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Solutions for Appendix A: CFA Questions and Problems
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, r3, should thus be
above 2.5 percent (the interest rate on Investment 2). If the liquidity 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 contrast 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 r3 to be less than 4.5 percent, the expected interest rate on Investment 4 if it had low liquidity. Thus 2.5
percent < r3 < 4.5 percent.
2.
The geometric mean requires that all the numbers be greater than or equal to 0. To ensure that the returns satisfy
this requirement, after converting the returns to decimal form we add 1 to each return. For the geometric mean
return, RG:
 10

RG   (1  R1 ) 
 t 1

(1/10)
1
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.
- 160 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
RG  10 (1  R1 )(1  R2 )
(1  R10 )  1
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 + Rt.
Return
Return in Decimal Form
1 + Return
46.21%
0.4621
1.4621
−6.18%
−0.0618
0.9382
8.04%
0.0804
1.0804
22.87%
0.2287
1.2287
45.90%
0.4590
1.4590
20.32%
0.2032
1.2032
41.20%
0.4120
1.4120
−9.53%
−0.0953
0.9047
−17.75%
−0.1775
0.8225
−43.06%
−0.4306
0.5694
iii.
Multiply together all the numbers in the third column to get 1.9124.
iv.
Take the 10th root of 1.9124 to get
10
1.9124  1.0670 . On most calculators, we evaluate
10
1.9124 using
the yx key. Enter 1.9124 with the yx 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 6.70 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 long as a return series has any variability, the geometric mean return must be less than the arithmetic
mean return. In the solution to Problem 2, we computed the geometric mean annual return as 6.7 percent. In
general, the difference between the geometric and arithmetic means increases with the variability of the periodby-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 compound rate of growth, so it
directly 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 growth, aims to
summarize what a return series means for the growth rate of an investment over many periods.
- 161 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
4.
A. Security 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  Risk-free rate  Beta  (Market return 
Risk-free 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 Undervalue
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 estimated a 14% return.
Level III
5.
A.
Real risk-free
rate (%)
1-year U.S.
Expected
+
inflation
Spreads or
+
(%)
premiums
Expected annual
=
(%)
fixed-income
return (%)
1.2
+
2.6
+
0
=
3.8
1.2
+
2.6
+
1.0 + 0.8 +
=
6.5
T-note
10-year corp.
bond
0.9
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 South-Western.
Reprinted with permission of South-Western, a division of Thomson Learning. All other solutions copyright © CFA
Institute.

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.
- 162 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
10-0year
1.2
+
2.6
+
0.95
=
4.75
MBS
Note: We assign the 10-year corporate a 1% maturity premium based on the 10-year over 1year 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.
ra
A.
For Swennson, the annualized rate of return is:
 [(1  0.275)(1  0.189)(1  0.146)(1  0.324)
(1  0.123)]1/ 5  1
 0.0209  2.09%
For Mattsson, the annualized rate of return is:
ra
 [(1  0.057)(1  0.049)(1  0.078)(1  0.067)
(1  0.053)]1/ 5  1
 0.0327 or 3.27%
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.
- 163 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
Chapter 1 Appendix
Level I
A1.
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(46.21) + 0.40(15.74) =
34.02%
1994
0.60(−6.18) + 0.40(−3,40) =
−5.07%
1995
0.60(8.04) + 0.40(18.30) =
12.14%
1996
0.60(22.87) + 0.40(8.35) =
17.06%
1997
0.60(45.90) + 0.40(6.65) =
30.20%
1998
0.60(20.32) + 0.40(12.45) =
17.17%
1999
0.60(41.20) + 0.40(−2.19) =
23.84%
2000
0.60(−9.53) + 0.40(7.44) =
−2.74%
2001
0.60(−17.75) + 0.40(5.55) =
−8.43%
2002
0.60(−43.06) + 0.40(10.27) =
−21.73%
Sum =
96.46%
Mean Annual Return =
9.65%
Note: The sum of the portfolio returns carried without rounding is 96.48.
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  s / R  18.31/ 9.65  1.90 .
ii.
For the MSCI Germany Index, CV  s / R  29.95 /10.80  2.77 .
iii.
For the JPM Germany 5–7 Year GBl, CV  s / R  6.94 / 7.92  0.88 .
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.
A3.
Portfolio
CV
Risk
MSCI Germany Index
2.77
Highest
60/40 Equity/bond portfolio
1.90
JPM Germany GBI
0.88
Lowest
The covariance is 25, computed as follows. First, we calculate expected values:
E ( R B )  (0.25  30%)  (0.50  15%)  (0.25  10%)  17.5%
E ( RZ )  (0.25  15%)  (0.50  10%)  (0.25  5%)  10%
- 164 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
Then we find the covariance as follows:
Cov ( RB , RZ )  P(30,15)  [(30  17.5)  (15  10)]  P(15,10)
 [(15  17.5)  (10  10)]  P(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
Level II
A4.
For AOL Time Warner, the required return is
r  RF  β[ E ( RM )  RF ]  4.35%  2.50(8.04%)  4.35%
 20.10%  24.45%
For J.P. Morgan Chase, the required return is
r  RF  β[ E ( RM )  RF ]  4.35%  1.50(8.04%)  4.35%
 12.06%  16.41%
For Boeing, the required return is
r  RF  β[ E ( RM )  RF ]  4.35%  0.80(8.04%)  4.35%
 6.43%  10.78%
Level III
A5.
A.
If the correlation between bond market returns and exchange rate movements were equal to zero,
the dollar volatility of the German bond market would be
σ 2f
 σ 2  σ 2s  2ρσσ s  (5.5) 2  (11.7) 2  2(0)(5.5)(11.7)
 167.14
σf
B.
 12.93%
Because the actual dollar volatility is 13.6 percent, we conclude that the correlation between bond market
returns and exchange rate movements is positive. When the euro gets weaker, U.S. investors 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 Edition, 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.
- 165 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
negative correlation (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. The comments about investment policy statements made by Stephenson’s patients are
incorrect. The IPS should identify pertinent investment objectives and constraints for a particular 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 policy 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. Stephenson’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 above-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
- 166 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
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 have 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 salary 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 their 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 will 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 years 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%].
Christopher’s annual salary
£80,000
Less: Taxes (40%)
−32,000
Living expenses
−74,000
−£26,000
Net annual cash flow
Inheritance
900,000
Barnett Co. common stock
220,000
Stocks and bonds
160,000
Cash
Subtotal
5,000
£1,285,000
Less one-time needs:
Down payment on house
−30,000
Charitable donation
−20,000
Investable asset base
£1,235,000
- 167 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
Note: No inflation adjustment is required in the return
calculation because increases in living expenses will be offset
by increases in Christopher’s salary.
B.
The Maclins’ 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 tobacco stocks is another constraint on investment.
8.
r*
B is correct.
 r (1  p t  p t  p t )
d d
ii
cg cg
 0.06 *[1  (0.30)(0.15)  (0.20)(0.35)  (0.40)(0.25)]
 0.0471 or 4.71 percent
 t (1  p  p  p ) /(1  p t  p t  p t )
cg
d
i
cg
d d
ii
cg cg
 t (1  0.30  0.20  0.40) /[1  (0.30)(0.15)
cg
 (0.20)(0.35)  (0.40)(0.25)]
T*
 0.0318
FVIF
Taxable
 £1, 000, 000[(1  r*)n (1  T *)  T *]
 £1, 000, 000[(1  0.0471)15 (1  0.0318)  0.0318]
 £1, 962, 776
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 primary objective should be to make it financially stronger. The risk
inherent in attempting to maximize total returns would be inappropriate.
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.
- 168 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
ii. Risk 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 monthly 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 liabilities. 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 investments 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 investors (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
contrast, tax-exempt bonds sometimes 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 the strategic asset allocation of substantial investors, both institutional and
individual. A major foundation 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 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.

Managing Investment Portfolios: A Dynamic Process, Third Edition, John L. Maginn, CFA, Donald L. Tuttle, CFA,
- 169 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
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 portfolio 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 ready 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
change 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 the long
term if the inflation outlook has changed over the 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 other aspect of the 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
equities.
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 scheme 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.
- 170 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
►
Investable. The benchmark should be available as a passive option.
►
Measurable. It 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 should 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 the 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 the constituents and
performance of the benchmark.
14.
Kim Lee Ltd.’s benchmark is not valid. The chief criticism of this type of benchmark is that it is not, and
cannot be, specified in advance.
Furthermore, since no one knows who the top-quartile managers will be at the beginning of an evaluation period, the
benchmark is not investable; i.e., there is no passive option for investment Kim Lee Ltd. can inform existing and
prospective clients where the firm’s past performance has ranked in its peer group, but the universe should not be
used ex ante as a performance benchmark. Furthermore, the firm should disclose sufficient information about the
composition of the peer group for recipients to evaluate the 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.
- 171 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
Tracking error = √
2.
0.0073
4
= 0.0427, or 4.3%
If the German firm invests funds (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 oneyear 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 the 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 (Jorion, 1989). Also, if the portfolio consists of multiple currencies, some portion of the risk is
diversified away.
►
Currency risk decreases with the length of the investment horizon, because exchange rates tend to revert to
fundamentals.
4.
Yes. The risk that counts is the contribution of the foreign assets to the total 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
σρ2  x2σ2d  (1  x)2 σ2f  2x(1  x)ρσd σ f
where
σp is the risk of the portfolio
σd is the risk of domestic stocks
σf 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
- 172 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
Here, we will take ρ = −0.10, because the U.S. portfolio is very strongly correlated with the U.S. stock index. 
σ 2p
 (0.92 )(152 )  (0.12 )(202 )  2(0.9)(0.1)(0.1)(15)(20)
σ
 182.25  4  5.4  180.85
2
p
σp
 13.45%
Thus, the addition of foreign equity allows us both to increase the return (here, Rp (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 value − Dividends − Trans. costs − Interest
Beginning value of investment = $56.00 × 100 shares = $5,600 (sold under a short sale arrangement)
Your investment = Margin requirement  Commission
= (.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 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.

Solution to 3 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 South-Western.
Reprinted with permission of South-Western, a division of Thomson Learning. All other solutions copyright © CFA
Institute.
- 173 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
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 per 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
Percentage change 
46.67  32.67 14.00

 42.85%
32.67
32.67
B.
Period T
Stock
A

Price/Share
# of Shares
Market Value
$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 South-Western. Reprinted with permission of
South-Western, a division of Thomson Learning.
- 174 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
B
20
10,000,000
200,000,000
C
18
30,000,000
540,000,000
Total
$800,000,000
Period T+1
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
Stock
Total
Percentage change 
C.
$1,180,000,000
1,180  800 380

 47.50%
800
800
The percentage change for the price-weighted series is a simple average of the differences in price from one
period to the next. Equal weights are applied to each price change.
The percentage change for the value-weighted series is a weighted average of the 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, it is
easy to see that the percentage change would be larger for this series than the price-weighted series.
- 175 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
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
$4,472.60
Percentage change 
4, 472.60  3, 000 1, 472.60

 49.09%
3, 000
3, 000
B.
A 
B
=
C
=
80  60 20

 33.33%
60
60
35  20 15

 75.00%
20
20
25  18 7

 38.89%
18
18
33.33%  75.00%  38.89%
3
147.22%

 49.07%
3
Arithmetic average 
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 the nth root of the product of n items.
Geometric average  [(1.3333)(1.75)(1.3889)]1/ 3  1
 [3.2407]1/ 3  1
 1.4798  1
 .4798 or 47.98%
- 176 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
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
the 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 took place at the ask price and a sale took
place at the bid price.
8.
A.
Missed trade opportunity cost is the unfilled size times the difference between the subsequent
price and the benchmark price for buys (or times the difference between the benchmark price and the 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 the 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 measure 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 these 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 in 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
permission.
- 177 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
3%. Therefore, the expected return net of execution costs is 8% − 3% = 5%.
Chapter 5
Level III
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 the 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 the longer time horizons appropriate for pension fund investing.
5.
C is correct. The endorsement effect refers to the 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 inefficiencies may
exist for a number of years. Rigidly adhering to a one-year time horizon may force the manager to sell at a
significant loss. The policy of price-target revision is consistent of adhering to a well thought out plan.
7.
A. Overall, the domestic 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 manager B has underperformed by 18 basis
points.
The international equity asset class as a whole has outperformed its benchmark. In addition, both international
equity managers have also outperformed their respective benchmarks.
The fixed-income asset class 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.
- 178 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
B.
Overall, the total fund has outperformed its benchmark by 11 basis points. Nevertheless, the fund may be
able to improve its relative performance by considering some changes to the manager lineup.
C.
For each manager that underperformed his or her assigned benchmark (equity manager B and both fixed-
income managers), the plan sponsor should first verify that the benchmarks in place are appropriate for the particular
managers’ investment styles. If the benchmarks are appropriate, and if performance is not expected to improve
(based on many factors, including quality of people, organizational issues, etc.), then the plan sponsor may consider
replacing these managers with other active managers following similar investment disciplines, or perhaps replacing
them with passive investment alternatives corresponding to the benchmarks those managers are being measured
against.
8.
fees).
The average performance should be that of the market index minus costs (transaction costs, management

If international investors, as a group, beat some national index, it tells us that local investors, as a group, probably
underperform the index.
Not necessarily. Because of costs, both 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 portfolio 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 have 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 weighted average of
the expected returns for each of the individual securities in the portfolio.
Level II
3.

The expected return is 0.75E(return on stocks) + 0.25E(return 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 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 AIMR. Reprinted with
permission.
- 179 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
 0.75(15)  0.25(5)
 12.5 percent
The standard deviation is
2
2
2
2
σ  [ wstocks
σstocks
 wbonds
σ bonds
 2 wstocks wbonds
Corr ( Rstocks Rbonds )σstocks σ bonds ]1/ 2
 [0.752 (225)  0.252 (100)  2(0.75)(0.25)(0.5)(15)(10)]1/ 2
 (126.5625  6.25  28.125)1/ 2
 (160.9375)1/ 2
 12.69%
4.
Use the expression
1 ρ

σ2p  σ2 
 ρ
 n

The square root of this expression is standard deviation. With variance equal to 625 and correlation equal to 0.3,
σp
 1  0.3

625 
 0.3 
 100

 13.85%

5.
σ 2p
σ 2p
Find portfolio variance using the following expression
1 ρ

 σ2 
 ρ
 n

 625[(1  0.3) / 24  0.3]  205.73
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:
σ 2min  σ 2ρ  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
σ 2p
σ 2min

205.73
 1.097
187.5
The variance of the 24-stock portfolio is approximately 110 percent of the variance of the portfolio with an
unlimited number 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
covariance with the market portfolio than McGettrick, it also has a higher beta and a higher required rate of return.
- 180 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
Because Jimma’s estimated rate of return is below the required rate of return, the stock is overvalued.
2.
A is correct. The beta for the stock is computed by dividing the covariance of the stock with the market by
the variance of the market. In this case, the covariance and variance 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.
E ( Ri )  RFR  βi ( RM  RFR)
3.
 .10  βi (.14  .10)
 .10  .04βi
Stock
Beta
(Required Return) E(Ri) = .10 + .04βi
U
85
.10 + .04(.85) = .10 + .034 = .134
N
1.25
.10 + .04(1.25) = .10 + .05 = .150
D
−.20
.10 + .04(−.20) = .10 - .008 = .092
4.
C is correct. A portfolio that is on the CML to the left of the market portfolio is a lending portfolio with
part of the investor’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.
R  Expected return  1.5(Interest rate surprise)  2(GDP surprise) 
Company-specific surprise
 11%  1.5(2%)  2(3%)  3%
 5%
Chapter 8
Level II

Solution to 3 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 South-Western.
Reprinted with permission of South-Western, a division of Thomson Learning. All other solutions copyright © CFA
Institute.

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.
- 181 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
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 selection. 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 table 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 growth 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
Low
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-Gordon growth model with the assumed 5.9 percent dividend growth rate results in an
estimated value of $1,398.38 trillion for the S&P 500 index.
V0 
D1
27.73(1  0.059)

 $1, 398.38 trillion
rg
0.08  0.059
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 Valuation, 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.
- 182 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
FVN
7
1 r
r
 PV(1  r ) N
 4(1  r ) 4
 (7 / 4)1/ 4
 (7 / 4)1/ 4  1
 0.1502  15.02%
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
5
+ r) . 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.
C is correct. The required rate of return for the company is 6% + 1.2(11% − 6%) = 12%. Dividends are
4.
expected to grow at a supernormal rate for two years:
D(1)
 €3.00(1.20) = €3.60
D(2)  €3.60(1.20) = €4.32
D(3)
 €4.32(1.09) = €4.7088.
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 D1/(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%. D0 (dollar dividend per share) is $5/2.0 = $2.50 per share. D1 = $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
WACC = 9%(1 − 0.30) (0.40) + 13%(0.60) = 10.32%
The value of the firm (in euro) is
- 183 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
Firm value 
FCFF0 (1  g )
FCFF1
235(1.06)


WACC  g
WACC  g
0.1032  0.06
249.1
 5, 766.20 million
0.0432

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 V0 = €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 percent 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,
FCFE1 FCFE 0 (1  g ) 178(1.07)


rg
rg
0.13  0.07
= 190.46
 €3,174.33 million
0.06
Equity value =
The value per share is V0 = €3,174.33 million/10 million = €317.43 per share.
7.
A.
The required return on equity is
r = E(Ri) = RF + βi[E(RM) − RF] = 5.5% + 0.90(5.5%) = 10.45%
The weighted-average cost of capital is
WACC = 0.25(7.0%) (1 − 0.40) + 0.75(10.45%) = 8.89%
B.
Firm value 
Firm value 
C.
FCFF0 (1  g )
WACC  g
1.1559(1.04)
 $24.583
0.0889  0.04
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.
- 184 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
8.
In 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
overvalued.
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 characteristics (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 decline, 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 particular 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 sinking fund provision.
C.

It is commonly thought that the presence of a sinking fund provision reduces the risk that the issuer will not
have sufficient funds to pay off the amount due at the maturity date. But this must be balanced against the fact that a
bondholder might have his or her bonds taken away at par value when the 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 trading 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 the issuer to make additional payments beyond the required
amount of the sinking fund will reduce the likelihood that the issuer will have insufficient funds to pay off the issue
at the maturity date, there is still the potential loss if the 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.
- 185 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
additional payments permitted to retire the issue via the sinking fund special call price of 100 when the bond is
trading at a premium, because that is when interest rates in the 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 the sinking fund provision, a portion of their
particular bonds might be called to satisfy the sinking fund requirement (One of the major topics in fixed income
analysis is that because of the uncertainty about the 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 loans are included in the pool can at lower interest rates refinance their loans if
interest rates decline below the rate on their loans. Consequently, the security holder cannot rely on the schedule of
principal and interest payments of the pool of loans to determine with certainty future cash flow.
3.
A.
Since the inflation rate (as measured by the CPI-U) is 3.6%, the 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 principal
 $1, 000, 000  $18, 000  $1, 018, 000
iii.
The coupon payment is equal to
Inflation-adjusted 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 principal
 $1, 018, 000  $20,360  $1, 038,360
iii.
The coupon payment is equal to
Inflation-adjusted 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, the 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.
- 186 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
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 high 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 business and to
sustain current dividends without 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 obligation. 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 is 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 the future can alter cash flows.
5.
All the financial ratios—actual and projected for 2001—clearly indicate that the credit-worthiness of Krane
Products is improving. Using as benchmarks the S&P median ratios, the coverage ratios were already by fiscal year
2000 approaching that of the median BBB rated issuer. The capitalization ratios, while improving, were still well
below that of the median BBB rated issuer. 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’ projections 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 to trade like a BB credit since, based on her analysis, the bonds
are likely to be upgraded to BBB.
- 187 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
Level III
6.
Two factors that affect the yields available on inflation-indexed bonds (IIBs) are as follows:
►
Overall economic growth and its corresponding impact on real interest rates bear a direct impact on IIB
yields. A growing economy places upward pressure on all bond yields. Though the impact may be muted due to the
nature of the IIB structure, IIBs are not immune to interest rate risk.
►
Investor demand for bonds in general and for IIBs in particular has an inverse impact on IIB yields. As with
non-IIBs, rising investor demand serves to drive interest rates lower and the lack of investor demand drives up the
yields that issuers must pay in order to sell the bonds they need to issue.
7.
First, let us compute the amount in each of the three tranches in the CDO. The senior tranche is 70 percent
of $250 million = $175 million. The junior tranche is 20 percent of $250 million = $50 million. The rest is the equity
tranche = $250 million − $175 million − $50 million = $25 million.
Now let us compute the amount that would be received by the equity tranche. Annual interest generated by the
collateral would be 6 + 5 = 11 percent of $250 million = $27.5 million. Annual interest received by the senior
tranche would be 7.5 + 0.5 = 8 percent of $175 million = $14 million. Annual interest received by the junior tranche
would be 6 + 3 = 9 percent of $50 million = $4.5 million. So, the amount to be received by the equity tranche is 27.5
− 14 − 4.5 = $9 million. This amount represents a return of 9/25 = 0.36 or 36 percent.
Chapter 12
Level I
1.
The present value of the cash flows of a 6.5% 20-year semiannual-pay bond using the three discount rates
is shown below:
Discount Rate (Annual BEY)
Semiannual Rate (Half Annual Rate)
Present Value of Cash
Flows
7.2%
3.6%
92.64
7.4
3.7
90.68
7.8
3.9
86.94
Since 3.7% equates the present value of the cash flows to the price of 90.68, 3.7% is the semiannual yield to

Solutions to 6 and 7 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.

Solutions to 1 – 4 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.
- 188 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
maturity. Doubling that rate gives a 7.4% yield to maturity on a bond-equivalent basis.
2.
This question requires no calculations. (Note that the maturity of each bond is intentionally omitted.) The
question tests for an understanding of the relationship between coupon rate, current yield, and yield to maturity for a
bond trading at par, a discount, and a premium.
►
Bond A’s current yield is incorrect. The current yield should be equal to the coupon rate.
►
Bond B is fine. That is, it has the expected relationship between coupon rate, current yield, and yield to
maturity for a bond trading at a premium.
►
Bond C’s yield to maturity is incorrect. Since the bond is a premium bond, the yield to maturity should be
less than the coupon rate.
►
Bond D is fine. That is, it has the expected relationship between coupon rate, current yield, and yield to
maturity for a bond trading at a discount.
►
Bond E is incorrect. Both the current yield and the yield to maturity should be greater than the coupon rate
since the bond is trading at a discount.
3.
A.
Bond X has no dependence on reinvestment income since it is a zero-coupon bond. So it is either
Bond Y or Bond Z. The two bonds have the same maturity. Since they are both selling at the same yield, Bond Z,
the one with the higher coupon rate, is more dependent on reinvestment income.
B.
As explained in Part A, since Bond X is a zero-coupon bond, it has the least dependence (in fact, no
dependence) on reinvestment income.
4.
The problem here is in the definition of price volatility. It can be measured in terms of dollar price change
or percentage price change. Smith is correct that there is greater price volatility for bond B because of its higher
modified duration—that is, a higher percentage price change. Robertson is correct that bond A has greater price
volatility but in terms of dollar price change. Specifically, for a 100 basis point change in rates, bond A will change
by $3.60 (4% times 90); for bond B the dollar price change will be $3 (6% times 50) for a 100 basis point rate
change.
5.
B is correct. The portfolio duration is the weighted-average of the individual bonds in the portfolio and is
calculated as follows:
Total portfolio value = ($300,521 + 567,000) = $867,521.
The weighted average = (3000,521/867,521) × 2.67 + (567,000/867,521) × 6.41 = 5.11.
6.
A is correct. The formula is:
% change in price  (duration)(change in yield)(100)
 6.2(.0015)(100)  0.93%.
- 189 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
Level II
7.
A.
Proponents of the pure expectations theory would assert that an upward-sloping yield curve is a
market’s forecast of a rise in interest rates. If that is correct, an expected rise in interest rates would mean that the
manager should shorten or reduce the duration (i.e., interest rate risk) of the portfolio. However, the pure
expectations theory has serious pitfalls and the forward rates are not good predictors of future interest rates.
B.
The preferred habitat form of the biased expectations theory is consistent with the shape of the spot rate
curve observed. The preferred habitat theory asserts that if there is an imbalance between the supply and demand for
funds within a given maturity sector, market participants (i.e., borrowers and investors) will agree to shift their
financing and investing activities out of their preferred maturity sector to take advantage of any such imbalance.
However, participants will demand compensation for shifting out of their preferred maturity sector in the form of a
yield premium. Consequently, any shape for the spot rate curve (and yield curve) can result, such as the one
observed in the question. Therefore, the trustee’s statement is incorrect.
(Note: The question only asked about expectations theories of the term structure of interest rates. Another theory, the
market segmentation theory asserts that when there are supply and demand imbalances within a maturity sector,
market participants will not shift out of their preferred maturity sector. Consequently, different maturity sectors
reflect supply and demand imbalances within each sector, and the type of yield curve observed in the question is
possible.)
Chapter 13
Level I
1.
We can illustrate put–call parity by showing that for the fiduciary call and the protective put, the current
values and values at expiration are the same.
Call price, c0 = $6.64
Put price, p0 = $2.75
Exercise price, X = $30
Risk-free rate, r = 4 percent
Time to expiration = 219/365 = 0.6
Current stock price, S0 = $33.19

Solution to 7 taken from Fixed Income Analysis for the Chartered Financial Analyst® Program, Second Edition, by
Frank J. Fabozzi, CFA, editor Copyright ©2005 by CFA Institute. Reprinted with permission. All other solutions
copyright ©CFA Institute.
Solutions to 1-3 taken from Analysis of Derivatives for the Chartered Financial Analyst® Program, by Don M.
Chance, CFA. Copyright ©2003 by AIMR. Reprinted with permission. All other solutions copyright ©CFA
Institute.
- 190 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
Bond price, X/(l + r)T = 30/(1 + 0.04)0.6 = $29.30
Value at Expiration
Transaction
Current Value
ST = 20
ST = 40
Fiduciary call
Buy call
6.64
0
40 − 30 = 10
Buy bond
29.30
30
30
Total
35.94
30
40
Buy put
2.75
30 − 20 = 10
0
Buy stock
33.19
20
40
Total
35.94
30
40
Protective put
The values in the table show that the current values and values at expiration for the fiduciary call and the protective
put are the same. That is, c0 + X/(1 + r)T = p0 + S0.
2.
A.
B.
i.
This position is commonly called a covered call.
VT  ST  max(0,ST  X)  70  max(0, 70  80)  70  0  70
  VT  V0  70  (S0  c0 )  70  (77  6)  70  71  1
ii
VT  ST  max(0,ST  X)  75  max(0, 75  80)  75  0  75
  VT  V0  75  (S0  c0 )  75  (77  6)  4
iii
VT  ST  max(0,ST  X)  80  max(0,80  80)  80  0  80
  VT  V0  80  (S0  c0 )  80  (77  6)  9
iv
VT  ST  max(0,ST  X)  85  max(0,85  80)  85  5  80
  VT  V0  80  (S0  c0 )  80  (77  6)  9
Maximum profit = X − S0 + c0 = 80 − 77 + 6 = 9
C.
i.
ii.
Maximum loss = S0 − c0 = 77 − 6 = 71
iii.
The maximum profit would be realized if the expiration price of the underlying is at or above the exercise
price of $80.
iv.
The maximum loss would be incurred if the underlying price drops to zero.
D.
ST* = S0 − c0 = 77 − 6 = 71
3.
A.
B.
i.
This position is commonly called a protective put.
VT  ST  max(0, X  ST )  70  max(0, 75  70)  70  5  75
  VT  V0  75  (S0  p0 )  75  (77  3)  75  80  5
- 191 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
ii.
VT  ST  max(0, X  ST )  75  max(0, 75  75)  75  0  75
  VT  V0  75  (S0  p0 )  75  (77  3)  75  80  5
iii.
VT  ST  max(0, X  ST )  80  max(0, 75  80)  80  0  80
  VT  V0  80  (S0  p0 )  80  (77  3)  80  80  0
iv.
VT  ST  max(0, X  ST )  85  max(0, 75  85)  85  0  85
  VT  V0  85  (S0  p0 )  85  (77  3)  85  80  5
v.
VT  ST  max(0, X  ST )  90  max(0, 75  90)  90  0  90
  VT  V0  90  (S0  p0 )  90  (77  3)  90  80  10
Maximum profit = ∞
C.
i.
ii.
Maximum loss = − (X − S0 − p0) = − (75 − 77 − 3) = 5
iii.
The maximum loss would be incurred if the expiration price of the underlying were at or below the exercise
price of $75.
D.
ST* = S0 + p0 = 77 + 3 = 80
4.
B is correct. Buying the stock at $50 and delivering it against the $50 strike call generates a payoff of zero.
The premium is retained by the writer. The net profit is $6.00 per share × 100 shares or $600.
Level II
5.
A.
S0 = $225
T= 1
r = 0.0475
F(0,T) = $225(1.0475) = $235.69
B.
St = $250
t = 4/12 = 0.3333
T=1
T − t = 0.6667
r = 0.0475
Vt(0,T) = $250.00 − $235.69/(1.0475)0.6667 = $21.49
The investor is long, so a positive value represents a gain.
C.
St = $200
t = 8/12 = 0.6667
T=1
T − t = 0.3333
r = 0.0475
Vt(0,T) = $200.00 − $235.69/(1.0475)0.3333 = −$32.07
- 192 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
The investor is long, so this represents a loss to the long position.
D.
St = $190
F(0,T) = $235.69
VT(0,T) = $190.00 − $235.69 = −$45.69
Loss to long position  $45.69
Gain on asset
 $35.00 (based on $225  $190)
Net loss
 $10.69
E.
St = $240
F(0,T) = $235.69
VT(0,T) = $240.00 − $235.69 = $4.31
Gain to long position  $4.31
Loss on asset
 $15.00 (based on $240  $225)
Net loss
 $10.69
This loss is the same as the loss in Part D. In fact, the loss would be the same for any other price as well, because the
forward contract was executed at the no-arbitrage price of $235.69. The loss of $10.69 is the risk-free rate of 4.75
percent applied to the initial asset price of $225.
Level III
6.
Covered call writing is a good strategy if the rates are not going to change much from their present level.
The sale of the calls brings in premium income that provides partial protection in case rates increase. The additional
income from writing calls can be used to offset declining prices. If rates fall, portfolio appreciation is limited
because the short call position is a liability for the seller, and this liability increases as rates go down. Consequently,
there is limited upside potential for the covered call writer. Overall, this drawback does not have negative
consequences if rates do not change because the added income from the sale of calls would be obtained without
sacrificing any gains. Thus, Consultant A, who suggested selling covered calls, probably believes that the interest
rates would not change much in either direction.
Doing nothing would be a good strategy for a bondholder if he believes that rates are going down. The bondholder
could simply gain from the increasing bond prices. Thus, Consultant B, who suggested doing nothing, likely
believes that the interest rates would go down.
If one has no clear opinion about the interest rate outlook but would like to avoid risk, selling interest rate futures

Analysis of Derivatives for the Chartered Financial Analyst® Program, by Don M. Chance, CFA. Copyright
©2003 by AIMR. Reprinted with permission.

Solution to 6 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.
- 193 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
would be a good strategy. If interest rates were to increase, the loss in value of bonds would be offset by the gains
from futures. Thus, Consultant C, who suggested selling interest rate futures, is likely the one who has no opinion.
Paying the premium for buying the puts would not be a bad idea if a bondholder believes that interest rates are going
to increase. Thus, Consultant D is likely the one who believes that the interest rates are headed upward.
This position is commonly called a bull spread.
7.
A.
B.
Let X1 be the lower of the two strike prices and X2 be the higher of the two strike prices.
i.
VT  max(0,ST  X1 )  max(0,ST  X 2 )
 max(0,89  75)  max(0,89  85)  14  4  10
  VT  V0  VT  (c1  c2 )  10  (10  2)  2
ii.
VT  max(0,ST  X1 )  max(0,ST  X 2 )
 max(0, 78  75)  max(0, 70  85)  3  0  3
  VT  V0  VT  (c1  c2 )  3  (10  2)  5
iii.
VT  max(0,ST  X1 )  max(0,ST  X 2 )
 max(0, 70  75)  max(0, 70  85)  0  0  0
  VT  V0  VT  (c1  c 2 )  0  (10  2)  8
Maximum profit = X2 − X1 − (c1 − c2) = 85 − 75 − (10 − 2) = 2
C.
i.
ii.
Maximum loss = c1 − c2 = 10 − 2 = 8
D.
ST* = X1 + (c1 − c2) = 75 + (10 − 2) = 83
E.
VT  max(0,ST  X1 )  max(0,ST  X 2 )
 max(0.83  75)  max(0,83  85)  8  0  8
  VT  V0  VT  (c1  c 2 )  8  (10  2)  0
Therefore, the profit or loss if the price of the underlying increases to 83 at expiration is indeed zero.

Analysis of Derivatives for the Chartered Financial Analyst® Program, by Don M. Chance, CFA. Copyright
©2003 by AIMR. Reprinted with permission. All other solutions copyright ©CFA Institute.
- 194 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
8.
A.
Let X1 be 110, X2 be 115, and X3 be 120.
V0 = c1 − 2c2 + c3 = 8 − 2(5) + 3 = 1
i.
VT  max(0,ST  X1 )  2 max(0,ST  X 2 )  max(0,ST  X 3 )
VT  max(0,106  110)  2 max(0,106  115)
 max(0,106  120)  0
  VT  V0  0  1  1
ii.
VT  max(0,ST  X1 )  2 max(0,ST  X 2 )  max(0,ST  X 3 )
VT  max(0,110  110)  2 max(0,110  115)
 max(0,110  120)  0
  VT  V0  0  1  1
iii.
VT  max(0,ST  X1 )  2 max(0,ST  X 2 )  max(0,ST  X 3 )
VT  max(0,115  110)  2 max(0,115  115)
 max(0,115  120)  5
 =VT  V0  5  1  4
iv.
VT  max(0,ST  X t )  2 max(0,ST  X 2 )  max(0,ST  X3 )
VT  max(0,120  110)  2 max(0,120  115)
 max(0,120  120)  10  10  0  0
  VT  V0  0  1  1
v.
VT  max(0,ST  X1 )  2 max(0,ST  X 2 )  max(0,ST  X 3 )
VT  max(0,123  110)  2 max(0,123  115)
 max(0,123  120)  13  16  3  0
 =VT  V0  0  1  1
Maximum profit = X2 − X1 − (c1 − 2c2 + c3) = 115 − 110 − 1 = 4
B.
i.
ii.
Maximum loss = c1 − 2c2 + c3 = 1
iii.
The maximum profit would be realized if the price of the stock at expiration of the options is at the exercise
price of $115.
iv.
The maximum loss would be incurred if the price of the stock is at or below the exercise price of $110, or if
the price of the stock is at or above the exercise price of $120.
C.
Breakeven: ST* = X1 + (c1 − 2c2 + c3) and ST* = 2X2 − X1 − (c1 − 2c2 + c3). So, ST* = 110 + 1 = 111 and
ST* = 2(115) − 110 − 1 = 119
- 195 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
Chapter 14
Level II
1.
A.
A convertible bond grants the investor the option to call the common stock of the issuer. Thus, a
convertible bond has an embedded call option on the common stock. However, most convertible bonds are callable.
That is, there is a second embedded call option granting the issuer the right to retire the bond.
B.
The complication that arises is that one of the options, the call on the common stock granted to the investor,
depends on the future price of the common stock. However, the call on the bond granted to the issuer depends on
future interest rates. Thus, valuing a callable convertible bond requires including in one valuation model both future
stock price movements and future interest rate movements.
2.
The conversion ratio is found by dividing the par value of $1,000 by the conversion price stated in the
prospectus of $45 per share. The conversion ratio is then 22.22 ($l,000/$45).
3.
Her gain caused by the increase in the price of Dow Jones industrial Average futures is $10(9,086 − 9,020)
= $660. Because Craft had a short position in S&P Midcap 400 futures, her loss caused by the increase in the price
of S&P Midcap 400 futures is $500(370.20 − 369.40) = $400. Craft’s net gain is $660 − $400 = $260.
4.
A.
T = 90/365 = 0.2466. The futures price is
f 0 (T)  S0 (1  r) T
f 0 (0.2466)  300(1.06) 0.2466  $304.34 per ounce
B.
Do the following:
►
Enter a short futures position—that is, sell the futures at $306.
►
Buy gold at $300.
►
At expiration, deliver an ounce of gold and receive $306.
This amount is $1.66 more than $304.34, which is the sum of the cost of the asset ($300) and the loss of interest on
this amount at the rate of 6 percent a year ($4.34). Thus, the overall strategy results in a riskless arbitrage profit of
$1.66 per futures contract. You can also look at this scenario in terms of returns: Investing $300 and receiving $306
90 days later is an annual return of 8.36 percent, because 300(1.0836)(90/365) = 306. This return is clearly greater than
the risk-free return of 6 percent.
C.
The steps in this case would be the reverse of the steps in Part B above. So, do the following:
►
Enter a long futures position; that is, buy the futures at $303.
Solutions to 1 and 2 taken from Fixed Income Analysis for the Chartered Financial Analyst® Program, Second
Edition, by Frank J. Fabozzi, CFA, editor.Copyright ©2005 by CFA Institute. Reprinted with permission. All other
solutions copyright ©CFA Institute.

Solutions to 3-7 taken from Analysis of Derivatives for the Chartered Financial Analyst® Program, by Don M.
Chance, CFA. Copyright ©2003 by AIMR. Reprinted with permission. All other solutions copyright ©CFA
Institute.
- 196 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
►
Sell short the gold at $300.
►
At expiration, take the delivery of an ounce of gold and pay $303.
This amount paid is $1.34 less than $304.34, which is the sum of the funds received from the short sale of the asset
($300) and the interest earned on this at the rate of 6 percent per year ($4.34). Thus, the overall strategy results in a
riskless arbitrage profit of $1.34 per futures contract. In terms of rates, receiving $300 up front and paying $303 90
days later represents an annual rate of 4.12 percent, because 300(1.0412) (90/365) = 303. This rate is clearly less than
the risk-free rate of 6 percent. Thus, the overall transaction is equivalent to borrowing at a rate less than the risk-free
rate.
5.
Call price, c0 = $4.50
Put price, p0 = $6.80
Exercise price, X = $70
Risk-free rate, r = 5 percent
Time to expiration = 139/365 = 0.3808
Current stock price, S0 = $67.32
Bond price = X/(l + r)T = 70/(1 + 0.05)0.3808 = $68.71
A.
Synthetic call = p0 + S0 − X/(1 + r)T = 6.8 + 67.32 − 68.71 = $5.41
Synthetic put − c0 + X/(1 + r)T − S0 = 4.5 + 68.71 − 67.32 = $5.89
Synthetic bond = p0 + S0 − c0 = 6.8 + 67.32 − 4.5 = $69.62
Synthetic underlying = c0 + X/(1 + r)T − p0 = 4.5 + 68.71 − 6.8 = $66.41
B.
Instrument
Actual Price ($)
Synthetic Price ($)
Mispricing/Profit ($)
Call
4.50
5.41
0.91
Put
6.80
5.89
0.91
Bond
68.71
69.62
0.91
Stock
67.32
66.41
0.91
Thus, the mispricing is the same regardless of the instrument used to look at it.
C.
The actual call is cheaper than the synthetic call. Therefore, an arbitrage transaction where you buy the call
(underpriced) and sell the synthetic call (overpriced) will yield a risk-free profit of $5.41 − $4.50 = $0.91.
As shown below, at expiration no cash will be received or paid out.
Value at Expiration
Transaction
ST < 70
ST > 70
Buy call
0
ST − 70
Sell synthetic call
- 197 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
D.
Short put
−(70 − ST)
0
Short stock
−ST
−ST
Long bond
70
70
Total
0
0
The actual put is more expensive than the synthetic put. Therefore, an arbitrage transaction in which you
buy the synthetic put (underpriced) and sell the put (overpriced) will yield a risk-free profit of $6.80 − $5.89 =
$0.91. As shown below, at expiration no cash will be received or paid out.
Value at Expiration
Transaction
ST < 70
Sell put
−(70 − ST)
ST > 70
Buy synthetic put
6.
Long call
0
ST − 70
Long bond
70
70
Short stock
−ST
−ST
Total
0
0
Current stock price, S = $100
Up move, u = 1.1
Down move, d = 0.85
Exercise price, X = $90
Risk-free rate, r = 6.5 percent
A.
Stock prices one period from now are
S  Su  100(1.1)  $110
S  Sd  100(0.85)  $85
Call option values at expiration one period from now are
c   Max(0,110  90)  $20
c   Max(0,85  90)  $0
The risk-neutral probability is
π
1.065  0.85
 0.86 and 1  π  0.14
1.1  0.85
The call price today is
c
B.
0.86(20)  0.14(0)
 16.15
1.065
If the current call price is $17.50, it is overpriced. Therefore, we should sell the call and buy the underlying
stock. The hedge ratio is
- 198 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
n
20  0
 0.8
110  85
For every option sold we should purchase 0.8 shares of stock. If we sell 100 calls we should buy 80 shares of stock.
Sell 100 calls at 17.50  1, 750
Buy 80 shares at 100
 8, 000
Net cash flow
 6, 250
At expiration the value of this combination will be
80(110)  100(20)  $6,800 if ST  110
80(85)  100(0)  $6,800 if ST  85
We invested $6,250 for a payoff of $6,800. The rate of return is (6,800/6,250) − 1 = 0.088. This rate is higher than
the risk-free rate of 0.065.
C.
If the current call price is $14, it is underpriced. Therefore, we should buy the call and sell the underlying
stock. The hedge ratio is
n
20  0
 0.8
110  85
For every option purchased we should sell 0.8 shares of stock. If we buy 100 calls we should sell 80 shares of stock.
Buy 100 calls at 14
 1, 400
Sell 80 shares at 100 
8, 000

6, 600
Net cash flow
Thus, we generate $6,600 up front.
At expiration the value of this combination will be
100(20)  80(110)  $6,800 if ST  110
100(0)  80(85)  $6,800 if ST  85
We generated $6,600 up front and pay back $6,800. The rate of return is (6,800/6,600) − 1 = 0.0303. This borrowing
rate is lower than the risk-free rate of 0.065.
Level III
7.
The company can enter into a swap to pay a fixed rate of 6.5 percent and receive a floating rate. The first
floating payment will be at 5 percent.
Interest payment on the floating rate note = $50,000,000(0.05 + 0.0125) (90/360) = $781,250
Swap fixed payment = $50,000,000(0.065) (90/360) = $812,500
Swap floating receipts = $50,000,000(0.05) (90/360) = $625,000
The overall cash payment made by the company is $812,500 + $781,250 − $625,000 = $968,750
- 199 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
Chapter 15
Level III
1.
The relatively constant elements in the asset allocation process are the prediction procedure, the investor’s
risk tolerance function, and the optimizer. Most of the investor’s expertise goes into formulating these stable
elements. The prediction procedure represents the investor’s perception of best process for developing capital
market expectations. The investor’s risk tolerance function represents a quantification of his risk attitudes. The
optimizer is the procedure for producing the best asset allocation. By contrast, the other elements of the process are
inputs or outputs that are regularly revised.
2.
A.
U.S. equities, and ex-U.S. equities represent respectively 30%/60% = 0.5 and 30%/60% = 0.5 of
global equities. Therefore, for global equities,
A  (0.5  8%)  (0.5  10%)  9%
B  (0.5  14%)  (0.5  10%)  12%
Global equities’ short-term expected return at 12 percent is above the long-term expectation of 9 percent because
U.S. equities are expected in the short-term to outperform their long-term expected return.
U.S. bonds and ex-U.S. bonds represent respectively 30%/40% = 0.75 and 10%/40% = 0.25 of global fixed income.
Therefore, for global fixed income,
C  (0.75  6%)  (0.25  5%)  5.75%
D  (0.75  8%)  (0.25  4%)  7%
Global fixed income’s short-term expected return at 7 percent is above its long-term expectation of 5.75 percent.
However within global fixed income U.S. bonds are expected short-term at 8 percent to outperform their long-term
expected return while ex-U.S. bonds are expected short term at 4 percent to underperform their long-term expected
return.
B.
The results in Part A suggest three actions:
►
In absolute terms, the global equities short-term expected return is 300 basis points above its expected long-
term value of 9 percent; in relative terms, that is equivalent to a 12%/9% − 1.0 = 33% higher expected return. For
global fixed income, the absolute and relative expected return differences are 125 basis points and 22 percent,
respectively. Because global equities appear more undervalued than global bonds, increase the weight on global
equities from 60 percent and decrease the weight on global fixed income from 40 percent.
►
Within global equities, overweight U.S. equities versus their target weight of 30 percent and decrease the
weight on ex-U.S. equities from 30 percent. Although the short-term expected return on ex-U.S. equities is the same
as the long-term expectation, U.S. equities are expected to outperform their long-term expected return by 600 basis

Solutions to 1-4 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.
- 200 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
points in the short term.
►
Within the new global fixed-income allocation, overweight U.S. bonds and underweight ex-U.S. bonds,
reflecting their short-term expected performance.
3.
The portfolio managed by Galicia is experiencing style drift. The threefold increase in the weighting of
growth stocks suggests that Galicia has decided to shift to more of a market orientation, although some or all of the
drift may have occurred because the stocks in the portfolio have become less value-like during the two year period.
The relatively low percentages given to “Other” suggest that Galicia’s style bets explain the overwhelming majority
of the portfolio’s performance.
4.
A.
The principal benefit of all stocks being categorized as either growth or value (MSCI approach) is
that it is collectively exhaustive. That said, many stocks are “border” stocks (i.e., have characteristics that place
them near the value/growth border) that don’t really exhibit significant value or growth characteristics but are
categorized in one of these styles anyway. The Dow Jones method’s neutral/core category eliminates this problem,
but the value and growth indices by definition do not contain all of the stocks in the broad index.
B.
Either set of indices can be used for returns-based style analysis. That said, Miller is likely to obtain a
higher R2 in a regression of the portfolio returns on the style index returns if he uses the more “granular” set of style
indices—those by Dow Jones. For example, if the portfolio is a deep value portfolio or a strong growth portfolio, the
Dow Jones indices are more likely to better explain the portfolio’s style than a set of style indices in which every
stock is forced into either value or growth. Specifically, the deep value portfolio will be better represented by the
Dow Jones Value Index because that index focuses more on deep value stocks. That same portfolio’s returns
regressed versus the MSCI Value Index is likely to show a lower R2
Chapter 16
Level III
1.
The tracking risk is the standard deviation of the active returns. For the data shown in the problem, the
tracking risk is 28.284 bps, as shown below:
Period

(AR – Avg. AR)2
Portfolio
Benchmark
Active
Return
Return
Return
1
14.10%
13.70%
0.400%
0.00090%
2
8.20
8.00
0.200
0.00010
3
7.80
8.00
−0.200
0.00090
Solutions to 1 and 2 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.
- 201 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
4
3.20
3.50
−0.300
0.00160
5
2.60
2.40
0.200
0.00010
6
3.30
3.00
0.300
0.00040
Average active return per period =
0.100%
Sum of the squared deviations =
0.00400%
Tracking risk (std. dev.) =
0.28284%
2.
Dollar duration is a measure of the change in portfolio value for a 100 bps change in market yields. It is
defined as Dollar duration = Duration × Dollar value × 0.01
A.
A portfolio’s dollar duration is the sum of the dollar durations of the component securities. The dollar
duration of this portfolio at the beginning of the period is $162,636, which is calculated as
initial Values
Security
Price
Market Value
Duration
Dollar Duration
Bond #1
$106.110
$1,060,531
5.909
$62,667
Bond #2
98.200
981,686
3.691
36,234
Bond #3
109.140
1,090,797
5.843
63,735
Portfolio dollar duration =
$162,636
At the end of one year, the portfolio’s dollar duration has changed to $136,318, as shown below.
After 1 Year
Security
Price
Market Value
Duration
Dollar Duration
Bond #1
$104.240
$1,042,043
5.177
$53,947
Bond #2
98.084
980,461
2.817
27,620
Bond #3
106.931
1,068,319
5.125
54,751
Portfolio dollar duration =
B.
$136,318
The rebalancing ratio is a ratio of the original dollar duration to the new dollar duration:
Rebalancing ratio = $162,636/$136,318 = 1.193
C.
The portfolio requires each position to be increased by 19.3 percent. The cash required for this rebalancing
is calculated as:
Cash required  0.193  ($1, 042, 043  980, 461  1, 068,319)
 $596,529
3.
B is correct. Chow’s statement #1 is incorrect because what she describes does not remove all risks. Credit
risk destroys the immunization match; therefore, the statement is incorrect. The risk to immunization comes from
non-parallel shifts in the yield curve.
4.
C is correct. Portfolio A is a zero-coupon bond and thus has no reinvestment rate risk. Portfolio B has lower
- 202 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
dispersion in maturities than Portfolio C. Therefore, Portfolio C has more reinvestment rate risk than Portfolio B.
5.
B is correct. The SRB will accept (i.e., require) a return of 4.50% (semiannual compounding). Find the time
ten future value of $100 million at this rate. The answer is $100,000,000 × (1 + .045/2)20 = $156,050,920.
6.
A is correct. Haley’s statement #1 defines the risk-costs tradeoffs of cash flow matching versus multiple
liabilities immunization.
7.
C is correct. If the distribution of the durations of the assets is wider than that of the liabilities, the durations
of the assets after a parallel yield curve shift (whether up or down) will envelope the durations of the liabilities after
the shift. The immunization can be maintained, although rebalancing may be necessary.
8.
C is correct. Horizon matching creates a duration-matched portfolio with the added constraint that it he
cash-flow matched in the first few years. Cash flow matching the initial portion of the liability stream reduces the
risk associated with nonparallel shifts of the yield curve.
Chapter 17
Level I
1.
A.
Efficient market hypothesis (EMH) states that a market is efficient if security prices immediately
and fully reflect all available relevant information. Efficient means informationally efficient, not operationally
efficient. Operational efficiency deals with the cost of transferring funds. If the market fully reflects information, the
knowledge that information would not allow anyone to profit from it because stock prices already incorporate the
information.
i.
Weak form asserts that stock prices already reflect all information that can be derived by examining market
trading data such as the history of past prices and trading volume.
Empirical evidence supports the weak form.
A strong body of evidence supports weak-form efficiency in the major U.S. securities markets. For example, test
results suggest that technical trading rules do not produce superior returns after adjusting for transaction costs and
taxes.
ii.
Semistrong form says that a firm’s stock price already reflects all publicly available information about a
firm’s prospects. Examples of publicly available information are annual reports of companies and investment data.
Empirical evidence mostly supports the semistrong form.
Evidence strongly supports the notion of semistrong efficiency, but occasional studies (e.g., those identifying market
anomalies including the small-firm effect and the January effect) and events (e.g., stock market crash of October
1987) are inconsistent with this form of market efficiency. Black suggests that most so-called “anomalies” result
from data mining.
- 203 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
iii.
Strong form of EMH holds that current market prices reflect all information, whether publicly available or
privately held, that is relevant to the firm.
Empirical evidence does not support the strong form.
Empirical evidence suggests that strong-form efficiency does not hold. If this form were correct, prices would fully
reflect all information, although a corporate insider might exclusively hold such information. Therefore, insiders
could not earn excess returns. Research evidence shows that corporate officers have access to pertinent information
long enough before public release to enable them to profit from trading on this information.
B.
Technical analysis in the form of charring involves the search for recurrent and predictable patterns in stock
prices to enhance returns. The EMH implies that this type of technical analysis is without value. If past prices
contain no useful information for predicting future prices, there is no point in following any technical trading rule
for timing the purchases and sales of securities. According to weak-form efficiency, no investor can earn excess
returns by developing trading rules based on historical price and return information. A simple policy of buying and
holding will be at least as good as any technical procedure. Tests generally show that technical trading rules do not
produce superior returns after making adjustments for transactions costs and taxes.
Fundamental analysis uses earnings and dividend prospects of the firm, expectations of future interest rates, and risk
evaluation of the firm to determine proper stock prices. The EMH predicts that most fundamental analysis is
doomed to failure. According to semi-strong form efficiency, no investor can earn excess returns from trading rules
based on any publicly available information. Only analysts with unique insight receive superior returns.
Fundamental analysis is no better than technical analysis in enabling investors to capture above-average returns.
However, the presence of many analysts contributes to market efficiency.
In summary, the EMH holds that the market appears to adjust so quickly to information about individual stocks and
the economy as a whole that no technique of selecting a portfolio—using either technical or fundamental analysis—
can consistently outperform a strategy of simply buying and holding a diversified group of securities, such as those
making up the popular market averages.
C.
Portfolio managers have several roles or responsibilities even in perfectly efficient markets. The most
important responsibility is to:
i.
Identify the risk/return objectives for the portfolio given the investor’s constraints. In an efficient market,
portfolio managers are responsible for tailoring the portfolio to meet the investor’s needs rather than requirements
and risk tolerance. Rational portfolio management also requires examining the investor’s constraints, such as
liquidity, time horizon, laws and regulations, taxes, and such unique preferences and circumstances as age and
employment.
Other roles and responsibilities include:
ii.
Developing a well-diversified portfolio with the selected risk level. Although an efficient market prices
securities fairly, each security still has firm-specific risk that portfolio managers can eliminate through
diversification. Therefore, rational security selection requires selecting a well-diversified portfolio that provides the
- 204 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
level of systematic risk that matches the investor’s risk tolerance.
iii.
Reducing transaction costs with a buy-and-hold strategy. Proponents of the EMH advocate a passive
investment strategy that does not try to find under or overvalued stocks. A buy-and-hold strategy is consistent with
passive management. Because the efficient market theory suggests that securities are fairly priced, frequently buying
and selling securities, which generate large brokerage fees without increasing expected performance, makes little
sense. One common strategy for passive management is to create an index fund that is designed to replicate the
performance of a broad-based index of stocks.
iv.
Developing capital market expectations. As part of the asset-allocation decision, portfolio managers need to
consider their expectations for the relative returns of tire various capital markets to choose an appropriate asset
allocation.
v.
Implement the chosen investment strategy and review it regularly for any needed adjustments. Under the
EMH, portfolio managers have the responsibility of implementing and updating the previously determined
investment strategy of each client.
D.
Whether active asset allocation among countries could consistently outperform a world market index
depends on the degree of international market efficiency and the skill of the portfolio manager. Investment
professionals often view the basic issue of international market efficiency in terms of cross-border financial market
integration or segmentation. An integrated world financial market would achieve international efficiency in the
sense that arbitrage across markets would take advantage of any new information throughout the world. In an
efficient integrated international market, prices of all assets would be in line with their relative investment values.
Some claim that international markets are not integrated, but segmented. Each national market might be efficient,
but factors might prevent international capital flows from taking advantage of relative mispricing among countries.
These factors include psychological barriers, legal restrictions, transaction costs, discriminatory taxation, political
risks, and exchange risks.
Markets do not appear fully integrated or fully segmented. Markets may or may not become more correlated as they
become more integrated since other factors help to determine correlation. Therefore, the degree of international
market efficiency is an empirical question that has not yet been answered.
2.
Let us compute the terminal value of $1 invested. The share class with the highest terminal value net of all
expenses would be the most appropriate, because all classes are based on the same portfolio and thus have the same
portfolio risk characteristics.

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 South-Western. Reprinted with permission
of South-Western, a division of Thomson Learning.

Solution to 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,
- 205 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
A.
Class A. $1 × (1 − 0.05) = $0.95 is the amount available for investment at t = 0, after paying the front-end
sales charge. Because this amount grows at 9% per year, reduced by annual expenses of 0.0125, the terminal value
per $1 invested after one year is $0.95 × 1.09 × (1 − 0.0125) = $1.0226.
Class B. Ignoring any deferred sales charge, after one year, $1 invested grows to $1 × 1.09 × (1 − 0.015) = $1.0737.
According to the table, the deferred sales charge would be 4%; therefore, the terminal value is $1.0737 × 0.96 =
$1.0308.
Class C. Ignoring any deferred sales charge, after one year, $1 invested grows to $1 × 1.09 × (1 − 0.015) = $1.0737.
According to the table, the deferred sales charge would be 1%; therefore, the terminal value is $1.0737 × 0.99 =
$1.063.
Class C is the best.
B.
Class A. The terminal value per $1 invested after three years is $0.95 × 1.093 × (1 − 0.0125)3 = $1.1847.
Class B. Ignoring any deferred sales charge, after three years, $1 invested glows to $1 × 1.093 × (1 − 0.015)3 =
$1.2376. The deferred sales charge would be 2%; therefore, the terminal value is $1.2376 × 0.98 = $1.2128.
Class C. There would be no deferred sales charge. Thus, after three years, $1 invested grows to $1 × 1.093 × (1 −
0.015)3 = $1.2376.
Class C is the best.
C.
Class A. The terminal value per $1 invested after five years is $0.95 × 1.095 × (1 − 0.0125)5 = $1.3726.
Class B. There would be no deferred sales charge. So, the terminal value per $1 invested after five years is $1 ×
1.095 × (1 − 0.015)5 = $1.4266.
Class C. There would be no deferred sales charge. So, the terminal value per $1 invested after five years is $1 ×
1.095 × (1 − 0.015)5 = $1.4266.
Classes B and C are the best.
D.
Class A. The terminal value per $1 invested after 15 years is $0.95 × 1.0915 × (1 − 0.0125)15 = $2.8653.
Class B. There would be no deferred sales charge. So, the terminal value per $1 invested after 15 years is $1 × 1.0915
× (1 − 0.015)6 × (1 − 0.0125)9 = $2.9706.
Class C. There would be no deferred sales charge. So, the terminal value per $1 invested after 15 years is $1 × 1.0915
× (1 − 0.015)15 = $2.9036.
Class B is the best.
Level II
3.
C is correct. This question-asks about compliance procedures relating to personal investments of members
and candidates. The statement in answer C clearly conflicts with the recommended procedures in the Handbook.
Employers should compare personal transactions of employees with those of clients on a regular basis regardless of
the existence of a requirement by a regulatory organization. Such comparisons ensure that employees’ personal
publishing as Pearson Addison Wesley. All other solutions copyright © CFA Institute.
- 206 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
trades do not conflict with their duty to their clients, and the comparisons can be conducted in a confidential manner.
The statement in answer A does not conflict with the procedures in the Handbook. Disclosure of such policies will
give full information to clients regarding potential conflicts of interest on the part of those entrusted to manage their
money. Answer B is incorrect because firms are encouraged to establish policies whereby employees clear personal
holdings and transactions. Answer D describes the categories of securities that compliance procedures designed to
monitor personal transactions should cover.
Level III
4.
The real return from the recommended allocation should meet the minimum required return identified in
the IPS. The allocation philosophy will reflect the Foundation’s return objective, above-average risk tolerance, low
liquidity requirements, and tax-exempt status. In general the portfolio allocation should include the following:
►
An allocation to fixed-income instruments of less than 50 percent, because real returns of bonds are
forecasted to be lower than those of stocks. Bonds will be included primarily for diversification and risk reduction.
The ongoing cash flow from the bond portfolio should easily provide for all normal working capital needs.
►An allocation to equities greater than 50 percent. A number of factors support a high allocation to equities:
historical and expected real returns are high, the horizon is long, risk tolerance is above average, and taxes are not a
consideration.
►
Within the equity universe, large-cap, small-cap, international stocks and venture capital should be
considered. Diversifying within the equity universe will contribute to risk reduction, and total return could be
enhanced.
►
Real estate should be included in the portfolio as an alternative to stocks and bonds. It will provide
diversification as well as inflation protection in the long term.
An example of an appropriate modestly aggressive allocation is shown below:
Asset Class
7-Year Forecast of
Recommended
Real Return
Real Returns
Allocation
Contribution
0.7%
0%
—
Intermediate
2.3
5
0.115%
Long treasury
4.2
10
0.420
Corporate
5.2
10
0.520
Cash (U.S.): T-bills
Bonds
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.
- 207 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
International
4.9
10
0.490
Large cap
5.5
30
1.650
Small cap
8.5
10
0.850
International
6.6
10
0.660
Venture capital
12.0
5
0.600
Real estate
5.0
10
0.500
100%
5.805%
Stocks
Total expected real return
The three main large-cap styles are value, growth, and market oriented.
5.
A.
B.
Value managers seek 10 buy stocks below their intrinsic value. That said, the stocks may be cheap for good
reason. Also, it may take a long time for stocks to reach their intrinsic value. Growth managers buy stocks of
companies with either steadily growing earnings or companies whose earnings they expect to sharply appreciate. On
the other hand, they may overpay for these earnings or the expected earnings may not materialize. Managers
following the third style, market oriented, may forecast stock returns using a combination of growth or value
considerations but endeavor to build portfolios that more closely resemble the market than either value or growth
managers. If their fees are relatively high for achieving market-like returns, indexing or enhanced indexing may be a
more cost-effective alternative.
6.
A.
Equity market-neutral strategies identify over-and undervalued stocks while neutralizing the
fund’s exposure to market risk by combining long and short positions with similar exposure to related market or
sector factors. Therefore, as their name suggests, they have little or no market risk. They also have low credit risk
because their long–short positions result in net low leverage. As expected, there is virtually no correlation between
funds using this strategy and the S&P 500.
Convertible arbitrage strategies exploit anomalies in the prices of corporate convertible bonds, warrants, and
preferred stock. The convertible arbitrage funds buy or sell these securities and then hedge the risk of changes in
price and volatility of the underlying securities, changes in interest rates, and changes in the issuers’ credit ratings.
The many small, individual positions taken, and hedging of these risks, result in low market exposure. However, this
strategy also increases credit risk considerably because hedging via derivative instruments creates high leverage
exposure. Convertible arbitrage strategies have a relatively low correlation with the S&P 500 or the Lehman
Government/Corporate Bond Index because hedging the risks mitigates underlying market exposure.
Global macro strategies trade on systematic moves in major financial and nonfinancial markets by using futures and

Solutions to 5 and 6 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.
- 208 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
options contracts. They may also take positions in traditional equity and fixed-income markets. Because they tend to
make large bets on the direction of currencies, commodities, or stock and bond markets globally, they have high
market exposure. Given their extensive use of leverage via futures and options, they are also exposed to significant
credit (leverage) risk. Because of their large positions with regard to anticipated changes in market levels, the
correlation of global macro with the S&P 500 and Lehman Government/Corporate Bond Index tends to be greater
than those of the first two strategies discussed here.
B.
The usefulness of historical hedge fund data continues to be controversial. Research has shown that the
volatility of returns is more persistent through time than the level of returns. Issues such as survivorship and backfill
bias have a significant impact on historical tests of performance persistence. Additionally, lock-up periods,
restrictions on redemptions/withdrawals, and the relatively short track record of many hedge funds complicate the
extrapolation of past performance to expected (future) performance of hedge funds.
Chapter 18
Level III
1.
We begin by calculating the information ratio for each of the two managers. The formula for the
information ratio is:
IR A 
R A  RB
 A B
In our problem statement, the value-added for Manchester (1.5%) is the numerator in this formula, and the
variability of excess returns (2.24%) is the denominator. Thus, for Manchester we can calculate an information ratio
of 0.67.
Similarly, for Oakleaf we can calculate an information ratio of 0.4 (4% excess returns divided by 10% variability).
When we review our table, it gives the probability of outperformance. Since the question refers to
underperformance, we must subtract the values in the table from 1 to determine the probability of
underperformance.
Year
Manchester
Manchester
Oakleaf
Oakleaf
Outperformance
Underperformance
Outperformance
Underperformance
1
74.75%
25.25%
65.54%
34.46%
5
93.20
6.80
81.45
18.55
10
98.25
1.75
89.70
10.30
In this case, Oakleaf has a larger chance of underperforming the benchmark at all three time periods: 1, 5, and 10

Solutions to 1-4 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.
- 209 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
years. This is interesting, since Oakleaf has a much larger expected value-added return (4% annually versus 1.5%
for Manchester). However, the much larger variability of excess returns (10% for Oakleaf versus 2.24% for
Manchester) clearly is an important factor in this situation.
2.
In general terms, equity will earn higher returns than cash on average over the long term. However, there
are periods of declining equity performance when cash may outperform equities.
In the case of Acorn and Zebra, Acorn would be preferable over Zebra, all else but the cash levels being equal.
During most time periods when equities are outperforming cash, it would be better to have less cash and more
equities in the portfolio. But during the time periods when equities are declining, it may be preferable to have more
cash. Unfortunately, it is extremely difficult to forecast ahead of time when these time periods of declining equity
performance will occur.
3.
A. and B.
To calculate annual performance for Year 1 and Year 2, convert the quarterly returns to
relative form (1 + r), link them multiplicatively, and subtract 1.
For Year 1:
1QYear 1: 1  4.76%  1.0476
2QYear 1: 1+12.08%  1.1208
3QYear 1: 1  (  4.88%)  0.9512
4QYear 1: 1  7.14%  1.0714
rYear1 = (1.0476 × 1.1208 × 0.9512 × 1.0714) − 1 = 0.1966 = 19.66%
For Year 2:
1QYear 2 : 1+(  13.57%)  0.8643
2QYear 2 : 1  17.65%  1.1765
3QYear 2:
1  1.08%  1.0108
4QYear 2: 1  0.97%  1.0097
rYear2 = (0.8643 × 1.1765 × 1.0108 × 1.0097) − 1 = 0.0378 = 3.78%
C.
To calculate cumulative performance, convert the quarterly returns for the entire two-year period to relative
form (1 + r), link them multiplicatively, and subtract 1:
rCum
 (1.0476 1.1208  0.9512  1.0714  0.8643  1.1765
1.0108  1.0097)  1
 0.2418  24.18%
Alternately, express the annual returns for Year 1 and Year 2 in relative form, multiply them together, and subtract
1:
rCum
 (1.1966  1.0378)  1
 0.2418  24.18%
D.
To calculate annualized compound performance, convert the cumulative rate of return to relative form (1 +
- 210 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
rcum) and raise it to the reciprocal of the number of years in the period (1/n), and subtract 1. In this problem, there are
two years in the period, so the compound annual rate of return is
1.2418(1/ 2)  1  1.2418  1
 0.1144  11.44%
4.
The GIPS standards require that the total return of a benchmark (or benchmarks) that reflects the
investment strategy or mandate represented by the composite must be presented for each annual period. If no
benchmark is presented, the presentation must explain why not (Provision II.5.A.6).
Benchmarks provide an objective test of a firm’s implementation of an investment strategy in the spirit of fair
representation and full disclosure of investment results. Stating that most of the firm’s clients are uninterested in
performance relative to a benchmark does not give a compelling reason for failing to provide the independent
returns of an appropriate benchmark. Renner, Williams & Woods should attempt to identify a benchmark that
reflects the income-oriented strategy of the fixed-income composite.
- 211 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
Web Chapter 19
Level I
1.
C is correct. Impairment write-downs reduce equity in the denominator of the debt-to-equity ratio but do
not affect debt, so the debt-to-equity ratio is expected to increase. Impairment write-downs reduce total assets but do
not affect revenue. Thus, total asset turnover is expected to increase.
2.
B is correct. Higher reported tax expense relative to taxes paid will increase the deferred tax asset, whereas
lower reported tax expense relative to taxes paid increases the deferred tax liability. 
3.
C is correct. The deferred tax liability should be excluded from both debt and equity when both the
amounts and timing of tax payments resulting from the reversals of temporary differences are uncertain.
4.
A is correct. In the early years, a finance lease generally results in higher reported expenses, lower
profitability, and a lower ROE. This difference reverses over the life of the lease such that finance leases will result
in an ROE that rises over time and ends higher than would result if an operating lease were used. 
5.
C is correct. ROE = Return on assets × Financial leverage. ROA can be decomposed into the product of net
profit margin (net income divided by revenue) and total asset turnover (revenue divided by average total assets).
Because ROA has been decreasing over 2003 to 2005 while total asset turnover has been increasing, it must be the
case that the net profit margin has been declining. Furthermore, because ROE has increased despite the drop in
ROA, financial leverage must have increased. Statement C is the only statement that correctly identifies the trends in
net profit margin and financial leverage.
6.
C is correct. The increase in the average tax rate in 2005, as indicated by the decrease in the value of the tax
burden (the tax burden equals one minus the average tax rate), offset the improvement in efficiency indicated by
higher asset turnover); as a result, ROE remained unchanged at 18.90 percent. Statement A is not correct because the
EBIT margin, measuring profitability, was unchanged in 2005; furthermore, no information is given on liquidity.
Statement B is not correct because profitability was unchanged in 2005.
Level II
7.

C is correct. The ROE has been trending higher. ROE can be calculated by multiplying (Net profit margin)
International Financial Statement Analysis, by Thomas R. Robinson, CFA, Jan Hendrik van Gruening, CFA, R.
Elaine Henry, CFA, and Michael A. Broihahn, CFA. Copyright ©2008 by CFA Institute. Reprinted with permission.

International Financial Statement Analysis, by Thomas R. Robinson, CFA, Jan Hendrik van Gruening, CFA, R.
Elaine Henry, CFA, and Michael A. Broihahn, CFA. Copyright ©2008 by CFA Institute. Reprinted with permission.
- 212 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
× (Asset turnover) × (Financial leverage). Net profit margin is Net income/Sales. In 2007 the net profit margin was
2,576/55781 = 4.6% and the ROE = 4.6% × 0.68 × 3.43 = 10.8%. Using the same method, ROE was 12.9 percent in
2008 and 13.6 percent in 2009.
8.
A is correct. The DuPont analysis shows that profit margins and asset turnover have both increased over the
last three years, but leverage has declined. The reduction in leverage offsets a portion of the improvement in
profitability and turnover. Thus, ROE would have been higher if leverage had not decreased.
9.
B is correct. The Power and Industrial segment has the lowest EBIT margins but uses about 31 percent of
the capital employed. Further, Power and industrial’s proportion of the capital expenditures has increased from 32
percent to 36 percent over the three years. Its capital intensity only looked to get worse, as the segment’s percentage
of total capital expenditures was higher than its percentage of total capital in each of the three years. If Abay is
considering divesting segments that do not earn sufficient returns on capital employed, this segment is most suitable.
10.
A is correct. The cash-flow-based accruals ratio = [NI − (CFO + CFI)]/(Average NOA) = [4,038 − (9,822 −
10,068)]/43,192 = 9.9%.
11.
A is correct. The cash-flow-based accruals ratio falls from 11.0 percent in 2007 to 5.9 percent in 2008, and
then rises to 9.9 percent in 2009. However, the change over the three-year period is a net modest decline, indicating
a slight improvement in earnings quality.
12.
B is correct. Net cash flow provided by (used in) operating activity has to be adjusted for interest and taxes,
as necessary, in order to be comparable to operating income (EBIT). Bickchip, reporting under IFRS, chose to
classify interest expense as a financing cash flow so the only necessary adjustment is for taxes. The operating cash
flow before interest and taxes = 9,822 + 1,930 = 11,752. Dividing this by EBIT of 6,270 yields 1.9.
13.
A is correct. Operating cash flow before interest and taxes to operating income rises steadily (not
erratically) from 1.2 to 1.3 to 1.9. The ratios over 1.0 and the trend indicate that earnings are supported by cash flow.
Web Chapter 20
Level I
1.

C is correct. Credit analysts consider both business risk and financial risk.
International Financial Statement Analysis, by Thomas R. Robinson, CFA, Jan Hendrik van Gruening, CFA, R.
Elaine Henry, CFA, and Michael A. Broihahn, CFA. Copyright ©2008 by CFA Institute. Reprinted with permission.
- 213 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
2.
A.
P/E: EPS equals net income divided by the number of shares outstanding or 289/440 = 0.66. P/E =
13.89/0.66 = 21.
P/S: per-share sales equals net sales divided by the number of shares outstanding or 6,032/440 = 13.71. P/S =
13.89/13.71 = 1.
B.
One advantage of P/S over P/E is that companies’ accounting decisions can have a much greater impact
upon reported earnings than they are likely to have on reported sales. Although companies are able to make a
number of legitimate business and accounting decisions that affect earnings, their discretion over reported sales
(revenue recognition) is more limited. Other possible advantages include:
►
Analysts can use P/S when EPS is negative, whereas the P/E ratio based upon negative EPS is not
meaningful.
►
The P/S ratio is relatively more stable than P/E and P/S may be more meaningful than P/E when EPS is
abnormally high or low.
C.
The net profit margin, calculated as net income/net sales, is a financial ratio, calculable using the
information given, which reflects the company’s cost structure. For Abitibi, the profit margin equals 289/6,032 =
0.048 or 4.8 percent. Sales is the top line in the income statement: It does not reflect costs. Thus differences in P/S
ratios may reflect differences in cost structure; the net profit margin, reflect cost structures, is relevant to
determining whether this possible explanation for different P/S ratios may be valid in a given instance.
3.
A.
Book value per share = [(Shareholders’ equity) − (Total value of equity claims that are senior to
common stock)]/(Number of common stock shares outstanding) = (11,707 − 8,442)/440 = 3,265/440 = 7.42. P/B =
13.89/7.42 = 1.9.
B.
One advantage of P/B over P/E is that book value is more stable than EPS and P/B may be more
meaningful than P/E when EPS is abnormally high or low.
One possible disadvantage is that book value ignores assets such as human capital that are important for some
companies. Another is that differences in P/B may just reflect differences in the business model of companies as it
pertains to asset use.
C.
Recognizing that both goodwill and deferred charges are intangible assets, Tangible book value = book
value − intangible assets = 3,265 − (1,420 + 379) = 3,265 − 1,799 = 1,466. Then, on a per-share basis, 1,466/440 =
3.33. Thus price to tangible book value is 13.89/3.33 = 4.2.
Such a large fraction of Abitibi’s assets were composed of intangibles that the price to tangible book value ratio is
much larger than the P/B ratio.
4.
A.
Per-share CF = EPS plus per-share depreciation, amortization, and depletion. CF = net income of
289 + depreciation and amortization of 707 = 996 million. So per-share CF = 996/440 = 2.26. P/CF = 13.89/2.26 =
6.1.
Copyright © 2003 by AIMR. Reprinted with permission.
- 214 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
Note that “other noncash expenses” of 91 were not added back to net income in computing CF.
B.
Advantage: P/CF is generally more stable than P/E. Note too that cash flow is generally less subject to
manipulation by management than earnings, although CF may be more vulnerable in this respect than CFO which
can only be affected by real activities such as the sale of receivables. Limitation: CF ignores changes in working
capital and noncash revenue. CF is not a free cash flow concept.
Level II
5.
A.
Intrinsic P/E ratio 
P0 1  b(ROE  r ) 
 1
.
Er r  r  ROE  b 
In this case, b = 0, because the company pays out all its earnings. So, P0/E1 = 1/r = 1/0.13 = 7.69.
B.
Again, P0/E1 = 1/r = 1/0.13 = 7.69.
C.
It is clear from the expression in Part A that if b = 0, the intrinsic P/E value is independent of ROE. To
further explore this, realize that the intrinsic P/E value can also be expressed as P0/E1 = (1/r) + FF × G, where the
franchise factor is FF = (ROE − r)/(ROE × r) or 1/r − 1/ROE, and the growth factor is G = g/(r − g). If b = 0, then g
= 0, and therefore, the growth factor G = 0. Thus, regardless of how big the ROE—and consequently the franchise
factor FF—is, the franchise value, FF × G, is zero, and the intrinsic P/E value is simply 1/r.
D.
Again, P0/E1 = 1/r = 1/0.13 = 7.69.
E.
In Part D. ROE = r = 13%. It is clear from the expression in Part A that if ROE = r, the intrinsic P/E value
is independent of the retention ratio, b. To further explore this, let us again look at the expression for intrinsic P/E
value discussed in Part C. If ROE = r, then the franchise factor FF = 0. Thus, regardless of how large the retention
ratio—and consequently the growth factor G—is, the franchise value, FF × G, is zero, and the intrinsic P/E value is
simply 1/r.
6.
The dividends in Stages 2 and 3 can be valued with the H-model, which estimates their value at the
beginning of Stage 2. In this case, V6 would capture the value of Stages 2 and 3 dividends. V6 would then be
discounted to the present. Also, the present values of dividends D1 through D6 need to be added to the present value
of V6.
V6 
D6 (1  g L )  D6 H ( g S  g L )
r  gL
where

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.

Equity Asset Valuation, Second Edition, by Jerald Pinto, CFA, Elaine Henry, CFA, Thomas Robinson, CFA, and
John Stowe, CFA. Copyright © 2009 by CFA Institute. Reprinted with permission.
- 215 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
r
 D0 (1  g S )6  9(1.14)6  19.7548
 0.16
H
 10 / 2  5
gS
 0.14
gL
 0.10
V6 
19.7548(1.10)  19.7548(5)(0.14  0.10)
 428.02
0.16  0.10
D6
PV of V6
PV of D1
PV of D2
PV of D3
PV of D4
PV of D5
PV of D6
 428.02 /1.166  175.68
 9(1.14) /1.16  8.8448
 9(1.14) 2 /1.162  8.6923
 9(1.14)3 /1.163  8.5425
 9(1.14) 4 /1.164  8.3952
 9(1.14)5 /1.165  8.2504
 9(1.14)6 /1.166  8.1082
Value of stock = 8.8448  8.6923  8.5425  8.3952  8.2504  8.1082 
175.68  Rs. 226.51
7.
A.
The table on the following page provides the details from the spreadsheet model. The constant
growth rate after Year 4 is 2 percent less than that in Year 4. So,
g
V4
 0.1180  0.0200  0.098 or 9.8 percent.
 D4 (1  g ) /(r  g )  1.80(1.098) /(0.13  0.098)  $61.76
Year
1
2
3
4
Sales ($ millions)
300.00
345.00
396.75
436.43
EBIT
51.00
58.65
67.45
74.19
Interest (%)
10.00
10.00
10.00
10.00
EBT
41.00
48.65
57.45
64.19
Taxes (30%)
12.30
14.60
17.23
19.26
Net income
28.70
34.06
40.21
44.93
Dividends
11.48
13.62
16.09
17.97
DPS
1.15
1.36
1.61
1.80
18.26%
18.38%
11.80%
1.07
1.12
1.10
Growth rate of DPS
PV of DPS
1.02
V4 = D4(1+g)/(r − g)
61.76
PV of V4
$37.87
B.
V0 = Sum of PV of DPS and PV of V4 = 1.02 + 1.07 + 1.12 + 1.10 + 61.76/(1 +0.13)4 = $42.18.
C.
The following table provides the details if the sales growth rate in Year 3 is 10 percent.
- 216 Copyright © 2010 by Nelson Education Ltd.
Solutions for Appendix A: CFA Questions and Problems
Year
1
2
3
4
Sales ($ millions)
300.00
345.00
379.50
417.45
EBIT
51.00
58.65
64.52
70.97
Interest (%)
10.00
10.00
10.00
10.00
EBT
41.00
48.65
54.52
60.97
Taxes (%)
12.30
14.60
16.35
18.29
Net income
28.70
34.06
38.16
42.68
Dividends
11.48
13.62
15.26
17.07
DPS
1.15
1.36
1.53
1.71
18.26%
12.50%
11.76%
1.07
1.06
1.05
Growth rate of DPS
PV of DPS
1.02
V4 = D4(1+g)/(r − g)
35.52
PV of V4
$39.72
V0 = Sum of PV of DPS and PV of V4 = $39.72
- 217 Copyright © 2010 by Nelson Education Ltd.