax return required to accumulate £2 million in 18 ye
ars beginning with an investable asset base of
£1,235,000 (calculated below) and with annual outflows of £26,000 is 4.427 percent, which when adjusted for the
40 percent tax rate, results in a 7.38 percent pretax return [4.427%
/
(
1
−
0.40) = 7.38%].
Chris
topher’s annual salary
=
£80,000
=
i敳s㨠:慸敳
40┩
=
−
P2,000
=
iiving=exp敮ses
=
−
T4,000
=
乥琠慮nu慬a捡sh=f汯w
=
−
£26,000
=
f
nh敲楴in捥
=
900,000
=
B慲n整琠Co.=捯mmon
=
s瑯捫
=
220,000
=
却p捫s=and=bonds
=
160,000
=
C慳h
=
5,000
=
卵b瑯瑡t
=
£1,285,000
=
i敳s=one

瑩m攠n敥ds:
=
=
䑯wn
=
paym敮琠tn=house
=
−
P0,000
=
Ch慲楴慢汥ldon慴楯n
=
−
20,000
=
fnves瑡t汥l慳a整eb慳a
=
£1,2P5,000
=
Solutions for Appendix A: CFA Questions and Problems

168

Copyright
© 2010 by Nelson Education Ltd.
Note
:
No inflation adjustment is required in the return
calculation because increases in living expenses will be offset
by increases in Christopher’s salary.
=
䈮
=
qh攠
䵡捬楮s
’
investment policy statement should include the following constraints:
i.
Time horizon.
The Maclins have a two

stage time horizon, because of their changing cash flow and
resource needs. The first stage is the next 18 years. The second stage begins
with their retirement and the university
education years for their children.
ii.
Liquidity requirements.
The Maclins have one

time immediate expenses totaling £50,000 that include the
deposit on the house they are purchasing and the charitable donation in
honor of Louise
’
s father.
iii.
Tax concerns.
A 40 percent tax rate applies to both ordinary income and capital gains.
iv.
Unique circumstances.
The large holding of the Barnett Co. common stock represents almost 18 percent of
the Maclins
’
investable asset
base. The concentrated holding in Barnett Co. stock is a key risk factor of the Maclins
’
portfolio, and achieving better diversification will be a factor in the future management of the Maclins
’
assets.
The Maclins
’
desire not to invest in alcohol and tob
acco stocks is another constraint on investment.
8.
B is correct.
* (1 )
0.06*[1 (0.30)(0.15) (0.20)(0.35) (0.40)(0.
25)]
0.0471 or 4.71 percent
* (1 )/(1 )
(1 0.30 0.20 0.40)/[1 (0.30)(0.15)
(0.20)(0.35) (0.40)(0.25)
r r p t p t p t
d d i i cg cg
T t p p p p t p t p t
cg d i cg d d i i cg cg
t
cg
]
0.0318
£1,000,000[(1 *) (1 *) *]
15
£1,000,000[(1 0.0471) (1 0.0318) 0.0318]
£1,962,776
n
FVIF r T T
Taxable
9.
Worden Technology, Inc.
IPS
Y
and IPS X offer different components that are appropriate for
Worden
Technology
’
s pension plan:
i.
Return requirement.
IPS
Y
has the appropriate return requirement for
Worden
’
s
pension plan. Because the
plan is currently underfunded, the manager
’
s
primar
y
objective should be to make it financially stronger. The risk
inherent in attempting to maximize total returns would be inapp
ropriate.
Managing Investment Portfolios: A Dy
namic Process
, Third Edition, John L. Maginn, CFA, Donald L. Tuttle, CFA,
Jerald E. Pinto, CFA, and Dennis W. McLeavey, CFA, editors. Copyright © 2007 by CFA Institute. Reprinted with
permission.
Solutions for Appendix A: CFA Questions and Problems

169

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© 2010 by Nelson Education Ltd.
ii
.
R
isk tolerance.
IPS
Y
has the appropriate risk tolerance for
Worden
’
s
plan. Because of its underfunded status, the
plan has a limited risk tolerance; a substantial loss in the fund could further jeopardize payments to beneficiaries.
iii.
Time
horizon.
IPS
Y
has the appropriate time horizon for
Worden
’
s
plan. Although going

concern pension plans
usually have long time horizons, the
Worden
plan has a comparatively short time horizon because of the company
’
s
reduced retirement age and relatively
high median age of its workforce.
iv.
Liquidity
.
IPS X has the appropriate liquidity constraint for
Worden
’
s
plan. Because of the early retirement
feature starting next month and the age of the workforce (which indicates an increasing number of retirees in
the
near future), the plan needs a moderate level of liquidity to fund mon
thly payments.
10
.
A.
Long

term bond holdings are important for life insurers because of their
ALM
(Asset Liability
Management)
emphasis and the long

term nature of their liabiliti
es. In contrast, individual investors do not have
ALM
concerns to the same degree, in general. As discussed in the reading as well, because of the importance of
human capital in relation to financial capital during youth, for many young investors equity in
vestments will be very
large relative to fixed

income holdings. In conclusion, long

term bonds are generally more important in strategic
asset allocation for life insurers than for young investors.
B.
Banks are generally restricted by regulations in their
holdings of
common stock. Overall, common stock
plays a minimal role in banks
’
securities portfolio. By contrast, because of human capital considerations mentioned
in the solution to Part A, common stock investments tend to be very important for young inve
stors (with the
possible
exception
of those investors whose employment income is linked to equity market returns).
C.
Because endowments are tax exempt, tax

exempt bonds play no role in their strategic asset allocation. In
con
tr
ast, tax

exempt bonds someti
mes play a substantive role for individual investors in high tax brackets, such as
many mid

career professionals.
D
.
Private equity may play a role in
th
e strategic asset allocation of substantial investors, both institutional and
individual. A major foun
dation is much more likely to have the resources to research and invest in private
companies than young investors and to play a role in
strategic asset allocation.
11.
A.
Accumulating funds for the child
’
s education is a new investment goal. Prior to the
adoption, the
couple
’
s time horizon was two

stage
(preretirement and postretirement). In their late 40s, they will have a period in
which they need to pay for the cost of the child
’
s education; this will involve substantial costs for which they must
plan.
The couple
’
s multistage time horizon now includes the period up to the child
’
s entering college, the child
’
s
college years, the remaining period to retirement, and retirement.
Managing Investment Portfolios: A Dynamic Process
, Third Ed
ition, John L. Maginn, CFA, Donald L. Tuttle, CFA,
Jerald E. Pinto, CFA, and Dennis W. McLeavey, CFA, editors. Copyright © 2007 by CFA Institute. Reprinted with
permission.
Managing Investment Portfolios: A Dynamic Process
, Third Edition, John L. Maginn,
CFA, Donald L. Tuttle, CFA,
Solutions for Appendix A: CFA Questions and Problems

170

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B.
Given the investor
’
s circumstances, the decision to buy a house in one year
’
s time makes the addition of a
shortfall risk objective appropriate. He needs to earn at least 2 percent if he is to have sufficient funds to buy the
house. An appropriate shortfall risk objective is to minimize the probability that the return on the portf
olio falls
below 2
%
percent over a one

year horizon. The decision also creates a liquidity requirement. The need for $102,000
in cash at the end of the investment period means that the investor cannot tie up his money in a way such that he
does not have re
ady access to it in a year
’
s time.
C.
The approval of the grant has created a liquidity requirement of €15,000,000
−
€1,000,000 = €14,000,000.
12.
The first action (
“
Revise the investment policy statement of the pension scheme to take into account a
chang
e in the forecast for inflation in the U.K.
”
) is incorrect. The Investment Policy Statement depends on the
client
’
s particular circumstances, including risk tolerance, time horizon, liquidity and legal constraints, and unique
needs. Therefore, a change in
economic forecast would not affect the Investment Policy Statement. The Investment
Policy Statement also considers a client
’
s return requirement. This return requirement may change over
th
e long
term if the inflation outlook has changed over
th
e long term.
A change in the inflation outlook over a short period,
such as in this question, would not necessitate a change in the return portion or any o
th
er aspect of
th
e Investment
Policy Statement
.
The second action (
“
Reallocate pension assets from domestic [U.K
.] to international equities because he also expects
inflation in the U.K. to be higher than in other countries
”
) is correct
.
A change in economic forecast might
necessitate a change in asset allocation and investment strategy. An expectation of increased
inflation in the U.K.
might lead to expectations that U.K. equity performance will slow and would likely result in both weaker U.K.
equity returns and stronger returns from overseas markets. This would justify an increased allocation to international
equit
ies.
The third action (
“
Initiate a program to protect the financial strength of the pension scheme from the effects of U.K.
inflation by indexing benefits paid by the scheme
”
) is incorrect
.
The implementation of an inflation index
adjustment program would protect the plan participants, not the plan itself, from the effects of higher U.K. inflation.
With an inflation index adjustment program, Summit
’
s costs of funding the defined benefit sche
me would actually
increase (thereby weakening the plan
’
s financial position) as U.K. inflation increases.
13.
In practice, an acceptable benchmark is one that both the investment manager and the plan sponsor agree
represents the manager
’
s investment
process. However, in order to function effectively in performance evaluation, a
benchmark should possess certain basic properties. It should be
►
Unambiguous
.
The names of securities and their corresponding weights in the benchmark should be
clearly noted
.
Jerald E. Pinto, CFA, and Dennis W. McLeavey, CFA, editors. Copyright © 2007 by CFA Institute. Reprinted with
permission.
Solutions for Appendix A: CFA Questions and Problems

171

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© 2010 by Nelson Education Ltd.
►
Investable
.
The benchmark should be available as a passive option.
►
Measurable
.
I
t
should be possible to calculate the benchmark
’
s return on a timely basis, for various time
periods (e.g., monthly, quarterly, annually).
►
Appropriate
.
The benchmark sho
uld be consistent with the manager
’
s investment style or area of
expertise.
►
Reflective of current investment opinions
.
The manager should have opinions and investment knowledge
of
th
e individual securities within the benchmark.
►
Specified in advance
.
The benchmark should be specified prior to
the beginning of an evaluation period
and known to both the
investment manager and the fund sponsor.
►
Owned
.
The investment manager should be aware of and accept
accountability for
th
e constituents and
performan
ce of the
benchmark.
14.
Kim Lee Ltd.
’
s benchmark is not valid. The chief criticism of
th
is
type of benchmark is that it is not, and
cannot be, specified in advance.
Furthermore, since no one knows who
th
e top

quartile managers will be at
th
e beginning of
an evaluation period,
th
e
benchmark is not investable; i.e.,
th
ere
is no passive option for investment Kim Lee Ltd. can inform existing and
prospective clients where
th
e firm
’
s past performance has ranked in its peer group, but
th
e universe should not be
used
ex ante
as a performance benchmark. Fur
th
ermore,
th
e firm should disclose sufficient information about
th
e
composition of
th
e peer group for recipients to evaluate
th
e meaningfulness of the firm
’
s
ex post
ranking.
Chapter 3
Level II
1.
Year
Portfolio Return
Benchmark Return
Excess Return
Squared Deviation
2008
12%
14%

2.0%
0.18%
2009
14%
10%
4.0%
0.03%
2010
20%
12%
8.0%
0.34%
2011
14%
16%

2.0%
0.18%
2012
16%
13%
3.0%
0.01%
The squared deviation column is the squared deviation of the
excess return for each period from the mean excess
return of 2.20 percent.
Solutions to 1 and 2 taken from
Solutions Manual
to accompany
Global Investments
, Sixth Edition, by Bruno
Solnik and Dennis McLeavey, CFA. Copyright © 2009 by Pearson Education. Reprinted with permission of Pearson
Education, publishing as Pearson Addison Wesley.
Solutions for Appendix A: CFA Questions and Problems

172

Copyright
© 2010 by Nelson Education Ltd.
√
2
.
If the German firm invests
fu
nds
(say, €1) in one

year euro bonds, at the end of one year it will have 1(1 +
0.0335) = €1,0335.
Alternatively the German firm could convert €1 into $(1/1.12)
=
$0.8929.
This amount would be invested in one

year U.S. bonds, and at the end of
one year it will have 0.8929(1 + 0.0225) = $0.913.
This can be converted back to euros = 0.913(1.25) = €1.1412.
The firm is better off investing in U.S. bonds.
Level III
3
.
Currency
fluctuations have an impact on
th
e total return and volatility of foreign currency
–
denominated
investments. However, there are at least four reasons why currency risk is not a barrier
to international investment:
►
Market and currency risks are not additive. This is because the correlation between currency and market
movements is quite weak and sometimes negative. Consequently, the contribution of currency risk to the risk of a
foreign
investment is quite small.
►
Currency risk can be hedged away by selling currency futures or forward contracts.
►
If foreign assets represent a small portion of the portfolio, then the contribution of currency risk is
insignificant (Jor
ion
, 1989). Also, if
the portfolio consists of multiple currencies, some portion of the risk is
diversified away.
►
Currency risk decreases with
th
e length of the investment horizon, because exchange rates tend to revert to
fundamentals.
4
.
Yes. The risk that counts is the c
ontribution of the foreign assets to the
tota
l
risk of the global portfolio. In
the proposed example, foreign stocks have a larger standard deviation (20%) than U.S. stocks (15%). However, let
’
s
calculate the standard deviation of the diversified portfolio
made up of 90 percent domestic stocks and 10 percent
foreign stocks. We have
2 2 2 2 2
ρ
σ σ (1 ) σ 2 (1 )ρσ σ
d f d f
x x x x
where
σ
p
is the risk of the portfolio
σ
d
is the risk of domestic stocks
σ
f
is the risk of foreign stocks
ρ
is the correlation between domestic and foreign stocks
x
is the proportion of the portfolio invested in domestic stocks
Solutions for Appendix A: CFA Questions and Problems

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Here, we will take
ρ
=
−
0.10, because the U.S. portfolio is very strongly correlated with the U.S. stock index.
2 2 2 2 2
2
σ (0.9 )(15 ) (0.1 )(20 ) 2(0.9)(0.1)( 0.1)(15)(
20)
σ 182.25 4 5.4 180.85
σ 13.45%
p
p
p
Thus, the addition of foreign equity allows us both to increase the return (here,
R
p
(0.9) (10) + (0.1)(11) = 10.1%)
and reduce the risk of a domestic portfolio.
Chapter 4
Level I
1.
B is correct. The division of tax between buyers and sellers
depends in part on the elasticity of demand and
the elasticity of supply. In the extreme, sellers pay when the demand is perfectly elastic and the supply is perfectly
inelastic.
2.
A is
correct.
Inflation for 2005 = (196.8/190.3)
−
1 = 1.0342
−
1 = 3.42% or (196.8
−
190.3)/190.3 =
3.42%. The compound annual inflation for 2000
–
2005 is found using a financial calculator. Inputs are
PV
=
−
174.0,
FV
=
196.8,
N
=
5,
PMT
=
0, and compute
I
/
Y=
2.49%.
3.
Profit
on
a short sale = Begin, value
−
Ending va
lue
−
Dividends
−
Trans
.
costs
−
I
nterest
Beginning value of investment = $56.00
×
100 shares = $5,600 (sold under a short sale arrangement)
Your investment = Margin requirement Commis
sion
= (.45 $5,600) $155
$2,520 $155
$2,675
Ending value of investment = $45.00
×
100 = $4,500 (Cost of closing out position)
Dividends = $2.50
×
100 shares = $250.00
Transaction costs = $155 + $145 = $300.00
Therefore:
Solution to 3 taken from
Solutions Manual
to accompany
Global Investments
, Sixth Edition, by Bru
no Solnik and
Dennis McLeavey, CFA. Copyright © 2008 by Pearson Education. Reprinted with permission of Pearson Education,
publishing as Pearson Addison Wesley.
All other solutions copyright © CFA Institute.
Solution to 3 taken from
Solutions Manual
to ac
company
Investment Analysis and Portfolio Management,
Eighth
Edition, by Frank K. Reilly, CFA and Keith C. Brown, CFA. Copyright 2005 by Thomson
S
outh

Western.
Reprinted with permission of South

Western, a division of Thomson Learning.
All other solutions
copyright © CFA
Institute.
Solutions for Appendix A: CFA Questions and Problems

174

Copyright
© 2010 by Nelson Education Ltd.
Profit = $5,600 $4,500 $250 $300
= $550.00
The rate of return on your investment of $2,675 is:
$550.00/$2,675 = 20.56%
4.
C is correct.
The total market value of the position is
equal to:
(Initial purchase price/share)
×
(# of shares)
×
(1 + (Return %))
$70
×
100
×
(1.15) =
$8,050
The investor
’
s equity is equal to:
(Current market value of the stock)
−
(Initial margin position)
Initial margin position (Initial price pe
r share) (# of shares) (% Margin)
($70) (100) (0.50) $3,500
Investor
’
s equity = ($8,050
−
$3,500) = $4,550
5.
A.
Given a three security series and a price change from period T to T+
1
, the percentage change in
the series would be 42.85 percent.
Period T
Period T+1
A
$60
$ 80
B
20
35
C
18
25
Sum
$98
$140
Divisor
3
3
Average
32.67
46.67
46.67 32.67 14.00
Percentage change 42.85%
32.67 32.67
B.
Period T
Stock
Price/Share
# of Shares
Market Value
A
$60
1,000,000
$ 60,000,000
Solutions Manual
to accompany
Investment Analysis and Portfolio Management,
Eighth Edition, by Frank K.
Reilly, CFA and Keith C. Brown, CFA. Copyright 2005 by Thomson
S
outh

Western. Reprinted with permission of
South

Western, a
division of Thomson Learning.
Solutions for Appendix A: CFA Questions and Problems

175

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B
20
10,000,000
200,000,000
C
18
30,000,000
540,000,000
Total
$
800,000,000
Period T+1
Stock
Price/Share
#
of Shares
Market Value
A
$80
1,000,000
$ 80,000,000
B
35
10,000,000
350,000,000
C
25
30,000,000
750,000,000
Total
$1,180,000,000
1,180 800 380
Percentage change 47.50%
800 800
C.
The percentage change for the price

weighted series is a simple average of the differences in price from one
period to the next.
E
qual
weights are applied to each price change.
The percentage change for the value

weighted series is a weighted average of th
e differences in price from one
period T to T
+1
. These weights are the relative market values for each stock. Thus, Stock C carries the greatest
weight followed by B and then A. Because Stock C had the greatest percentage increase and the largest weight, i
t is
easy to see that the percentage change would be larger for this series than the price

weighted series
.
Solutions for Appendix A: CFA Questions and Problems

176

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6.
A.
Period T
Stock
Price/Share
# of Shares
Market
Value
A
$60
16.67
$
1,000
B
20
50.00
1
,
000
C
18
55.56
1,000
Total
$
3,000
Period
T+1
Stock
Price/Share
# of Shares
Market Value
A
$
80
16.67
$
1,333.60
B
35
50.00
1,750.00
C
25
55.56
1,389.00
Total
$4,47
2
.60
4,472.60 3,000 1,472.60
Percentage change 49.09%
3,000 3,000
B.
80 60 20
A 33.33%
60 60
35 20 15
B = 75.00%
20 20
25 18 7
C = 38.89%
18 18
33.33% 75.00% 38.89%
Arithmetic average
3
147.22%
49.07%
3
The answers are the same (slight
difference due to rounding). This is what you would expect since part A represents
the percentage change of an equal

weighted series and part B applies an equal weight to the separate stocks in
calculating the arithmetic average.
C.
Geometric average is th
e nth root of the product of n items.
1/3
1/3
Geometric average [(1.3333)(1.75)(1.3889)
] 1
[3.2407] 1
1.4798 1
.4798 or 47.98%
Solutions for Appendix A: CFA Questions and Problems

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The geometric average is less than the arithmetic average. This is because variability of return has a greater affect on
the arithmetic average than the geometric
average.
Level III
7.
A.
Quoted spread is the difference between the ask and bid prices in the quote prevailing at the time
th
e trade is entered. The prevailing quote is the one at 10:50:06, with a bid of
$
4.69 and an ask of $4.75. So, Quoted
spread = Ask
−
Bid
=
$4.75
−
$
4.69 = $
0.06.
B.
The time

of

trade quotation midpoint = ($4.69 + $4.75)/2 = $4.72. Effective spread = 2
×
(Trade price
−
Time

of

trade quotation midpoint)
=
2
×
($4.74
−
$4.72)
=
2
×
$0.02 = $0.04.
C.
The effective and quoted spreads would be equal if a purchase t
ook place at the ask price and a sale took
place at the bid price.
8.
A.
Missed trade opportunity cost is
th
e unfilled size times the difference between the subsequent
price and the benchmark price for buys (or times the difference between the benchmark price and
th
e subsequent
price for sells). So, using the closing price on 8 February as the subsequent price,
the estimated missed trade
opportunity cost is 460,000
×
($23.60
−
$21.35) = $1,035,000.
B.
Using the closing price on 14 February as the subsequent price, the estimated missed trade opportunity cost
is 460,000
×
($21.74
−
$21.35) = $179,400.
C.
One of th
e problems in estimating missed trade opportunity cost is that the estimate depends upon when the
cost is measured. As the solutions to Parts A and B of this problem indicate, the estimate could vary substantially
when a different interval is used to measu
re the missed trade opportunity cost. Another problem in estimating the
missed trade opportunity cost is that it does not consider the impact of order size on prices. For example, the
estimates above assume that if the investment manager had bought the 500
,000 shares on 8 February, he would have
been able to sell
th
ese
500,000 shares at $23.60 each on 8 February (or at $21.74 each on 14 February). However, an
order to sell 500,000 shares on 8 February (or on 14 February) would have likely led to a
decline i
n price, and the
entire order of 500,000 shares would not have been sold at $23.60 (or at $21.74). Thus, the missed trade opportunity
costs above are likely to be overestimates.
9.
The average execution cost for a purchase of securities is 75 basis points
, or 0.75 percent, and the average
execution cost for a sale of securities is also 0.75 percent
.
So, the average execution for a round

trip trade is 2
×
0.75%, or 1.5%. Since the portfolio is expected to be turned over twice, expected execution costs are 1
.5%
×
2 =
Managing Investment Portfolios: A Dynamic Process
, Third Edition, John L. Maginn, CFA, Donald I. Tuttle, CFA,
Jerald E. Pinto, CFA, and Dennis W. McLeavey, CFA, editors. Copyright © 2007 by CFA Institute. Reprinted with
permi
ssion.
Solutions for Appendix A: CFA Questions and Problems

178

Copyright
© 2010 by Nelson Education Ltd.
3%. Therefore, the expected return net of execution costs is 8%
−
3
% = 5%.
Chapter 5
Level I
II
1.
A is correct. The economist
’
s forecast assumed the Fed would keep rates low, but instead the Fed raised
rates. This argument is the
“
if only
”
excuse.
2.
C
is correct. The first comment is incorrect because trading risk is a chronic inefficiency that can persist
and be hard to
exploit.
The second comment is correct because it exploits an acute inefficiency, mispricing based on
fundamentals.
3.
C is correct. The phenomenon of blaming someone else for
th
e decision is an example of self

attribution
bias.
4.
C is correct. Myopic loss aversion is behavior associated with investors who focus on short time horizons.
They tend to look at one

year returns rather than
th
e longer time horizons appropriate for pension fund investing.
5.
C is correct
.
The endorsement effect refers to
th
e participant inferring the range of fund choices offered as a
suggestion (endorsement) of the best way to allocate funds.
6.
C is correct. Only the second guideline is consistent with Alpha Fund
’
s mission. Chronic inef
ficiencies may
exist for a number of years. Rigidly adhering to a one

year time horizon may force the manager to
se
l
l
at a
significant loss. The policy of price

target revision is consistent of adhering to a well thought out
p
l
an.
7.
A. Overall, the domes
tic equities asset class has performed well relative to the benchmark (4.54% vs.
4.04%). However, only one of the two domestic equities managers has outperformed his respective benchmark.
Equity manager A has outperformed by 15 basis points, while equity m
anager B has underperformed by 18 basis
points.
The international equity asset class as a whole has outperformed its benchmark
.
I
n addition, both international
equity managers have also outperformed their respective benchmarks.
The fixed

income asset clas
s underperformed its benchmark. Both fixed

income managers have underperformed
their respective benchmarks as well.
Managing Investment Portfolios: A Dynamic Process
, Third Edition, John L. Maginn, CFA, Donald I. Tuttle, CFA,
Jerald E. Pinto, CFA, and Dennis W. McLeavey, CFA , editors. Copyright © 2007 by CFA Institute. Reprinted with
permission.
Solutions for Appendix A: CFA Questions and Problems

179

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© 2010 by Nelson Education Ltd.
B.
Overall, the total fund has outperformed its benchmark by 11 basis points. Nevertheless, the fund may be
able to improve its relative per
formance by considering some changes to the manager lineup.
C.
For each manager that underperformed
hi
s or her assigned benchmark (equity manager B and
bo
th
fixed

income managers), the plan sponsor should first verify that the benchmarks in place are appro
priate for
th
e particular
managers
’
investment styles. If
th
e benchmarks are appropriate, and if performance is not expected to improve
(based on many factors, including quality of people, organizational issues, etc.), then
th
e plan sponsor may consider
re
placing these managers with other active managers following similar investment disciplines, or perhaps replacing
them with passive investment alternatives corresponding to
th
e benchmarks
th
ose managers are being measured
against
.
8.
The average performance
should be that of the market index minus costs (transaction costs, management
fees).
If international investors, as a group, beat some national index, it tells us that local investors, as a group, probably
underperform
th
e index.
Not necessarily. Because
of costs,
bo
th
international and local investors can, as a group, underperform the local
index.
Chapter 6
Level I
1.
A is correct
.
The current portfolio has an equal amount invested in each of the four securities. The expected
return on the current portf
olio is the simple average of the individual securities: (0.10 + 0.12 + 0.16 + 0.22)/4 = 0.15
or 15 percent. Replacing a security with a 16 percent return with a security having a 15 percent return will lower the
portfolio
’
s expected return. Correlations h
ave no effect on the return calculation.
2.
B is correct. Replacing a security with a 14 percent return with a security having only a 13 percent return
will lower the expected return of the portfolio. The expected return on a portfolio is simply a weighte
d average of
the expected returns for each of the individual securities in the portfolio.
Level II
3.
The expected return is 0.75
E
(return on stocks) + 0.
2
5
E
(retu
rn
on
bonds
)
Solutions
Manual
to accompany
Global Investments
, Sixth Edition, by Bruno Solnik and Dennis McLeavey, CFA.
Copyright © 2009 by Pearson Education. Reprinted with permission of Pearson Education, publishing as Pearson
Addison Wesley.
Quantitative Methods for Investme
nt Analysis,
Second Edition, by Richard A. DeFusco,
CFA,
Dennis W.
McLeav
e
y,
CFA, J
erald E. Pinto,
CFA,
and David E. Runkle,
CFA.
Copyright © 2004 by AIMR. Reprinted with
permission.
Solutions for Appendix A: CFA Questions and Problems

180

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0.75(15) 0.25(5)
12.5 percent
The standard deviation is
2 2 2 2
stocks stocks bonds bonds stocks bonds
1/2
stocks bonds stocks bonds
2 2 1/2
1/2
1/2
σ [ σ σ 2
Corr ( )
σ σ ]
[0.75 (225) 0.25 (100) 2(0.75)(0.25)(0.5)(15
)(10)]
(126.5625 6.25 28.125)
(160.9375)
12.69%
w w w w
R R
4.
Use the expression
2 2
1
ρ
σ σ ρ
p
n
The square root of this expression is standard deviation. With variance equal to 625 and correlation equal to 0.3,
1 0.3
σ 625 0.3
100
13.85%
p
5.
Find portfolio variance using the following expression
2 2
2
1
ρ
σ σ ρ
σ 625[(1 0.3)/24 0.3] 205.73
p
p
n
With 24 stocks, variance of return is 205.73 (equivalent to a standard deviation of 14.34 percent). With an unlimited
number of securities, the first term in square brackets is 0 and the smallest variance is achieved:
2 2
min
σ σ ρ 625(0.30) 187.5
This result is equivalent to a standard deviation of 13.69 percent
.
The ratio of the variance of the 24

stock portfolio
to the portfolio with an unlimited number of securities is
2
2
min
σ
205.73
1.097
σ 187.5
p
The variance of the 24

stock portfo
lio is approximately 110 percent of the variance of the portfolio with an
unlimited
nu
m
ber
of securities.
Chapter 7
Level I
1.
B is correct. The required rate of return for McGettrick is 12.8 percent using the CAPM: 4% + (1.1
×
8%)
=
12.8%. This is the same as the estimated rate of return and McGettrick is properly valued. If Jimma has a higher
covarian
c
e
with the market portfolio than McGettrick, it also has a higher beta and a higher required rate of return.
Solutions for Appendix A: CFA Questions and Problems

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Because Jimma
’
s estimate
d rate of return is below
th
e required rate of return, the stock is
ov
ervalued.
2.
A is correct. The beta for the stock is computed by dividing the covariance of the stock with the market by
the var
i
ance of the market. In this case, the covariance and var
iance are
equal, so the beta is 1.0. The required rate of
return for the stock is the same as the return expected for the market. The estimated return for the stock exceeds its
required return, so the stock is undervalued.
3.
i i M
i
i
( )
β ( )
.10
β (.14.10)
.10.04
β
E R RFR R RFR
Stock
Beta
(Required Return)
E
(
R
i
)
= .10 +
.04β
i
U
85
.10 + .04(.85) = .10 + .034 = .134
N
1.25
.10 + .04(1.25) = .10 + .05 = .150
D
−
.20
=
.10=⬠.04E
−
.20F===.10=

=
.008===.092
=
=
㐮
=
C=楳=捯rr散琮tA=por瑦o汩l=瑨慴ais=on=瑨攠CMi=瑯=th攠汥l琠tf=瑨攠m慲k整e
por瑦o汩l=楳=愠汥nd楮g=por瑦o汩l=w楴h=
p慲琠tf=瑨攠楮v敳瑯r
’
s wealth invested in the risk

free asset (loaned at the risk

free rate).
Level II
5.
The
surprise in a factor equals actual value minus expected value. For the (interest rate factor, the surprise
was 2 percent; for
the GDP factor, the
surprise was
−
3 percent
.
Expected return 1.5(Interest rate surpri
se) 2(GDP surprise)
Companyspecific surprise
11% 1.5(2%) 2( 3%) 3%
5%
R
Chapter 8
Level II
Solution to 3 taken from
Solutions Manual
to accompany
Investment
Analys
is and Portfolio Management
, Eighth
Edition, by Frank K. Reilly, CFA and Keith C. Brown, CFA. Copyright
©
2005 by Thomson
S
outh

Western.
Reprinted with permission of South

Western, a division of Thomson Learning.
All other solutions copyright © CFA
Institu
te.
Solutions Manual
to accompany
Global Investments
, Sixth Edition, by Bruno Solnik and Dennis McLeavey, CFA.
Copyright © 2008 by Pearson Education. Reprinted with permission of Pearson Education, publishing as Pearson
Addison Wesley.
Solutions for Appendix A: CFA Questions and Problems

182

Copyright
© 2010 by Nelson Education Ltd.
1.
In an efficient market, all available information is already incorporated in current stock prices. The fact that
economic growth is currently higher
in
Country A than in Country B implies that current stock prices are already
“
higher
”
in A than in B. Only
unanticipated news about future growth rates should affect future stock prices. Current
growth rates can explain past performance of stock prices, but only differences in future growth rates from their
current anticipated levels should guide your country s
election. Hence, you should decide whether your own
economic growth forecasts differ from those implicit in current stock prices.
2.
It is clear by looking at the
t
able that in each of the three size categories, the low price

to

book value stock
(P/BV) outperforms the high P/BV stock. Thus, there seems to be a
value effect,
as the value firms seem to
outperform the gro
w
th firms. That is, the value factor seems to be
significant.
To clearly see the
size effect,
we rearrange the stocks in the two P/BV categories, as follows:
Stock
Size
P/BV
Return (%)
A
Huge
High
4
C
Medium
High
9
E
Small
High
13
B
Huge
Low
6
D
Medium
L
ow
12
F
Small
Low
15
In both P/BV categories, smaller firms outperform bigger firms. Thus, there seems to be a
size effect
,
and the size
factor seems to be significant
.
3.
Applying the

Gordo
n
growth model with the assumed 5.9 percent dividend growth rate results in an
estimat
ed value of $1,398.38 trillion for
th
e S&P 500 index.
1
0
27.73(1 0.059)
$1,398.38 trillion
0.08 0.059
D
V
r g
Chapter 9
Level I
1.
To compute the compound growth rate, we only need the beginning and ending EPS values of $4.00 and
$7.00 respectively, and use the following equation:
Equity Asset Valuat
ion
, Second Edition, by Gerald Pinto, CFA, Elaine Henry, CFA Thomas Robinson, CFA, and
John Stowe, CFA. Copyright ©2009 by CFA Institute. Reprinted with permission.
Solutions to 1 and 2 taken from
Quantitative Methods for Investment Analysis
, Second
Edition, by Richard A.
DeFusco, CFA, Dennis W. McLeavey, CFA, Jerald E. Pinto, CFA, and David E. Runkle, CFA. Copyright © 2004
by CFA Institute. Reprinted with permission. All other solutions copyright ©CFA Institute.
Solutions for Appendix A: CFA Questions and Problems

183

Copyright
© 2010 by Nelson Education Ltd.
4
1/4
1/4
FV
PV(1 )
7
4(1 )
1
(7/4)
(7/4) 1
0.1502 15.02%
N
N
r
r
r
r
EPS grew at an annual rate of 15.02 percent during the four years.
2
.
A
is correct. Using the general time value of money formula, for sales, solve for
r
in the equation 2 = 1
×
(1
+
r
)
5
. For income, solve 3 = 1
×
(1 +
r
)
5
. Alternatively, using a financial calculator, for sales, enter
N
=
5, PV
= 1,
PMT=0, FV=
−
2 and compute I/Y
.
For income, change the FV to
−
3 and again solve for
1
/Y
.
The solution for sales
is 14.87%; and for income is 24.57%.
3.
B is correct. Free cash flow
to the firm can be computed as operating cash flows plus after

tax interest
expense less capital expenditures.
4.
C is correct. The required rate of return for the company is 6% + 1.2(11%
−
6%) = 12%. Dividends are
expected to grow at a supernormal rate
for two years:
(1) €3.00(1.20) = €3.60
(2) €3.60(1.20) = €4.32
(3) €4.32(1.09) = €4.7088.
D
D
D
The terminal value of the stock is €4.71/(12.0%
−
9.0%) = €156.96.
The present value of the dividends and the terminal value is €131.79.
3.214 + 3.444 + 125.128 = 131.79.
5.
C
is correct. The inputs to the DDM formula are
D
1
/
(
k
−
g
),
where
g
is
a
function of ROE
×
retention rate.
Using the breakdown of ROE formula, the
ROE
is
3%(2.0)(3.0) = 18% and the retention rate is 1
−
5/20
=
0.75, so
the growth rate = 18%(0.75) = 13.50%.
D
0
(dollar dividend per share) is $5/2.0 = $2.50 per share.
D
1
=
$
2.50(1.135)
= $2.8375. The price per share is $2.8375/(17.5%
−
13.5%)
=
$70.9375.
Level II
6.
A.
The FCFF
is (in
euros)
FCFF NI NCC Int(1 Tax rate) FCInv WCInv
FCFF 250 90 150(1 0.30) 170 40
FCFF 250 90 105 170 40 235 million
The weighted

average cost of capital is
WAC
C = 9%(1
−
0.30)
(
0.40) + 13
%
(0.60) = 10.32%
The value of the firm (in euro) is
Solutions for Appendix A: CFA Questions and Problems

184

Copyright
© 2010 by Nelson Education Ltd.
0
1
Firm value FCFF (1 )
FCFF
235(1.06)
WACC WACC 0.1032 0.06
249.1
5,766.20 million
0.0432
g
g g
The total value of equity is the total firm value minus the value of debt, Equity = €5,766.20 million
−
€1,800 million
= €3,966.20 million. Dividing by the number of shares gives the per share estimate of
V
0
= €3,966.20 million/10
million = €396.62 per share.
B.
The free cash flow to equity is
FCFE NI NCC FCInv WCInv Net borrowing
FCFE 250 90 170 40 0.40(170 90 40)
FCFE 250 90 170 40 48 €178 million.
Because the company is borrowing 40 p
ercent of the increase in net capital expenditures (170
−
90) and working
capital (40), net borrowing is €48 million.
The total value of equity is the FGFE discounted at the required rate of return of equity,
0
1
Equity value = FCFE (1 )
FCFE
178(1.07)
0.13 0.07
= 190.46
€3,174.33 million
0.06
g
r g r g
The value per share is
V
0
= €3,174.33 million/10 million = €317.43 per share.
7.
A.
The required return on equity is
r
=
E
(
R
i
) =
R
F
+
β
i
[
E
(
R
M
) −
R
F
] = 5.5% + 0.90(5.5%) = 10.45%
The weighted

average cost of capital is
WA
C
C
=
0.25(7.0%) (1
−
0.40) + 0.75(10.45%) = 8.89%
B.
0
Firm value FCFF (1 )
WACC
Firm value 1.1559(1.04)
$24.583
0.0889 0.04
g
g
C.
Equity value = Firm value
−
Market value of debt
Equity value
=
24.583
−
3.192 = $21.391 billion
D.
Value per share = Equity value/Number of shares
Value per share = $21.391 billion /1.852
billion = $11.55.
Quantitative Methods for Investment
Analysis
, Second Edition, by Richard DeFusco, CFA, Dennis W. McLeavey,
CFA, Jerald E. Pinto, CFA, and David E. Runkle, CFA. Copyright © 2009 by CFA Institute. Reprinted with
permission.
Solutions for Appendix A: CFA Questions and Problems

185

Copyright
© 2010 by Nelson Education Ltd.
8.
I
n
principle, the use of any price multiple for valuation is subject to the concern stated. If the stock market
is overvalued, an asset that appears to be fairly or even undervalued in relation to an equity index may also be
overvalue
d.
Level III
9.
The fund has a modest value orientation. Dividend yield, P/E, P/B, and EPS growth are all slightly lower
than the market benchmark. The sector weights are a bit more mixed. Some sectors that typically contain stocks with
value characteris
tics (consumer discretionary and utilities) are overweight, while others (finance and energy) are
underweight or equal weight to the benchmark. Also, traditionally growth oriented sectors like health care and
information technology are modestly overweight
—
unlikely in a deep value portfolio.
Chapter 11
Level I
1.
A.
While it may be true that the Company can call the issue if rates
d
ecline, there is a nonrefunding
restriction prior to January 1, 2006. The
Company may not refund the issue with a source of
funds that costs less
than 7.75% until after that date.
B.
This is only true if the issuer redeems the issue as permitted by the call schedule. In that case the premium
is paid. However, there is a sinking fund provision. If the issuer calls in the particu
lar certificates of the issue held by
the investor in order to satisfy the sinking fund provision, the issue is called at par value. So, there is no guarantee
that the issue will be paid off at a premium at any time if the issue is called to satisfy the si
nking fund provision.
C.
It is commonly thought that the presence of a sinking fund provision reduces the risk
th
at the issuer will not
have sufficient funds to pay off the amount due at the maturity date. But this must be balanced against
th
e fact that a
bondholder might have his or her bonds taken away at par value when
th
e issuer calls a part of the issue to satisfy
the sinking fund provision. If the issue is trading above par value, the bondholder only receives par. So, for example,
if the issue is tra
ding at 115 and it is called by the Company to satisfy the sinking fund provision, the investor
receives par value (100), realizing a loss of 15.
D.
As in part C, while it may seem that the right of t
he
issuer to make additional payments beyond the require
d
amount of the sinking fund will reduce
th
e likelihood
th
a
t
the issuer will have insufficient funds to pay off
th
e issue
at the maturity date,
th
ere
is still
th
e potential loss if
th
e issue is called at par. Moreover, the issuer is likely to make
Solution to 9
–
10
taken from
Managing Investment Portfolios: A Dynamic
Process
, Third Edition, John L. Maginn,
CFA, Donald I. Tuttle, CFA, Jerald E. Pinto, CFA, and Dennis W. McLeavey, CFA , editors. Copyright © 2007 by
CFA Institute. Reprinted with permission.
All other solutions copyright © CFA Institute.
Solutions to 1
to
5 taken from
Fixed Income Analysis for the Chartered Financial Analyst® Program
, Second
Edition, by Frank J. Fabozzi, CFA. Copyright ©2005 by CFA Institute. Reprinted with permission. All other
solutions copyright ©CFA Institute.
Solutions for Appendix A: CFA Questions and Problems

186

Copyright
© 2010 by Nelson Education Ltd.
additional payments permitted to retire the issue via
th
e sinking fund special call price of 100 when the bond is
trading at a premium, because that is when interest rates in
th
e market are less than the coupon rate on the issue
.
E.
The assistant portfolio
manager cannot know for certain how long the bond issue will be outstanding
because it can be called per the call schedule. Moreover, because of
th
e sinking fund provision, a portion of
th
eir
particular bonds might be called to satisfy
th
e sinking fund re
quirement (One of the major topics in fixed income
analysis is
th
at because of the uncertainty about
th
e cash flow of a bond due to the right to call an issue,
sophisticated analytical techniques and valuation models
are needed.)
2.
The borrowers whose loa
ns are included in the pool can at lower interest rates refinance their loans if
interest ra
t
es decline below the rate on t
h
eir loans.
Consequen
tl
y,
the security holder cannot rely on the schedule of
principal and interest payments of the pool of loans to
determine wit
h
certainty future cash flow.
3.
A.
Since the inflation rate (as measured by the CPI

U) is 3
.
6%,
th
e semiannual inflation rate for
adjusting the principal is 1.8%.
i
.
The inflation adjustment to the principal is
$1,000,000
×
0.018% = $18,000
ii
.
The inflation

adjusted principal is
$1,000,000 Inflation adjustment to the pr
incipal
$1,000,000 $18,000 $1,018,000
ii
i
.
The coupon payment is equal to
Inflationadjusted principal (Real rate/2
)
$1,018,000 (0.032/2) $16,288.00
B.
Since the inflation rate is 4.0%, the semiannual inflation rate for adjusting the principal is 2.0%.
i.
The inflation
adjustment to the principal is
$1,018,000
×
0.02% = $20,360
ii.
The inflation

adjusted principal is
$1,018,000 Inflation adjustment to the pr
incipal
$1,018,000 $20,360 $1,038,360
iii
.
The
coupon
payment is equal to
Inflationadjusted principal (Real rate/2
)
$1,038,360 (0.032/2) $16,613.76
Level II
4.
A.
With high

yield issuers there tends to be more bank loans in the debt structure and the loans tend
to be short term. Also, the loans tend to be floating rate rather than fixed. As a result,
th
e analyst must look at the
ability of the issuer to access short

term funding sources for liquidity to meet not only possible higher interest
payments (when interest rates rise), but to pay off a maturing loan. High

yield issuers, however, have fewer
alternatives for short

term funding sources than high

grade issuers
.
Solutions for Appendix A: CFA Questions and Problems

187

Copyright
© 2010 by Nelson Education Ltd.
B.
At any given point in time, the cushion (as measured by coverage ratios) may be high. However, the
concern is with future cash flows to satisfy obligations. If the coverage ratio is adequate and is predicted to change
little in the future and the degree
of confidence in the prediction is high, that situation would give greater comfort to
a bondholder than one where the coverage ratio is extremely high but can fluctuate substantially in the future.
Because of this variability it is difficult to assign a h
igh degree of confidence to coverage ratios that are projected,
and there must be recognition that the coverage ratio may fall well below acceptable levels.
C.
Financial flexibility means the ability to sustain operations should there be a down turn in bus
iness and to
sustain current dividends wi
th
out reliance on external funding.
D.
Unfunded pension liabilities may not be listed as debt, but they are effectively a form of borrowing by the
firm. Hence, Moody
’
s is considering them as part of the debt obligat
ion. Guarantees represent potential liabilities if
the corporate entity whose debt is guaranteed does not meet its obligations. If Moody
’
s views the obligation as one
that the company may have to satisfy, the obligation of the corporate entity whose debt i
s guaranteed is a form of
borrowing and should be included in total debt
.
E.
Ratios represent a snapshot of a particular aspect of a firm
’
s financial position at a given point in time.
Ratings reflect an assessment of the future financial position and
the
assessment of future cash flows. This involves
looking at a myriad of factors that impact future cash flows such as competition, potential earnings growth, and
future capital requirements. This is a major limitation of ratio analysis as a sole indicator of
an entity
’
s financial
strength
—
it is not forward looking in that it does not look at how factors in
th
e future can alter cash flows.
5.
All the financial ratios
—
actual and projected for 2001
—
clearly indicate that the credit

worthiness of
Krane
Products i
s improving. Using as benchmarks the S&P median ratios,
the
coverage ratios were already by fiscal year
2000 approaching
th
at of the median BBB rated issuer. The capitalization ratios, while improving, were still well
below that of the median BBB rated iss
uer. Consequently, by fiscal year 2000 an analyst would have been well
advised to monitor this issuer
’
s credit for a possible upgrade and to examine how it was trading in the market
.
That
is, was it trading like a BB or BBB credit?
If Ms. Andrews
’
projecti
ons are correct for fiscal year 2001, the ratios shown in the table are at least as good as the
median BBB rated company. Consequently, based on her projections she would recommend the purchase of
Krane
Products Inc. bonds if that issuer
’
s bonds continue t
o trade like a BB credit since, based on her analysis, the bonds
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