APPENDIX A CFA SOLUTIONS - muradsweb.weebly.com€¦ · maturity, Investment 3 should have a higher maturity premium. The interest rate on Investment 3, r 3, should thus be above

Solutions for Appendix A: CFA Questions and Problems

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Copyright © 2010 by Nelson Education Ltd.

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:

(1/10)10

1

1

(1 ) 1Gt

R R

which can also be written as

Solutions to 1-3 taken from Quantitative Methods for Investment Analysis, Second Edition by Richard A. DeFusco,

CFA, Dennis W. McLeavey, CFA, Jerald E. Pinto, CFA, and David E. Runkle, CFA. Copyright © 2004 by CFA

Institute. Reprinted with permission. All other solutions copyright © CFA Institute.


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101 2 10(1 )(1 ) (1 ) 1GR R R R

To find the geometric mean in this example, we take the following five steps:

i. Divide each figure in the table by 100 to put the returns into decimal representation.

ii. Add 1 to each return to obtain the terms 1 + 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 101.9124 1.0670 . On most calculators, we evaluate 101.9124 using

the yx key. Enter 1.9124 with the y

x key. Next, enter 1/10 = 0.10. Then press the = key to get 1.0670.

v. Subtract 1 to get 0.0670, or 6.70 percent a year. The geometric mean return is 6.70 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 period-

by-period observations.

B. The geometric mean return is more meaningful than the arithmetic mean return for an investor concerned

with the terminal value of an investment. The geometric mean return is the 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.


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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 (%) +

Expected

inflation

(%)

+

Spreads or

premiums

(%)

=

Expected annual

fixed-income

return (%)

1-year U.S.

T-note

1.2 + 2.6 + 0 = 3.8

10-year corp.

bond

1.2 + 2.6 + 1.0 + 0.8 +

0.9

= 6.5

Solution to 4 taken from Solutions Manual to accompany Investment Analysis and Portfolio Management, Eighth

Edition, by Frank K. Reilly, CFA and Keith C. Brown, CFA. Copyright © 2005 by Thomson 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.


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10-0year

MBS

1.2 + 2.6 + 0.95 = 4.75

Note: We assign the 10-year corporate a 1% maturity premium based on the 10-year over 1-

year government spread.

Estimate of the expected return of an equal-weighted investment in the three securities: (3.8% + 6.5% + 4.75%)/3 =

5.02%

B. The average spread at issue is [0 + (1.0% + 0.8% + 0.9%) + 0.95%]/3 = 1.22%. As 1.22% − 1% = 0.22% is

less than 0.5 percent, the investor will not make the investment.

6. A. For Swennson, the annualized rate of return is:

1/ 5

[(1 0.275)(1 0.189)(1 0.146)(1 0.324)

(1 0.123)] 1

0.0209 2.09%

ar

For Mattsson, the annualized rate of return is:

1/ 5

[(1 0.057)(1 0.049)(1 0.078)(1 0.067)

(1 0.053)] 1

0.0327 or 3.27%

ar

B. Mattsson’s annualized rate of return of 3.27% was higher than Swennson’s at −2.09%.


Jerald E. Pinto, CFA, and Dennis W. McLeavey, CFA , editors. Copyright © 2007 by CFA Institute. Reprinted with

permission.


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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 / 18.31/ 9.65 1.90s R .

ii. For the MSCI Germany Index, CV / 29.95/10.80 2.77s R .

iii. For the JPM Germany 5–7 Year GBl, CV / 6.94 / 7.92 0.88s R .

B. The coefficient of variation is a measure of relative dispersion. For returns, it measures the amount of risk

per unit of mean return. The MSCI Germany Index portfolio, the JPM Germany GBI, and the 60/40 equity/bond

portfolio, were respectively most risky, least risky, and intermediate in risk, based on their values of CV.

Portfolio CV Risk

MSCI Germany Index 2.77 Highest

60/40 Equity/bond portfolio 1.90

JPM Germany GBI 0.88 Lowest

A3. The covariance is 25, computed as follows. First, we calculate expected values:

B

Z

( ) (0.25 30%) (0.50 15%) (0.25 10%) 17.5%

( ) (0.25 15%) (0.50 10%) (0.25 5%) 10%

E R

E R


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Then we find the covariance as follows:

B ZCov ( , ) (30,15) [(30 17.5) (15 10)] (15,10)

[(15 17.5) (10 10)] (10,5) [(10 17.5)

(5 10)]

(0.25 12.5 5) [0.50 ( 2.5) 0] [0.25

( 7.5) ( 5)]

15.625 0 9.375 25

R R P P

P

Level II

A4. For AOL Time Warner, the required return is

β[ ( ) ] 4.35% 2.50(8.04%) 4.35%

20.10% 24.45%

F M Fr R E R R

For J.P. Morgan Chase, the required return is

β[ ( ) ] 4.35% 1.50(8.04%) 4.35%

12.06% 16.41%

F M Fr R E R R

For Boeing, the required return is

β[ ( ) ] 4.35% 0.80(8.04%) 4.35%

6.43% 10.78%

F M Fr R E R R

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

2 2 2 2 2σ σ σ 2ρσσ (5.5) (11.7) 2(0)(5.5)(11.7)

167.14

σ 12.93%

f s s

f

B. Because the actual dollar volatility is 13.6 percent, we conclude that the 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.


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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


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reasonably expect from the financial markets over long periods of time and to define an achievable return objective.

Level III

7. A. i. The Maclins’ overall risk objective must consider both willingness and ability to take

risk:

Willingness. The Maclins 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

Net annual cash flow −£26,000

Inheritance 900,000

Barnett Co. common stock 220,000

Stocks and bonds 160,000

Cash 5,000

Subtotal £1,285,000

Less one-time needs:

Down payment on house −30,000

Charitable donation −20,000

Investable asset base £1,235,000


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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. B is correct.

* (1 )

0.06*[1 (0.30)(0.15) (0.20)(0.35) (0.40)(0.25)]

0.0471 or 4.71 percent

* (1 ) /(1 )

(1 0.30 0.20 0.40) /[1 (0.30)(0.15)

(0.20)(0.35) (0.40)(0.25)

r r p t p t p td d i i cg cg

T t p p p p t p t p tcg d i cg d d i i cg cg

tcg

]

0.0318

£1,000,000[(1 *) (1 *) *]

15£1,000,000[(1 0.0471) (1 0.0318) 0.0318]

£1,962,776

nFVIF r T TTaxable

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.



permission.


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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.



permission.



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B. Given the investor’s circumstances, the decision to buy a house in one year’s time makes the addition of a

shortfall risk objective appropriate. He needs to earn at least 2 percent if he is to have sufficient funds to buy the

house. An appropriate shortfall risk objective is to minimize the probability that the return on the 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.


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► 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.


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Tracking error = 0.0073

4= 0.0427, or 4.3%

2. 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 one-

year U.S. bonds, and at the end of one year it will have 0.8929(1 + 0.0225) = $0.913.

This can be converted back to euros = 0.913(1.25) = €1.1412.

The firm is better off investing in U.S. bonds.

Level III

3. Currency fluctuations have an impact on 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

2 2 2 2 2

ρσ σ (1 ) σ 2 (1 )ρσ σd f d fx x x x

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


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Here, we will take ρ = −0.10, because the U.S. portfolio is very strongly correlated with the U.S. stock index.

2 2 2 2 2

2

σ (0.9 )(15 ) (0.1 )(20 ) 2(0.9)(0.1)( 0.1)(15)(20)

σ 182.25 4 5.4 180.85

σ 13.45%

p

p

p

Thus, the addition of foreign equity allows us both to increase the return (here, 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.


Edition, by Frank K. Reilly, CFA and Keith C. Brown, CFA. Copyright 2005 by Thomson South-Western.


Institute.


- 174 -


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

46.67 32.67 14.00Percentage change 42.85%

32.67 32.67

B.

Period T

Stock Price/Share # of Shares Market Value

A $60 1,000,000 $ 60,000,000

Solutions Manual to accompany Investment Analysis and Portfolio Management, Eighth Edition, by Frank K.

Reilly, CFA and Keith C. Brown, CFA. Copyright 2005 by Thomson South-Western. Reprinted with permission of

South-Western, a division of Thomson Learning.


- 175 -


B 20 10,000,000 200,000,000

C 18 30,000,000 540,000,000

Total $800,000,000

Period T+1


A $80 1,000,000 $ 80,000,000

B 35 10,000,000 350,000,000

C 25 30,000,000 750,000,000

Total $1,180,000,000

1,180 800 380Percentage change 47.50%

800 800

C. The percentage change for the price-weighted series is a simple average of the differences in price from one

period to the next. 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.


- 176 -


6. A.

Period T


A $60 16.67 $1,000

B 20 50.00 1,000

C 18 55.56 1,000

Total $ 3,000

Period T+1


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

4, 472.60 3,000 1, 472.60Percentage change 49.09%

3,000 3,000

B.

80 60 20A 33.33%

60 60

35 20 15B = 75.00%

20 20

25 18 7C = 38.89%

18 18

33.33% 75.00% 38.89%Arithmetic average

3

147.22%49.07%

3

The answers are the same (slight difference due to rounding). This is what you would expect since part A represents

the percentage change of an equal-weighted series and part B applies an equal weight to the separate stocks in

calculating the arithmetic average.

C. Geometric average is the nth root of the product of n items.

1/ 3

1/ 3

Geometric average [(1.3333)(1.75)(1.3889)] 1

[3.2407] 1

1.4798 1

.4798 or 47.98%


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The geometric average is less than the arithmetic average. This is because variability of return has a greater affect on

the arithmetic average than the geometric average.

Level III

7. A. Quoted spread is the difference between the ask and bid prices in the quote prevailing at the time

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,


permission.


- 178 -


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.


- 179 -


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. The average performance should be that of the market index minus costs (transaction costs, management

fees).

If international investors, as a group, beat some national index, it tells us that local investors, as a group, probably

underperform 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.


- 180 -


0.75(15) 0.25(5)

12.5 percent

The standard deviation is

2 2 2 2

stocks stocks bonds bonds stocks bonds

1/ 2

stocks bonds stocks bonds

2 2 1/ 2

1/ 2

1/ 2

σ [ σ σ 2

Corr ( )σ σ ]

[0.75 (225) 0.25 (100) 2(0.75)(0.25)(0.5)(15)(10)]

(126.5625 6.25 28.125)

(160.9375)

12.69%

w w w w

R R

4. Use the expression

2 2 1 ρσ σ ρpn

The square root of this expression is standard deviation. With variance equal to 625 and correlation equal to 0.3,

1 0.3σ 625 0.3

100

13.85%

p

5. Find portfolio variance using the following expression

2 2

2

1 ρσ σ ρ

σ 625[(1 0.3) / 24 0.3] 205.73

p

p

n

With 24 stocks, variance of return is 205.73 (equivalent to a standard deviation of 14.34 percent). With an unlimited

number of securities, the first term in square brackets is 0 and the smallest variance is achieved:

2 2

minσ σ ρ 625(0.30) 187.5

This result is equivalent to a standard deviation of 13.69 percent. The ratio of the variance of the 24-stock portfolio

to the portfolio with an unlimited number of securities is

2

2

min

σ 205.731.097

σ 187.5

p

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.


- 181 -


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.

3. i i M

i

i

( ) β ( )

.10 β (.14 .10)

.10 .04β

E R RFR R RFR

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.

Expected return 1.5(Interest rate surprise) 2(GDP surprise)

Company-specific surprise

11% 1.5(2%) 2( 3%) 3%

5%

R

Chapter 8

Level II


Edition, by Frank K. Reilly, CFA and Keith C. Brown, CFA. Copyright © 2005 by Thomson South-Western.


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.


- 182 -


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.

10

27.73(1 0.059)$1,398.38 trillion

0.08 0.059

DV

r g

Chapter 9

Level I

1. To compute the compound growth rate, we only need the beginning and ending EPS values of $4.00 and

$7.00 respectively, and use the following equation:

Equity Asset 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.


- 183 -


4

1/ 4

1/ 4

FV PV(1 )

7 4(1 )

1 (7 / 4)

(7 / 4) 1

0.1502 15.02%

NN r

r

r

r

EPS grew at an annual rate of 15.02 percent during the four years.

2. A is correct. Using the general time value of money formula, for sales, solve for r in the equation 2 = 1 × (1

+ r)5. For income, solve 3 = 1 × (1 + r)

5. Alternatively, using a financial calculator, for sales, enter N=5, PV = 1,

PMT=0, FV=−2 and compute I/Y. For income, change the FV to −3 and again solve for 1/Y. The solution for sales

is 14.87%; and for income is 24.57%.

3. B is correct. Free cash flow to the firm can be computed as operating cash flows plus after-tax interest

expense less capital expenditures.

4. C is correct. The required rate of return for the company is 6% + 1.2(11% − 6%) = 12%. Dividends are

expected to grow at a supernormal rate for two years:

(1) €3.00(1.20) = €3.60

(2) €3.60(1.20) = €4.32

(3) €4.32(1.09) = €4.7088.

D

D

D

The terminal value of the stock is €4.71/(12.0% − 9.0%) = €156.96.

The present value of the dividends and the terminal value is €131.79. 3.214 + 3.444 + 125.128 = 131.79.

5. C is correct. The inputs to the DDM formula are 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


- 184 -


01Firm value FCFF (1 )FCFF 235(1.06)

WACC WACC 0.1032 0.06

249.15,766.20 million

0.0432

g

g g

The total value of equity is the total firm value minus the value of debt, Equity = €5,766.20 million − €1,800 million

= €3,966.20 million. Dividing by the number of shares gives the per share estimate of 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,

01Equity value = FCFE (1 )FCFE 178(1.07)

0.13 0.07

= 190.46€3,174.33 million

0.06

g

r g r g

The value per share is 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. 0Firm value FCFF (1 )

WACC

Firm value 1.1559(1.04)$24.583

0.0889 0.04

g

g

C. Equity value = Firm value − Market value of debt

Equity value = 24.583 − 3.192 = $21.391 billion

D. Value per share = Equity value/Number of shares

Value per share = $21.391 billion /1.852 billion = $11.55.

Quantitative Methods for Investment Analysis, Second Edition, by Richard DeFusco, CFA, Dennis W. McLeavey,

CFA, Jerald E. Pinto, CFA, and David E. Runkle, CFA. Copyright © 2009 by CFA Institute. Reprinted with

permission.


- 185 -


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.


- 186 -


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.


- 187 -


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.


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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.


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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%.


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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.


- 191 -


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

Protective put

Buy put 2.75 30 − 20 = 10 0

Buy stock 33.19 20 40

Total 35.94 30 40

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. This position is commonly called a covered call.

B. i. T T T

T 0 0 0

V S max(0,S X) 70 max(0,70 80) 70 0 70

V V 70 (S c ) 70 (77 6) 70 71 1

ii T T T

T 0 0 0

V S max(0,S X) 75 max(0,75 80) 75 0 75

V V 75 (S c ) 75 (77 6) 4

iii T T T

T 0 0 0

V S max(0,S X) 80 max(0,80 80) 80 0 80

V V 80 (S c ) 80 (77 6) 9

iv T T T

T 0 0 0

V S max(0,S X) 85 max(0,85 80) 85 5 80

V V 80 (S c ) 80 (77 6) 9

C. i. Maximum profit = X − S0 + c0 = 80 − 77 + 6 = 9

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. This position is commonly called a protective put.

B. i. T T T

T 0 0 0

V S max(0, X S ) 70 max(0,75 70) 70 5 75

V V 75 (S p ) 75 (77 3) 75 80 5


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ii. T T T

T 0 0 0

V S max(0, X S ) 75 max(0,75 75) 75 0 75

V V 75 (S p ) 75 (77 3) 75 80 5

iii. T T T

T 0 0 0

V S max(0, X S ) 80 max(0,75 80) 80 0 80

V V 80 (S p ) 80 (77 3) 80 80 0

iv. T T T

T 0 0 0

V S max(0, X S ) 85 max(0,75 85) 85 0 85

V V 85 (S p ) 85 (77 3) 85 80 5

v. T T T

T 0 0 0

V S max(0, X S ) 90 max(0,75 90) 90 0 90

V V 90 (S p ) 90 (77 3) 90 80 10

C. i. Maximum profit = ∞

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


- 193 -


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.


- 194 -


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.

7. A. This position is commonly called a bull spread.

B. Let X1 be the lower of the two strike prices and X2 be the higher of the two strike prices.

i. T T 1 T 2

T 0 T 1 2

V max(0,S X ) max(0,S X )

max(0,89 75) max(0,89 85) 14 4 10

V V V (c c ) 10 (10 2) 2

ii. T T 1 T 2

T 0 T 1 2


max(0,78 75) max(0,70 85) 3 0 3

V V V (c c ) 3 (10 2) 5

iii. T T 1 T 2

T 0 T 1 2


max(0,70 75) max(0,70 85) 0 0 0

V V V (c c ) 0 (10 2) 8

C. i. Maximum profit = X2 − X1 − (c1 − c2) = 85 − 75 − (10 − 2) = 2

ii. Maximum loss = c1 − c2 = 10 − 2 = 8

D. ST* = X1 + (c1 − c2) = 75 + (10 − 2) = 83

E. T T 1 T 2

T 0 T 1 2


max(0.83 75) max(0,83 85) 8 0 8

V V V (c c ) 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.


- 195 -


8. A. Let X1 be 110, X2 be 115, and X3 be 120.

V0 = c1 − 2c2 + c3 = 8 − 2(5) + 3 = 1

i. T T 1 T 2 T 3

T

T 0

V max(0,S X ) 2max(0,S X ) max(0,S X )

V max(0,106 110) 2max(0,106 115)

max(0,106 120) 0

V V 0 1 1

ii. T T 1 T 2 T 3

T

T 0

V max(0,S X ) 2 max(0,S X ) max(0,S X )

V max(0,110 110) 2 max(0,110 115)

max(0,110 120) 0

V V 0 1 1

iii. T T 1 T 2 T 3

T

T 0


V max(0,115 110) 2 max(0,115 115)

max(0,115 120) 5

=V V 5 1 4

iv. T T t T 2 T 3

T

T 0

V max(0,S X ) 2max(0,S X ) max(0,S X )

V max(0,120 110) 2max(0,120 115)

max(0,120 120) 10 10 0 0

V V 0 1 1

v. T T 1 T 2 T 3

T

T 0


V max(0,123 110) 2 max(0,123 115)

max(0,123 120) 13 16 3 0

=V V 0 1 1

B. i. Maximum profit = X2 − X1 − (c1 − 2c2

APPENDIX A CFA SOLUTIONS - muradsweb.weebly.com€¦ · maturity, Investment 3 should have a higher maturity premium. The interest rate on Investment 3, r 3, should thus be above

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