Solution Manual For
Fundamentals of Investments Valuation and Management, 10th Edition Jordan
Chapter 1-21
Chapter 1
A Brief History of Risk and Return
Concept Questions
1.
For both risk and return, increasing order is b, c, a, d. On average, the higher the risk of an
investment, the higher is its expected return.
2.
Since the price didn’t change, the capital gains yield was zero. If the total return was four percent,
then the dividend yield must be four percent.
3.
It is impossible to lose more than –100 percent of your investment. Therefore, return distributions
are cut off on the lower tail at –100 percent; if returns were truly normally distributed, you could lose
much more.
4.
To calculate an arithmetic return, you sum the returns and divide by the number of returns. As such,
arithmetic returns do not account for the effects of compounding (and, in particular, the effect of
volatility). Geometric returns do account for the effects of compounding and for changes in the base
used for each year’s calculation of returns. As an investor, the more important return of an asset is
the geometric return.
5.
Blume’s formula uses the arithmetic and geometric returns along with the number of observations to
approximate a holding period return. When predicting a holding period return, the arithmetic return
will tend to be too high and the geometric return will tend to be too low. Blume’s formula adjusts
these returns for different holding period expected returns.
6.
T-bill rates were highest in the early eighties since inflation at the time was relatively high. As we
discuss in our chapter on interest rates, rates on T-bills will almost always be slightly higher than the
expected rate of inflation.
7.
Risk premiums are about the same regardless of whether we account for inflation. The reason is that
risk premiums are the difference between two returns, so inflation essentially nets out.
8.
Returns, risk premiums, and volatility would all be lower than we estimated because aftertax returns
are smaller than pretax returns.
9.
We have seen that T-bills barely kept up with inflation before taxes. After taxes, investors in T-bills
actually lost ground (assuming anything other than a very low tax rate). Thus, an all T-bill strategy
will probably lose money in real dollars for a taxable investor.
10. It is important not to lose sight of the fact that the results we have discussed cover over 80 years,
well beyond the investing lifetime for most of us. There have been extended periods during which
small stocks have done terribly. Thus, one reason most investors will choose not to pursue a 100
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percent stock (particularly small-cap stocks) strategy is that many investors have relatively short
horizons, and high volatility investments may be very inappropriate in such cases. There are other
reasons, but we will defer discussion of these to later chapters.
11.
Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this
solutions manual, rounding may appear to have occurred. However, the final answer for each problem is
found without rounding during any step in the problem.
Core Questions
1.
2.
Total dollar return = 100($41 – $37 + $.28) = $428.00
Whether you choose to sell the stock does not affect the gain or loss for the year; your stock is worth
what it would bring if you sold it. Whether you choose to do so or not is irrelevant (ignoring
commissions and taxes).
Capital gains yield   $41 – $37  / $37  .1081, or 10.81%
Dividend yield  $.28 / $37  .0076, or .76%
Total rate of return  10.81%  .76%  11.57%
3.
Dollar return = 500($34 – $37 + $.28) = –$1,360
Capital gains yield   $34 – $37  / $37  – .0811, or – 8.11%
Dividend yield  $.28 / $37  .0076, or .76%
Total rate of return = –8.11% + .76% = –7.35%
4.
a.
b.
c.
d.
5.
average return = 6.0%, average risk premium = 2.7%
average return = 3.3%, average risk premium = 0%
average return = 12.3%, average risk premium = 9.0%
average return = 16.3%, average risk premium = 13.0%
Cherry average return  17%  11% – 2%  3%  14%  / 5  8.60%
Straw average return  16%  18% – 6%  1%  22%  / 5  10.20%
6.
Cherry: R A  8.60%
Var  1 / 4 .17 – .086   .11 – .086    –.02 – .086   .03 – .086   .14 – .086    .00623

2
2
Standard deviation  .00623
1/2
2
2
2

 .0789, or 7.89%
Straw: R B  10.20%
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2
2
2
2
Var  1/ 4 .16 – .102   .18 – .102    –.06 – .102   .01 – .102   .22 – .102    .01452


Standard deviation  .01452 
1/2
7.
 .1205, or 12.05%
The capital gains yield is  $59 – $65  / $65  – .0923 , or –9.23% (notice the negative sign).
With a dividend yield of 1.2 percent, the total return is –8.03%.
8.
Geometric return  1  .17 1  .111  .02 1  .031  .14  
9.
Arithmetic return  .21  .12  .07 – .13 – .04  .26  / 6  .0817, or 8.17%
(1/5)
– 1  .0837, or 8.37%
Geometric return  1  .211  .12 1  .07 1 – .131 – .04 1  .26  
(1/ 6 )
– 1  .0730, or 7.30%
Intermediate Questions
10. That’s plus or minus one standard deviation, so about two-thirds of the time, or two years out of
three. In one year out of three, you will be outside this range, implying that you will be below it one
year out of six and above it one year out of six.
11. You lose money if you have a negative return. With a 12 percent expected return and a 6 percent
standard deviation, a zero return is two standard deviations below the average. The odds of being
outside (above or below) two standard deviations are 5 percent; the odds of being below are half
that, or 2.5 percent. (It’s actually 2.28 percent.) You should expect to lose money only 2.5 years out
of every 100. It’s a pretty safe investment.
12. The average return is 6.0 percent, with a standard deviation of 9.8 percent, so Prob(Return < –3.8 or
Return  15.8 )  1/ 3 , but we are only interested in one tail; Prob  Return  – 3.9   1/ 6
, which is half of 1/ 3 (or about 16%) .
95%: 6.0 ± 2σ = 6.0 ± 2(9.8) = –13.6% to 25.6%
99%: 6.0 ± 3σ = 6.0 ± 3(9.8) = –23.4% to 35.4%
13. Expected return = 16.4%; σ = 31.2%. Doubling your money is a 100% return, so if the return
distribution is normal, Z  100 – 16.4  / 31.2  2.68 standard deviations; this is in-between two
and three standard deviations, so the probability is small, somewhere between .5% and 2.5% (why?).
Referring to the nearest Z table, the actual probability is = 0.369%, or less than every 100 years.
Tripling your money would be Z   200 – 16.4  / 31.2  5.88 standard deviations; this
corresponds to a probability of (much) less than 0.01%. (The actual answer is less than once every 1
million years, so don’t hold your breath.)
14.
Year
1973
1974
1975
1796
1977
sum
Common stocks
–14.69%
–26.47%
37.23%
23.93%
–7.16%
12.84%
T-bill return
7.29%
7.99%
5.87%
5.07%
5.45%
31.67%
Risk premium
–21.98%
–34.46%
31.36%
18.86%
–12.61%
–18.83%
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a. Annual risk premium = Common stock return – T-bill return (see table above).
b. Average returns: Common stocks  12.84 / 5  .0257, or 2.57%; T-bills  31.67 / 5  .0633, or 6.33%
Risk premium  –18.83 / 5  – .0377, or – 3.77%
c.
Common stocks: Var  1/ 4[  –.1469 – .0257    –.2647 – .0257   .3723 – .0257  
2
2
2
.2393 – .0257    –.0716 – .0257  ]  .072337
1/2
Standard deviation   0.072337   .2690, or 26.90%
2
2
2
2
T-bills: Var  1/ 4 .0729 – .0633  .0799 – .0633  .0587 – .0633  .0507 – .0633  .0545 – .0633

2
2
Standard deviation  .000156 
1/2
 .0125, or 1.25%
Risk premium: Var  1/ 4[ –.2198 –  –.0377     –.3446 –  –.0377    .3136 –  –.0377   
2
2
.1886 –  –.0377    –.1261 –  –.0377  ]  .077446
2
2
Standard deviation  .077446 
1/2
 .2783, or 27.83%
d. Before the fact, for most assets the risk premium will be positive; investors demand
compensation over and above the risk-free return to invest their money in the risky asset. After
the fact, the observed risk premium can be negative if the asset’s nominal return is unexpectedly
low, the risk-free return is unexpectedly high, or any combination of these two events.
15.
 $324, 000 / $1, 000 
– 1  .1226, or 12.26%
16.
 $324, 000 / $1, 000 
– 1  .1226, or 12.26%
1/50
1/50
17. 5 year estimate   5 – 1 /  40 – 1   10.24%   40 – 5  /  40 – 1   12.60%  12.36%
10 year estimate  10 – 1 /  40 – 1   10.24%   40 – 10  /  40 – 1   12.60%  12.06%
20 year estimate   20 – 1 /  40 – 1  10.24%   40 – 20  /  40 – 1  12.60%  11.45%
18. Small-company stocks   $29, 781.01/ $1
1/93
Large-company stocks   $6, 462.39 / $1
1/93
– 1  .1171, or 11.71%
– 1  .0989, or 9.89%
Long-term government bonds   $129.95 / $1
1/93
Treasury bills   $23.05 / $1
1/93
Inflation   $14.03 / $1
1/90
– 1  .0537, or 5.37%
– 1  .0343, or 3.43%
– 1  .0288, or 2.88%
19. R A   –.09  .17  .09  .14 – .04  / 5  .0540, or 5.40%
R G  1 – .09 1  .17 1  .09 1  .14 1  .04  
1/5
– 1  .0490, or 4.90%
20. R1   $15.61 – $13.25  $.15  / $13.25  .1894, or 18.94%
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R 2   $16.72 – $15.61  $.18  / $15.61  .0826, or 8.26%
R 3   $15.18 – $16.72  $.20  / $16.72  – .0801, or – 8.01%
R 4   $17.12 – $15.18  $.24  / $15.18  .1436, or 14.36%
R 5   $20.43 – $17.12  $.28 / $17.12  .2097, or 20.97%
R A  .1894  .0826 – .0801  .1436  .2097  / 5  .1090, or 10.90%
R G  1  .1894 1  .0826 1 – .08011  .1436 1  .2097  
1/5
– 1  .1038, or 10.38%
21. Stock A: R A  .08  .08  .08  .08  .08  / 5  .0800, or 8.00%
2
2
2
2
2
Var  1/ 4 .08 – .08   .08 – .08   .08 – .08   .08 – .08   .08 – .08    .000000


Standard deviation  .000 
1/2
 .000, or 0.00%
R G  1  .08 1  .08 1  .08 1  .08 1  .08  
1/5
– 1  .0800, or 8.00%
Stock B: R A  .03  .13  .07  .05  .12  / 5  .0800, or 8.00%
2
2
2
2
2
Var  1/ 4 .03 – .08   .13 – .08   .07 – .08   .05 – .08   .12 – .08    .001900


Standard deviation  .001900 
1/2
 .0436, or 4.36%
R G  1  .031  .131  .07 1  .05 1  .12  
1/5
– 1  .0793, or 7.93%
Stock C: R A   –.24  .37  .14  .09  .04  / 5  .0800. or 8.00%
2
2
2
2
2
Var  1/ 4  –.24 – .08   .37 – .08   .14 – .08   .09 – .08   .04 – .08    .047950


Standard deviation  .047950 
1/2
 .2190, or 21.90%
R G  1 – .24 1  .37 1  .14 1  .09 1  .04  
1/5
– 1  .0612, or 6.12%
The larger the standard deviation, the greater will be the difference between the arithmetic return and
geometric return. In fact, for lognormally distributed returns, another formula to find the geometric
return is: arithmetic return – ½ variance. Therefore, for Stock C, we get
.0800 – ½ .047950   .0560. The difference in this case is because the return sample is not a true
lognormal distribution.
Spreadsheet Problems
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CFA Exam Review by Schweser
1. a
Geometric average return  .9 1.25.95 1.30 1.05  
1/5
 1  .0785, or 7.85%
2. b
CF0
Scenario 2
−100
Scenario 3
−100
CF1
0
0
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CF2
Scenario 2
−20
Scenario 3
+10
CF3
0
0
CF4
0
0
CF5
171.82
132.92
IRR
7.96%
7.78%
Scenario 2 Ending MV
End of Year 2 = 100(.9)(1.25) + 20 = 132.5
End of Year 5 = 132.5(.95)(1.30)(1.05) = 171.8194
Scenario 3 Ending MV
End of Year 2 = 100(.9)(1.25) − 10 = 102.5
End of Year 5 = 102.5(.95)(1.30)(1.05) = 132.9169
3. c
Annualized return  1.0163 – 1  .21412, or 21.412%
12
4. b
Geometric returns provide the best estimate of a portfolio manager’s return because it neutralizes
the impact of the client’s cash flow decisions. For the clients themselves, the dollar-weighted
return would be appropriate.
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Chapter 2
The Investment Process
Concept Questions
1.
Purchasing on margin means borrowing some of the money used to buy securities. You do it because
you desire a larger position than you can afford to pay for, recognizing that using margin is a form of
financial leverage. As such, your gains and losses will be magnified. Of course, you hope you only
experience the gains.
2.
Shorting a security means borrowing it and selling it, with the understanding that at some future
date, you will buy the security and return it, thereby ―covering‖ the short. You do it because you
believe the security’s value will decline, so you hope to sell high now, then buy low later.
3.
Margin requirements amount to security deposits. They exist to protect your broker against losses.
4.
Asset allocation means choosing among broad categories such as stocks and bonds. Security
selection means picking individual assets within a particular category, such as shares of stock in
particular companies.
5.
Tactical asset allocation is making small, short-term adjustments to your longer-term strategic
allocation. The idea is to overweight sectors with the greatest potential for gains. Since you are
effectively trying to determine which sectors will perform the best, tactical asset allocation can be
considered a form of market timing.
6.
A broker conducts trades on your behalf, and in return he receives a commission. An advisor is
typically a fee-based relationship, where you pay an annual percentage of assets, which covers the
cost of all advice and trades. With an advisory relationship, the interests of the advisor and investor
may be better aligned, as the incentive to ―churn‖ is eliminated.
7.
Probably none. The advice you receive is unconditionally not guaranteed. If the recommendation
was grossly unsuitable or improper, then arbitration is probably your only possible means of
recovery. Of course, you can close your account, or at least what’s left of it.
8.
If you buy (go long) 500 shares at $18, you have a total of $9,000 invested. This is the most you can
lose because the worst that could happen is that the company could go bankrupt, leaving you with
worthless shares. There is no limit to what you can make because there is no maximum value for
your shares – they can increase in value without limit. For a short, this is reversed. The most you can
make is if the stock goes to $0 and you keep the proceeds. There is no limit on the loss since shorts
lose as prices rise.
9.
If the asset is illiquid, it may be difficult to quickly sell it during market declines, or to purchase it
during market rallies. Hence, special care should always be given to investment positions in illiquid
assets, especially in times of market turmoil.
10. Traditional IRAs are tax-deferred, with withdrawals being taxed. Contributions to Roth IRAs are
taxed up-front, but all deposits grow tax free. Thus, an investor who is currently in a low tax bracket
(such as a college student) may prefer a Roth as the benefit of the tax-free growth outweighs the tax
benefit of the traditional tax-deferred IRA.
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Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this
solutions manual, rounding may appear to have occurred. However, the final answer for each problem is
found without rounding during any step in the problem.
Core questions
1.
Maximum investment  $31, 000 /.60  $51, 667
Number of shares  $51, 667 / $17 per share  3, 039.22  or 3, 039  shares
2. Margin loan = ($53 × 275) – $8,000 = $6,575
Margin requirement  $8, 000 /  $53  275   .5489, or 54.89%
3. Terminal price = $62
Without margin   $62 – 53 / $53  .1698, or 16.98%
With margin   $62  275  –  $53  275  / $8, 000  .3094, or 30.94%
Terminal price = $46
Without margin   $46 – 53 / $53  – .1321, or –13.21%
With margin   $46  275  –  $53  275  / $8, 000  – .2406, or – 24.06%
4. Initial deposit = .70 × ($53 × 275) = $10,202.50
Terminal price = $62
Without margin   $62 – 53 / $53  .1698, or 16.98%
With margin   $62  275 –  $53  275  / $10, 202.50  .2426, or 24.26%
Terminal price = $46
Without margin   $46 – 53 / $53  – .1321, or –13.21%
With margin   $46  275 –  $53  275 / $10, 202.50  – .1887, or –18.87%
A lower initial margin requirement will make the returns more volatile. In other words, a stock price
increase will increase the return, and a stock price decrease will cause a greater loss.
5.
Maximum purchase  $26, 000 /.50  $52, 000
6. Amount borrowed = (500 × $38) – (500 × $38)(.50) = $9,500
Margin call price   $9,500 / 500  / 1 – .35   $29.23
7. Amount borrowed = (1,600 × $64)(1 – .65) = $35,840
Margin call price   $35,840 / 1, 600  / 1 – .40   $37.33
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Stock price decline   $37.33 – $64  / $64  – .4167, or – 41.67%
8. Proceeds from short sale = 1,000 × $48 = $48,000
Initial deposit = $48,000(.60) = $28,800
Account value = $48,000 + $28,800 = $76,800
Margin call price  $76,800 / 1, 000  .30  1, 000    $59.08
9. Proceeds from short sale = 1,000($36) = $36,000
Initial deposit = $36,000(.55) = $19,800
Account value = $36,000 + 19,800 = $55,800
Margin call price  $55,800 / 1, 000  .35  1, 000    $41.33
Account equity = $55,800 – (1,000 × $41.33) = $14,470
10. Pretax return   $101 – 84  2.10  / $84  .2274, or 22.74%
Aftertax capital gains = ($101 – 84)(1 – .30) = $11.90
Aftertax dividend yield = $2.10(1 – .15) = $1.79
Aftertax return   $11.90  1.79  / $84  .1630, or 16.30%
Intermediate questions
11.
Assets
3039 shares
$51,663.00
Total
$51,663.00
Margin loan
Account equity
Total
Liabilities and account
equity
$20,665.20
30,997.80
$51,663.00
Margin loan
Account equity
Total
Liabilities and account
equity
$20,665.20
52,270.80
$72,936.00
Stock price = $24
Assets
3039 shares
$72,936.00
Total
$72,936.00
Margin  $52, 270.80 / $72,936  .7167, or 71.67%
Stock price = $14
Assets
3039 shares
$42,546.00
Total
$42,546.00
Margin loan
Account equity
Total
Liabilities and account
equity
$20,665.20
21,880.80
$42,546.00
Margin  $21,880.80 / $42,546  .5143, or 51.43%
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12. 500 shares × $60 per share = $30,000
Initial margin  $20, 000 / $30, 000  .6667, or 66.67%
Assets
500 shares
$30,000
Total
$30,000
Margin loan
Account equity
Total
Liabilities and
account equity
$10,000
20,000
$30,000
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13. Total purchase = 500 shares × $48 = $24,000
Margin loan = $24,000 – 8,000 = $16,000
Margin call price  $16, 000 / 500 – .30  500    $45.71
To meet a margin call, you can deposit additional cash into your trading account, liquidate shares
until your margin requirement is met, or deposit additional marketable securities against your account
as collateral.
14. Interest on loan = $16,000(1.065) = $1,040
a. Proceeds from sale = 500($56) = $28,000
Dollar return = $28,000 – 8,000 – 16,000 – 1,040 = $2,960
Rate of return  $2,960 / $8, 000  .3700, or 37.00%
Without margin, rate of return   $56 – 48 / $48  .1667, or 16.67%
b. Proceeds from sale = 500($48) = $24,000
Dollar return = $24,000 – 8,000 – 16,000 – 1,040 = –$1,040
Rate of return  – $1, 040 / $8, 000  – .1300, or –13.00%
Without margin, rate of return = $0%
c. Proceeds from sale = 500($32) = $16,000
Dollar return = $16,000 – 8,000 – 16,000 – 1,040 = –$9,040
Rate of return  – $9, 040 / $8, 000  –1.1300, or –113.00%
Without margin, rate of return   $32 – 48  / $48  – .3333, or – 33.33%
15. Initial equity = (1,000 × $40)(.50) = $20,000
Amount borrowed = (1,000 × $40)(1 – .50) = $20,000
Interest = $20,000 × .0680 = $1,360
Proceeds from sale = 1,000 × $45 = $45,000
Dollar return = $45,000 – 20,000 – 20,000 – 1,360 = $3,640
Rate of return  $3, 640/$20, 000  .1820, or 18.20%
16. Total purchase = 800 × $34 = $27,200
Loan = $27,200 – 15,000 = $12,200
Interest = $12,200 × .07 = $854
Proceeds from sale = 800 × $48 = $38,400
Dividends = 800 × $0.64 = $512
Dollar return = $38,400 + 512 – 15,000 – 12,200 – 854 = $10,858
Return  $10,858 / $15, 000  .7239, or 72.39%
17. $65, 000  .087  180 / 360   $2,827.50
18. $75, 000  .064   60 / 360   $800
19. 1  .14 
12/7
– 1  .2518, or 25.18%
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20. 1  .14 
12/5
– 1  .3695, or 36.95%
All else the same, the shorter the holding period, the larger the EAR for a given holding period return.
21. Holding period return   $61 – 57  .60  / $57  .0807, or 8.07%
Annualized return  1  .0807 
12/5
– 1  .2047, or 20.47%
22. Initial purchase = 500 × $60 = $30,000
Amount borrowed = $30,000 – 20,000 = $10,000
Interest on loan  $10, 000 .0625180 /360   $312.50
Dividends received = 500($0.25) = $125.00
Proceeds from stock sale = 500($65) = $32,500
Dollar return = $32,500 + 125 – 10,000 – 20,000 – 312.5 = $2,312.50
Rate of return  $2,312.50 / $20, 000  .1156, or 11.56% per six months
Effective annual return  1  .1156 
12/6
– 1  .2446, or 24.46%
23. Proceeds from sale = 800 × $47 = $37,600
Initial margin = $37,600 × 1.00 = $37,600
Assets
Proceeds from sale
Initial margin deposit
Total
$37,600
37,600
$75,200
Short position
Account equity
Total
Liabilities and
account equity
$37,600
37,600
$75,200
24. Proceeds from sale = 800 × $47 = $37,600
Initial margin = $37,600 × .60 = $22,560
Assets
Proceeds from sale
Initial margin deposit
Total
$37,600
22,560
$60,160
Short position
Account equity
Total
Liabilities and
account equity
$37,600
22,560
$60,160
25. Proceeds from short sale = 750($96) = $72,000
Initial margin deposit = $72,000(.60) = $43,200
Total assets = Total liabilities and equity = $72,000 + 43,200 = $115,200
Cost of covering short = 750($86.50) = $64,875
Account equity = $115,200 – 64,875 = $50,325
Cost of covering dividends = 750($0.75) = $563
Dollar profit = $50,325 – 43,200 – 563 = $6,563
Rate of return  $6,563 / $43, 200  .1519, or 15.19%
26. Proceeds from sale = 600 × $72 = $43,200
Initial margin = $43,200 × .50 = $21,600
Initial Balance Sheet
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Assets
Proceeds from sale
Initial margin deposit
Total
$ 43,200
21,600
$ 64,800
Short position
Account equity
Total
Stock price = $63
Assets
Proceeds from sale
Initial margin
deposit
Total
$ 43,200
21,600
Short position
Account equity
$ 64,800
Total
Liabilities and account
equity
$ 43,200
21,600
$ 64,800
Liabilities and account
equity
$ 37,800
27,000
$ 64,800
Margin  $27, 000 / $37,800  .7143, or 71.43%
Five-month return   $27, 000 – 21, 600  / $21, 600  .2500, or 25.00%
Effective annual return  1  .25 
12/5
– 1  .7084, or 70.84%
Stock price = $77
Assets
Proceeds from sale
Initial margin deposit
Total
$ 43,200
21,600
$ 64,800
Short position
Account equity
Total
Liabilities and account
equity
$ 46,200
18,600
$ 64,800
Margin  $18, 600/$46, 200  .4026, or 40.26%
Five-month return   $18, 600 – 21, 600  / $21, 600  – .1389, or –13.89%
Effective annual return  1 – .1389 
12/5
– 1  – .3015, or – 30.15%
27.
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28.
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CFA Exam Review by Kaplan Schweser
1. a
The Analee’s pre-tax return objective is computed as follows:
Living expenses
Travel expenses
College fund
Total
$75,000
15,000
20,000
$110,000
Portfolio Value = $3,000,000
Income objective  $110, 000 / 3, 000, 000  .0367, or
Plus inflation
Gross Return Objective
3.67%
3.00%
6.67%
2. a
Their risk tolerance is average. Their liquidity needs are high due to their living expenses, yet
their portfolio is large enough. Since they are in their retirement years, they will be living off their
portfolio and not adding to it other than the growth in the portfolio to stay even with inflation.
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3. a
Although Barbara’s willingness to assume risk may be high (above average) given her past
entrepreneurial pursuits and because the Analee’s time horizon is quite long, her ability to assume
risk is average given her current income needs.
4. a
The most appropriate portfolio is A, as it provides a good balance in terms of return objectives,
risk tolerance, and constraints. The portfolio provides an adequate return (8.8%) versus their
requirement (6.67%), and it provides sufficient income while minimizing the impact of inflation.
Portfolio B is inappropriate because it concentrates a higher proportion of assets into VC and
REITs, which are lower liquidity and higher volatility assets. Portfolio C is inappropriate because
it does not meet the return objective.
Chapter 3
Overview of Security Types
Concept Questions
1. The two distinguishing characteristics are: (1) all money market instruments are debt instruments
(i.e., IOUs), and (2) all have less than 12 months to maturity when originally issued.
2. Preferred stockholders have a dividend preference and a liquidation preference. The dividend
preference requires that preferred stockholders be paid before common stockholders. The liquidation
preference means that, in the event of liquidation, the preferred stockholders will receive a fixed face
value per share before the common stockholders receive anything.
3. The PE ratio is the price per share divided by annual earnings per share (EPS). EPS is the sum of the
most recent four quarters’ earnings per share.
4. The current yield on a bond is very similar in concept to the dividend yield on common and preferred
stock.
5. Volume in stocks is quoted in round lots (multiples of 100). Volume in corporate bonds is the actual
number of bonds. Volume in options is reported in contracts; each contract represents the right to buy
or sell 100 shares. Volume in futures contracts is reported in contracts, where each contract represents
a fixed amount of the underlying asset.
6. You make or lose money on a futures contract when the futures price changes, not the current price
for immediate delivery (although the two are closely related).
7. Open interest is the number of outstanding contracts. Since most contract positions will be closed
before maturity, it will usually shrink as maturity approaches.
8. A futures contact is a contract to buy or sell an asset at some point in the future. Both parties in the
contract are legally obligated to fulfill their side of the contract. In an option contract, the buyer has
the right, but not the obligation, to buy (call) or sell (put) the asset. This option is not available to the
buyer of a futures contract. The seller of a futures or option contract has the same responsibility to
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deliver the underlying asset. The difference is the seller of a future knows she must deliver the asset,
while the seller of an option contract is uncertain about delivery since delivery is at the option
purchaser’s discretion.
9. A real asset is a tangible asset such as land, buildings, precious metals, knowledge, etc. A financial
asset is a legal claim on a real asset. The two basic types of financial assets are primary assets and
derivative assets. A primary asset is a direct claim on a real asset. A derivative asset is basically a
claim (or potential claim) on a primary asset or even another derivative asset.
10. Initially, it might seem that the put and the call would have the same price, but this is incorrect. If the
strike price is exactly equal to the stock price, the call option must be worth more. Intuitively, there
are two reasons. First, there is no limit to what you can make on the call, but your potential gain on
the put is limited to $100 per share. Second, we generally expect that the stock price will increase, so
the odds are greater that the call option will be worth something at maturity.
Core Questions
1.
Dividend yield  .013  $0.75 / P0 thus P0  $0.75 / .013  $57.69
Stock closed up $.26, so yesterday’s closing price = $57.69 – .26 = $57.43
18,649,130 shares were traded, which means 18, 649,130 /100  186, 491 round lots of stock
were traded.
Technically, yesterday’s price could also be calculated as the change in price divided by the
percentage change, but small rounding errors will cause significant inaccuracies in the final answer.
2.
PE  15; EPS  P0 / 15  $57.69 / 15  $3.846
EPS  NI/shares; so NI  $3.846 100, 000, 000   $384, 615,385
3.
Dividend yield is 3.4%, so annualized dividend is .034($74.20) = $2.52. This is four times the last
quarterly dividend, which is thus $2.52 / 4  $0.63 per share.
4.
PE  21.5; EPS  P0 / 21.5  $74.20 / 21.50  $3.45
5.
The total par value of purchase = 4,000($1,000) = $4,000,000
Next payment   $4, 000, 000  .077  / 2  $154, 000
Payment at maturity = $154,000 + 4,000,000 = $4,154,000
Remember, the coupon payment is based on the par value of the bond, not the price.
6.
Contract to buy  300 / 50  6
Purchase price = 6 × 50 × $850 = $225,000
P = $900: Gain = ($900 – 850) × 6 × 50 = $15,000
P = $800: Gain = ($800 – 850) × 6 × 50 = –$15,000
7.
Cost of contracts = $1.95 × 10 × 100 = $1,950
If the stock price is $72, the value is: ($72 – 60) × 10 × 100 = $12,000
Dollar profit = $12,000 – 1,950 = $10,050
If the stock price is $57.95, the call is worthless, so the dollar return is –$1,950.
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8.
The stock is down 1.2%, so the price was $48.92 / 1 – .012   $49.51
9.
The YTM is given in the quote as 7.482%.
Price   93.231/100  $1, 000  $932.31
Current yield = Annual coupon payment/Price  $68.50 / $932.31  .07347, or 7.347%
10. Next payment  15 .06850 / 2  $1, 000   $513.75
Intermediate Questions
11. Open interest in the March contract is 597,913 contracts.
Since the standard contract size is 5,000 bushels, sell 225, 000 / 5, 000  45 contracts.
You’ll deliver 45(5,000) = 225,000 bushels of corn and receive 45(5,000)($4.52) = $1,017,000
12. The price you sold the contracts was 468 ($4.68) and you closed the position at 465.375 ($4.65375).
So, the total profit was ($4.68 – 4.65375) × 5,000 × 25 = $3,281.25
13. Initial value of position = 15(5,000)($4.7225) = $354,187.50
Final value of position = 15(5,000)($4.62125) = $346,593.75
Dollar profit = $346,593.75 – 354,187.50 = –$7,593.75
14. The right to sell shares is a put option on the stock; the March put with a strike price of $210 has an
ask price of $8.50. Since each stock option contract is for 100 shares of stock, you’re looking at
2, 000 /100  20 option contracts. Thus, the cost of purchasing this right is 20($8.50)(100) =
$17,000.
15. The cheapest put contract (within the set of quotes listed) is the January $210 exercise price. The
most expensive put option is the March $240. The first option is the nearest term and furthest out of
the money, while the second option is the furthest term and furthest in the money. Remember, a put
gives the right to sell, and we always want to ―sell high.‖ Also, the longer the option term, the more
valuable it is.
16. Case 1: Payoff = $210 – 200 = $10 per share. Dollar return = $10(20)(100) – $17,000 = $3,000
Return on investment per 3 months  $3, 000 / $17, 000  .1765, or 17.65%
Annualized return on investment  1.1765 
12/3
– 1  .9157, or 91.57%
Case 2: The option finishes worthless, so payoff = $0. Dollar return = –$17,000
Return on investment = –100% over all time periods.
17. The very first call option listed has a strike price of 10 and a quoted premium of $5.50. This can’t be
right because you could buy an option for $5.50 and immediately exercise it for another $10. You
can then sell the stock for its current price of about $20, earning a large, riskless profit. To prevent
this kind of easy money, the option premium must be at least $10.25. Similarly, the September 30
put is quoted at $8.75. You could buy the put and immediately exercise it. The put premium must be
at least $9.75.
18. If you buy the stock, your $28,000 will purchase 700 shares, or 7 round lots. A call contract costs
$400, so you can buy 70 of them. If, in six months, MMEE is selling for $48, your stock will be
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worth 700 shares × $48 = $33,600. Your dollar gain will be $33,600 less the $28,000 you invested,
or $5,600. Since you invested $28,000, your return for the six-month period is
$5, 600 / $28, 000  .20 , or 20%. To annualize your return, we need to compute the effective
annual return, recognizing that there are two six-month periods in a year.
1  EAR  1.202  1.44
EAR = .44, or 44%
Your annualized return on the stock is 44%.
If MMEE is selling for $36 per share, your loss on the stock investment is –10.00%, which
annualizes as follows:
1  EAR  .902  .81
EAR = –.19, or –19%
At the $48 price, your call options are worth $48 – 40 = $8 each, but now you control 7,000 shares
(70 contracts), so your options are worth 7,000 shares × $8 = $56,000 total. You invested $28,000,
so your dollar return is $56,000 – 28,000 = $28,000, and your percentage return is
$28, 000 / $28, 000  1.00 , or 100%, compared to 20% on the stock investment. This annualizes
to:
1  EAR  2.002  4.00
EAR = 3.00, or 300%
However, if MMEE is selling for $36 when your options mature, then you lose everything ($28,000
investment), and your return is –100%.
19. You only get the dividend if you own the stock. The dividend would increase the return on your
stock investment by the amount of the dividend yield, $0.80 / $40  .020 , or 2.0%, but it would
have no effect on your option investment. This question illustrates that an important difference
between owning the stock and the option is that you only get the dividend if you own the stock.
20. At the $36 stock price, your put options are worth $40 – 36 = $4 each. The premium was $2.80, so
you bought 100 contracts, meaning you control 10,000 shares. Your options are worth 10,00 shares
× $4 = $40,000 total. You invested $28,000, so your dollar return is $40,000 – 28,000 = $12,000,
and your percentage return is $12, 000 / $28, 000  .4286 , or 42.86%. This annualizes to:
1  EAR  1.42862  2.0408
EAR = 1.0408, or 104.08%
21. see next page
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Chapter 4
Mutual Funds
Concept Questions
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1. Mutual funds are owned by fund shareholders. A fund is run by the fund manager, who is hired by the
fund’s directors. The fund’s directors are elected by the shareholders.
2. A rational investor might pay a load because he or she desires a particular type of fund or fund
manager for which a no-load alternative does not exist. (This is rarely the case.) More generally, some
investors feel you get what you pay for and are willing to pay more. Whether they are correct or not is
a matter of some debate, although research tends to support the relative outperformance of no-load
funds (particularly when controlling for fees). Other investors are not aware of the full range of
alternatives, particularly if their advisors are recommending only load funds.
3. The NAV of a money market mutual fund is never supposed to change; it is supposed to stay at a
constant $1. It never rises; only in very rare instances does it fall. Maintaining a constant NAV is
possible by increasing the number of shares as needed such that the number of shares is always equal
to the total dollar value of the fund.
4. A money market deposit account is essentially a bank savings account. A money market mutual fund
is a true mutual fund. A bank deposit is insured by the FDIC, so it is safer, at least up to the maximum
insured amount.
5. ETFs are very popular with active traders since they allow an investor to use margin to purchase the
asset. They also provide the ability to short sell, and they are continuously priced. In contrast, mutual
funds have only end-of-day pricing. For periodic investors who are investing small amounts, mutual
funds may be a better choice since the commissions associated with investing in ETFs would be
costly.
6. In an up market, the cash balance will reduce the overall return since the fund is partly invested in
assets with a lower return. In a down market, a cash balance should help reduce the negative returns
from stocks or other instruments. An open-end fund typically keeps a cash balance to meet
shareholder redemptions. A closed-end fund does not have shareholder redemptions so very little
cash, if any, is kept in the portfolio.
7. 12b-1 fees are designed to pay for marketing and shareholder service costs. It does not really make
sense that a closed-end fund charges 12b-1 fees because there is no need to market the fund once it
has been sold at the IPO and there are no distributions necessary for the fund since the shares are sold
on the secondary market.
8. You should probably buy an open-end fund because the fund stands ready to buy back shares at
NAV. With a closed-end fund another buyer must make the purchase, so it may be more difficult to
sell at NAV. We should note that an open-end fund may have the right to delay redemption if it so
chooses.
9. The big issue here is ―survivorship‖ bias. Funds that accumulate a long record of poor performance
tend to not attract investors. They are often merged into other funds. This is a type of survivor bias,
meaning that a mutual fund family’s typical long-term track record may look pretty good, but only
because the poor performing funds did not survive. In fact, several hundred funds disappear each
year.
10. With a high-water mark, the fund manager must overcome any losses before performance fees can be
taken. So, a ―bad‖ return year is not ignored.
Core Questions
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NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this
solutions manual, rounding may appear to have occurred. However, the final answer for each problem is
found without rounding during any step in the problem.
1.
NAV  $8,500, 000, 000 / 410, 000, 000  $20.73
2.
Load   $21.89 – 20.73 / $21.89  .0529, or 5.29%
3. NAV = $15.95(1 – .02) = $15.63; Market value of assets = $15.63(19,200,000) = $300,115,200 (or
$300,096,000 if NAV is rounded to exactly $15.63)
4. Initial shares = 25,000. Final shares = 25,000(1.017) = 25,425, and final NAV = $1 because this is a
money market fund.
5. Total assets = (6,000 × $98) + (33,000 × $19) + (4,600 × $89) + (82,500 × $12) = $2,614,400
NAV  $2, 614, 400 / 50, 000  $52.29
6.
NAV   $2, 614, 400 – 110, 000  / 50, 000  $50.09
7.
Offering price  $50.09 / 1 – .0625   $53.43
8.
$32, 000, 000 / $96, 000, 000  .3333, or 33.33%
9.
NAV   $240, 000, 000 – 110, 000  / 11, 000, 000  $21.81
 $19.25 – 21.81 / $21.81  – .1174, or –11.74%
10.  $35.23 – 32.24  .24  .41 / $32.24  .1129, or 11.29%
Intermediate
11. Turnover = X / $3, 400, 000, 000  .42 ; X = $1,428,000,000. This is more than the $1.25 billion
in sales, so the turnover with the sales figure is $1, 250, 000, 000 / $3, 400, 000, 000  .368 .
In addition to the standard commission costs, there are two other potential costs associated with
excess turnover. First, added trading causes gains to be realized sooner, thereby increasing tax
liability. Second, if the trade provider has a soft dollar arrangement, there will be added costs.
12. Management fee = .0045($3,400,000,000) = $15,300,000
Miscellaneous and administrative expenses = (.0075 – .0045)$3,400,000,000 = $10,200,000
13. Initial NAV = $47.10(1 – .05) = $44.75
Final NAV = $44.75[1 + (.08 – .0195)] = $47.45 ($47.46 if initial NAV rounded)
Sale proceeds per share = $47.45(1 – .02) = $46.50 ($46.51 if initial NAV rounded)
Total return   $46.50 – 47.10  / $47.10  – .0127 , or –1.27% (–1.26% with initial NAV
rounded)
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You lost –1.27% even though the fund’s investments grew by 8%! The various fees and loads sharply
reduced your return.
Note, there is another interpretation of the solution. To calculate the final NAV including fees, we
would first find the final NAV excluding fees with an 8 percent return, which would be:
NAV excluding fees = $44.75(1 + .08) = $48.32
Now, we can find the final NAV after the fees, which would be:
Final NAV = $48.33(1 – .0195) = $47.38
Notice this answer is $0.07 different than our original calculation. The reason is the assumption
behind the fee withdrawal. The second calculation assumes the fees are withdrawn entirely at the end
of the year, which is generally not true. Generally, fees are withdrawn periodically throughout the
year, often quarterly. The actual relationship between the return on the underlying assets, the fees
charged, and the actual return earned is the same as the Fisher equation, which shows the relationship
between the inflation, the nominal interest rate, and the real interest rate. In this case, we can write the
relationship as:
(1 + Return on underlying assets) = (1 + Fees)(1 + Return earned)
As with the Fisher equation, effective annual rates must be used. So, we would need to know the
periodic fee withdrawal and the number of fee assessments during the year to find the exact final
NAV. Our first calculation is analogous to the approximation of the Fisher equation; hence it is the
method of calculation we will use going forward, that is:
Return earned = Return on underlying assets – Fees
Assuming a small fee (which we hope the mutual fund would have), the answer will be close to the
actual value without undue calculations.
14. Yr 1: There is no performance fee since the manager had a negative return. So, the only Year 1 fee is
the 2% management fee: $1,250,000 × .02 = $25,000.
Yr 2: The management fee is taken out at the beginning of the year on the new balance, so it is:
[($1,250,000 − 25,000) × (1+ (−.10))] × .02 = $1,102,500 × .02 = $22,050
The performance fee is 20% of everything over the $1,250,000 high water mark.
($1,102,500 − 22,050) × (1 + .20) = $1,296,540
($1,296,540 − 1,250,000) × .20 = $9,308
15. The cost of the ETF is ($25,000 × .0009) + $25 = $47.50
The cost of the mutual fund is $25,000 × .0021 = $52.50
Thus, the ETF is the better choice based on fees.
16. After 3 years: (For every dollar invested)
Class A: $0.9425 1  .10 – .0023 – .0073  $1.22191
3
Class B: $1.00 1  .10 – .01 – .0073   1 – .02   $1.24380
3


After 20 years:
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Class A: $0.9425 1  .10 – .0023 – .0073
Class B: $1.00 1  .10 – .01 – .0073 
20
20
 $5.32106
 $4.89962
17. 1  .033 – .001  1 – .06 1  R – .0175  ; 1.065  .94 1  R – .0175  ; R  8.19%
2
2
2
1  .033 – .001  1 – .06 1  R – .0175 ; 1.3702  .94 1  R – .0175 ; R  5.59%
10
10
10
18. National municipal fund: aftertax yield = .032(1 – .08) = .0294, or 2.94%
Taxable fund: aftertax yield = .049(1 – .35 – .08) = .0279, or 2.79%
New Jersey municipal fund: aftertax yield = .0300, or 3.00%
Choose the New Jersey fund.
19. National municipal fund: aftertax yield = .0320, or 3.20%
Taxable fund: aftertax yield = .049(1 – .35) = .0319, or 3.19%
New Jersey municipal fund: aftertax yield = .0300, or 3.00%
Choose the national municipal fund.
20.  $14.29 – NAV  / NAV  – .069; NAV  $15.35
Shares outstanding  $560, 000, 000 / $15.35  36, 484, 255 (36,482,085 with NAV rounded)
For closed-end funds, the total shares outstanding are fixed, just as with common stock (assuming no
net repurchases by the fund or new share issues to the public).
Spreadsheet Problem
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CFA Exam Review by Kaplan Schweser
1. a
The biggest disadvantage of the fund of funds is the extra layer of fees. Style drift could impact
both individual hedge funds and a fund of funds. Benchmark availability is probably more of an
issue for individual funds.
2. b
Arbitrage funds usually focus on mergers, spin-offs, takeovers, or convertibles, buying one
security and shorting a related one to take advantage of differences in prices.
3. a
Many alternative assets (i.e., hedge funds) provide high returns and are tax-friendly. However,
most are not easy to value and are difficult to track closely over short periods of time.
4. b
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Benchmarks are available for commodities, real estate, private equity, and hedge funds, though
not all of them are easy to interpret. There would be no such benchmark for an individual,
privately held firm such as Kelly.
Chapter 5
The Stock Market
Concept Questions
1. The new car lot is a primary market; every new car sold is an IPO. The used car lot is a secondary
market. The Chevy retailer is a dealer, buying and selling out of inventory.
2. The right to trade on the NYSE is a valuable asset. For floor brokers, they are able to trade on the
behalf of investors and, in return, receive a commission for their services. If trading volume is large
enough, these commissions more than offset the cost of the license.
3. A market order is an order to execute the trade at the current market price. A limit order specifies the
highest (lowest) price at which you are willing to purchase (sell) the stock. The downside of a market
order is that in a volatile market, the market price could change dramatically before your order is
executed. The downside of a limit order is that the stock may never hit the limit price, meaning your
trade will not be executed.
4. A stop-loss order is an order to sell at market price if the price declines to the stop price. As the name
suggests, it is a tool to limit losses. As with any stop order, however, the price received may be worse
than the stop price, so it may not work as well as the investor hopes. For example, suppose a stock is
selling for $50. An investor has a stop loss on at $45, thereby limiting the potential loss to $5, or so
the naive investor thinks. However, after the market closes, the company announces a disaster. The
next morning, the stock opens at $30. The investor’s sell order will be executed, but the loss suffered
will far exceed $5 per share.
5. You could submit either a limit order to sell or a stop order to sell. In this case, both order types
would sell when the price increased to $32. The difference would be the stop order would convert to a
market order and the price you receive could actually be below $32 if that is where the next trade
settled.
6. No, you should submit a stop order to buy at $17, also called a stop buy. A limit buy would be
executed immediately at the current price.
7. With a multiple market maker system, there are, in general, multiple bid and ask prices. The inside
quotes are the best ones, the highest bid and the lowest ask.
8. What market is covered; what types of stocks are included; how many stocks are included; and how
the index is calculated.
9. The issue is index staleness. As more stocks are added, we generally start moving into less frequently
traded issues; thus, the tradeoff is between comprehensiveness and recency.
10. Funding in stages reduces the risk faced by the venture capitalist. For example, if the VC invests in
the first round and the company is unsuccessful, the VC has limited its loss. This structure actually
provides the venture capitalist with an implicit call option on future financing rounds.
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Core Questions
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this
solutions manual, rounding may appear to have occurred. However, the final answer for each problem is
found without rounding during any step in the problem.
1.
d   $93  312 / 2  78  /  $93  312  78  / 3  2.03106
2.
d   $93  312 / 4  78  /  $93  312  78  / 3  1.54658
3.
a. 100 shares at $70.56
b. 200 shares at $70.53
c. 100 shares at $70.56 and 300 shares at $70.57
4.
Beginning index value   $37  84  / 2  $60.50
Ending index value   $42  91 / 2  $66.50
Return   $66.50 – 60.50  / $60.50  .0992, or 9.92%
5.
Beginning value   $37  35, 000    $84  26, 000   / 2  $1, 739,500
Ending value   $42  35, 000    $91  26, 000   / 2  $1,918, 000
Return   $1,918, 000 – 1, 739,500  / $1, 739, 500  .1026, or 10.26%
Note you could also solve the problem as:
Beginning value = ($37 × 35,000) + ($84 × 26,000) = $3,479,000
Ending value = ($42 × 35,000) + ($91 × 26,000) = $3,836,000
Return   $3,836, 000 – 3, 479, 000  / $3, 479, 000  .1026, or 10.26%
The interpretation in this case is the percentage increase in the market value of the index.
Ending index level = 408.16(1 + 0.1026) = 450.04
6. Beginning of year: $1, 739,500 / $1, 739,500  100  100.00
End of year: $1,918, 000 / $1, 739,500  100  110.26
7. 408.16(1 + .1026) = 450.04
8.
Year 1: $4,387 million / $4,387 million  1, 000  1, 000.00
Year 2 : $4, 671 million / $4,387 million  1, 000  1, 064.74
Year 3: $5, 032 million / $4,387 million  1, 000  1,147.03
Year 4 : $4,820 million / $4,387 million  1, 000  1, 098.70
Year 5 : $5,369 million / $4,387 million  1, 000  1, 223.84
Intermediate Questions
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9.
d 
 $93 / 1 / 2   312  78  / $93  312  78  / 3  3.57764
10. May 31 Open :  P / .15173  33,160.59;  P  5, 031.46
May 31 Close :  P  5,031.46  5  5,036.46; Index level  5,036.46 / .15173  33,193.54
Or, take the $5 change divided by the divisor, and add to the starting index level:
5 / .15173  33,160.59  33,193.54
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11. UNH: Index level  33,160.59   496.78  .05 / .15173  33,324.30
WBA: Index level  33,160.59   43.83  .05 / .15173  33,175.06
12.  P  5, 031.46  30 1  5, 061.46; Index level  5, 061.46 / .15173  33,358.31
Or, Index  33,160.59   30 / .15173  33,358.31
13. Change in index = 8,503.21 – 8,465.52 = 37.69
5 / d  37.69
d = .13266118
14.
a. 1/1/22: Index value  103  45  74 / 3  74.00
b. 1/1/23: Index value  106  39  63 / 3  69.33
2022 return   69.33 – 74.00  / 74.00  – .0631, or – 6.31%
1/1/24: Index value  118  53  79 / 3  83.33
2023 return  83.33 – 69.33 / 69.33  .2019, or 20.19%


15. Share price after the stock split is $35.33 $106  1/ 3 .
Index value on 1/1/23 without the split is 69.33 (see previous problem).
 35.33  39  63 /d  69.33; d  137.33 / 69.33  1.980769
1/1/24: Index value   39.33  53  79 / 1.980769  86.4984
2023 return   86.4984 – 69.33 / 69.33  .2476, or 24.76%.
16.
a. 1/1/22: Index value  103 340  45 450  74 410  / 10  8,561.00
b. 1/1/23: Index value  106  340  39 450  63 410  / 10  7,942.00
2022 return   7942 – 8561 / 8561  – .0723, or – 7.23%
1/1/24: Index value  118 340  53 450  79 410  / 10  9, 636.00
2023 return   9636 – 7942  / 7942  .2133, or 21.33%
17. The index values and returns will be unchanged; the stock split changes the share price, but not the
total value of the firm.
18. 2022:
Douglas McDonnell return  106 – 103 / 103  .0291, or 2.91%
Dynamics General return   39 – 45  / 45  – .1333, or –13.33%
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International Rockwell return   63 – 74  / 74  – .1486, or –14.86%
2022:
Index return  .0291 – .1333 – .1486  / 3  – .0843, or – 8.43%
1/1/23:
Index value = 100(1 – .0843) = 91.57
2023:
Douglas McDonnell return  118 – 106  / 106  .1132, or 11.32%
Dynamics General return   53 – 39  / 39  .3590, or 35.90%
International Rockwell return   79 – 63 / 63  .2540, or 25.40%
2023:
Index return  .1132  .3590  .2540  / 3  .2421, or 24.21%
1/1/24:
Index value = 91.57(1.2421) = 113.74
19. To sell 1,000 shares, the clearing price would need to be $18. Three bidders bid $18 or higher, with a
total request of 400 + 400 + 300 = 1,100 shares. So, each will receive 1, 000 /1,100  .909 , or
90.9% of their requested number. Thus, Bidder A will receive 400(.909) = 364 shares (rounded) and
pay a total of 364($18) = $6,552.
20. Looking back at Chapter 1, you can see that there are years in which small cap stocks outperform
large cap stocks. In years with better performance by small companies, we would expect the returns
from the equal-weighted index to outperform the value-weighted index since the value-weighted
index is weighted toward larger companies. In years where large cap stocks outperform small cap
stocks, we would see the value-weighted index with a higher return than an equal-weighted index.
21. 2022:
Douglas McDonnell return  106 – 103 / 103  .0291, or 2.91%
Dynamics General return   39 – 45  / 45  – .1333, or –13.33%
International Rockwell return   63 – 74  / 74  – .1486, or –14.86%
2022:
Index return  1  .02911 – .13331 – .1486   – 1  – .0877, or – 8.77%
1/1/23:
Index value = 100(1 – .0877) = 91.23
2023:
Douglas McDonnell return  118 – 106  / 106  .1132, or 11.32%
1/3
Dynamics General return   53 – 39  / 39  .3590, or 35.90%
International Rockwell return   79 – 63 / 63  .2540, or 25.40%
2023:
Index return  1  .1132 1  .3590 1  .2540   – 1  .2379, or 23.79%
1/1/24:
Index value = 91.23(1.2379) = 112.94
1/3
22. For price-weighted indices, purchase an equal number of shares for each firm in the index. For valueweighted indices, purchase shares (perhaps in fractional amounts) so that the investment in each
stock, relative to your total portfolio value, is equal to that stock’s proportional market value relative
to all firms in the index. In other words, if one company is twice as big as the other, put twice as
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much money in that company. Finally, for equally-weighted indices, purchase equal dollar amounts
of each stock in the index.
Assuming no cash dividends or stock splits, both the price-weighted and value-weighted
replication strategies require no additional rebalancing. However, an equally weighted index will not
stay equally weighted through time, so it will have to be rebalanced by selling off investments that
have gone up in value and buying investments that have gone down in value.
A typical small investor would most likely use something like the equally-weighted index
replication strategy, i.e., buying more-or-less equal dollar amounts of a basket of stocks, but the
portfolio probably would not stay equally weighted. The value-weighted and equally-weighted index
replication strategies are more difficult to implement than the price-weighted strategy because they
would likely involve the purchase of odd lots and fractional shares, raising transactions costs. The
value-weighted strategy is the most difficult because of the extra computation needed to determine
the initial amounts to invest.
23.
CFA Exam Review by Kaplan Schweser
1. a
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Market orders can be executed at any price, while the limit order may never get executed if the
limit price is never hit.
2. c
$25.44 – $25.40 = $0.04
3. b
The buy order increased demand for the stock, which pushed up the share price. Thus, their action
to buy actually increased their effective spread.
Chapter 6
Common Stock Valuation
Concept Questions
1.
The basic principle is that we can value a share of stock by computing the present value of all future
dividends, which is the relevant cash flow for equity holders.
2.
PE ratios measure the price of a share of stock relative to current earnings. All else the same, future
earnings will be larger for a growth stock than a value stock, so investors will pay more relative to
today’s earnings.
3.
As you know, firms can have negative earnings. But, for a firm to survive over a long period,
earnings must eventually become positive. The residual income model will give a negative stock
value when earnings are negative, thus it cannot be used reliably in this situation.
4.
FCF represents the total firm cash flow, which can be used to pay both debt and equity holders. So,
we need to value FCF using an asset beta rather than an equity beta. The asset beta controls for the
amount of leverage used by the firm.
5.
The value of any investment depends on its cash flows; i.e., what investors will actually receive. The
cash flows from a share of stock are the dividends.
6.
Investors believe the company will eventually start paying dividends (or be sold to another
company).
7.
The sustainable growth rate is positively related to ROE. If tax rates fall, margins (and ROE) rise.
Thus, the growth rate would increase, presumably because there is more profit to be reinvested (or
even paid out as a dividend). In either case, this would result in a higher PV of CF and, therefore, a
higher stock price.
8.
The general method for valuing a share of stock is to find the present value of all expected future
dividends. The constant perpetual growth model presented in the text is only valid (i) if dividends are
expected to occur forever, that is, the stock provides dividends in perpetuity, and (ii) if a constant
growth rate of dividends occurs forever. A violation of the first assumption might be a company that
is expected to cease operations and dissolve itself some finite number of years from now. A violation
of the second assumption might be a start-up firm that isn’t currently paying any dividends, but is
expected to eventually start making dividend payments some number of years from now. This stock
would also be valued by the general dividend valuation method we used in this chapter.
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9.
The two components are the dividend yield and the capital gains yield. For most companies, the
capital gains yield is larger. This is easy to see for companies that pay no dividends. For companies
that do pay dividends, the dividend yields are rarely over five percent and are often much less.
10. With no dividends, we cannot use the dividend discount model. With negative earnings, we cannot
use the residual income model. So, we could attempt to use price ratio analysis, enterprise value, or
free cash flow valuation.
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Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this
solutions manual, rounding may appear to have occurred. However, the final answer for each problem is
found without rounding during any step in the problem.
Core Questions
1.
P0  $2.40 / 1.10   $2.40 / 1.10   $2.40 / 1.10   $2.40 / 1.10   $40 / 1.10   $34.93
2.
P0  $2.40 / 1.10   $2.40 / 1.10   $2.40 / 1.10   $2.40 / 1.10   $LD / 1.10   $60.00
1
2
1
3
2
$52.39  LD / 1  .10 
3
4
4
4
4
4
LD = $76.71
3.
1.4  BAsset  1  .3 1 – .21 
BAsset  1.13
4.
k = 4% + 7% (1.13) = 11.92%
5.
FCF = $40(1 – .21) + $4 – $5 – $3 = $27.6 million
6.
Firm Value0  $27.6 1.03  / .1192 – .03  $318.61
To get equity value, we would need to subtract the value of the firm’s debt.
7.
EV Ratio  $750 / $165  4.55
8.
P0  $28  $1.62 1  g   / .10 – g  ; g  .0398, or 3.98%
9.
P0  $38  D1 / .09 – .038  ; D1  $1.98
D3  $1.98 1.038   $2.13
2
10. Retention ratio  1 –  $1.25 / $2.80   .5536
Sustainable growth rate = .14(.5536) = .0775, or 7.75%
11. Sustainable growth = .08 = .14r ; retention ratio = .5714
Payout ratio  1 – .5714  .4286  D/EPS  $1.65 / EPS; EPS  $1.65 / .4286  $3.85
PE = 19, EPS = $3.85, so P0  $3.85 19   $73.15
12. E(R) = .032 + 1.30(.075) = .1295, or 12.95%
E(R) = .032 + .75(.075) = .0883, or 8.83%
13. P0  $4.70  $2.56 –  $4.70  .11  / .11 – .03  $30.24
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14. P0  $4.70   $2.56  1.03 –  $4.70  .11  / .11 – .03  $31.20
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Intermediate Questions
15. P0  $1.10 1.20  / .12 – .20   1 – 1.20 /1.12    1.20  / 1.12   $1.10 1.04  / .12 – .04  
6
6


P0  $30.09
16. The growth rates will be 20%, 15%, and 10% in years 1-3, with a 5% rate thereafter.
D1  1.25 1.20   $1.50
D2  1.50 1.15   $1.73
D3  1.73 1.10   $1.90
D4  1.90 1.05   $1.99
P3  $1.99 / (.15 – .05)  $19.92
P0  $1.50 /1.15  $1.73 /1.152  $1.90 /1.153  $19.92 /1.153  $16.96
17. P14  D15 /  k – g   $4 / .15 – .055   $42.11
P0  P14 / 1.15   $42.11/ 1.15   $5.95
14
14
18. EV = $420 + $38 − $12 = $446
EV ratio  $446 / $65  6.86
19. P4  $2.20 1.04  / .10 – .04   $38.13
P0  $15.00 /1.10  $10.00 /1.102  $5.00 /1.103   $2.20  $38.13 /1.104  $53.21
20. P6  D7 /  k – g   $1.68 1.055  / .11 – .055   $44.43
7
P3  $1.68 1.055 /1.13  $1.68 1.055 /1.132  $1.68 1.055 /1.133  $44.43 /1.133  $35.96
4
5
6
P0  $1.68 1.055 /1.18  $1.68 1.055  /1.182  $1.68 1.055 /1.183  $35.96 /1.183  $25.93
2
3
21. PE ratio values are: 21.77, 19.88, 18.98, 16.16, 17.36, 17.10 ; average = 18.54
EPS growth rates: 16.36%, 3.37%, 16.09%, 15.51%, 14.29% ; average = 13.12%
Expected share price using PE = 18.54($8.00)(1.1312) = $167.80
P/CFPS values are: 13.00, 12.18, 11.38, 9.67, 10.30, 10.44 ; average = 11.16
CFPS growth rates = 13.34%; 5.70%, 16.19%, 16.60%, 11.02% ; average = 12.57%
Expected share price using P/CFPS= 11.16($13.10)(1.1257) = $164.61
P/S values are: 1.797, 1.716, 1.712, 1.613, 1.697, 1.738 ; average = 1.712
SPS growth rates: 11.25%, –1.06%, 4.82%, 17.98%, 9.92% ; average = 8.58%
Expected share price = 1.712($78.70)(1.0858) = $146.30
A reasonable price range would seem to be $146 to $168 per share, although both the PE and P/CFPS
are at the high end of the price range.
22. k = .03 + 1.10(.075) = 11.25%
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Dividend growth rates: 8.00%, 8.33%, 6.84%, 8.00%, 3.70% ; average = 6.97%
P2022  $1.40 1.0697  / .1125 – .0697   $35.03
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23. PE ratio: N/A, N/A, N/A, N/A, 2,075.00, 225.00 ; average = 1,150.00
EPS growth rates: 17.50%, 45.45%, 69.44%, 107.27%, 50.00% ; average = 57.93%
Expected share price using PE = 1,150($0.06)(1.5793) = $108.97
P/CFPS: N/A, N/A, N/A, N/A, 2,766.67, 168.75 ; average = 1,467.71
CFPS growth rates: 27.78%, 56.92%, 91.07%, 112.00%, 166.67% ; average = 90.89%
Expected share price using P/CFPS = 1,467.71($0.08)(1.9089) = $224.13
P/S values are: 1.600, 3.296, 6.409, 9.507, 3.487, 0.615 ; average = 4.152
SPS growth rates: 170.00%, 34.07%, 12.15%, 17.24%, –7.77% ; average = 45.14%
Expected share price using P/S = 4.152($21.95)(1.4514) = $132.29
This price range is from $109 to $224! As long as the stellar growth continues, the stock should do
well. But any stumble will likely tank the stock. Be careful out there!
24. PE ratios and P/CFPS are all negative, so these ratios are unusable.
P/S: values are 16.615, 14.018, 12.814; average = 14.482
SPS growth rates = 65.85%, 19.56% ; average = 42.71%
Expected share price using SPS = 14.482($8.13)(1.4271) = $168.02
This price is ridiculous, $168! Notice that sales have been exploding, but the company still can’t
make money. A much lower market price might be fair considering the risks involved. Might be a
buyout candidate, but at what price?
25. Parador’s expected future stock price is $67 × 1.13 = $75.71, and expected future earnings per share
is $3.40 × 1.06 = $3.60. Thus, Parador’s expected future PE ratio is $75.71/ $3.60  21.01 .
26. Parador’s expected future stock price is $67 × 1.13 = $75.71, and expected future sales per share is
$18.75 × 1.08 = $20.25. Thus, Parador’s expected future P/S ratio is $75.71/ $20.25  3.739 .
27. b  1 –  $2.04 / $5.00   .5920; g  9.50%  .5920  5.62%
k = 2.75% + 1.40(7%) = 12.55%
P0  $2.04 1  .0562  / .1255 – .0562   $31.11
28. PE price: 13.10(1.1348)($5.00) = $74.33
P/CF price = 9.42(1.1141)($6.60) = $69.27
P/S price = 2.36(1.0734)($25.65) = $64.98
29. EPS next year = $5.00(1.0562) = $5.28
Book value next year = $17.05(1.0562) = $18.01
P0  $17.05  $5.28 –  $17.05  .1255   /  0.1255 – 0.0562   $62.41
30. Clean dividend = $5.28 – ($18.01 – 17.05) = $4.32
P0  $4.32 / .1255 – .0562   $62.41
31. Based on price ratio analysis, it appears the stock might be overpriced at $82.
32. The values for the end of the year are:
Book value = $12.95(1.1250) = $14.57
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EPS = $3.41(1.11) = $3.79
Note, to find the book value in the first year, we can use the following relationship:
B2 – B1 = B1 1 + g  – B1 = B1 + B1g – B1 = B1g
We will use this relationship to calculate the book value in the following years, so:
$3.79 - ($14.57 - 12.95) ($3.79  1.11) - ($14.57  .1250)

1.082
1.0822
($3.79  1.112 ) - ($14.57  1.125  .1250) ($3.79  1.113 ) - ($14.57  1.1252  .1250)


1.0823
1.0824
$14.57  1.12503 ($3.79  1.113  1.06) - ($14.57  1.12503  .0820)


1.0824
1.082 4  (.0820 - .06)
P0  $148.90
P0 
33.
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34.
CFA Exam Review by Kaplan Schweser
1. b
To estimate FCF, we can construct the following table:
$ (millions)
2019
2020
2021
Net Income
10
15
20
Plus Depr.
5
6
5
Less CapEx
7
8
9
FCFF
8
13
16
2022
25
6
10
21
2023
30
5
12
23
2. a
Since there is not debt, the cost of capital is equal to the cost of equity. Nguyen said she used the
return on equity as an estimate. ROE for 2010 is 10 / 55.6  .18 , or 18%.
3. a
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The terminal value is $223.7 million. Free cash flow in 2023 is $23 million (from Question 1
above). The formula for the terminal value is:
$223 .7 
$23 × (1  g )
.18  g
So, the growth rate = .07, or 7%.
4. a
The risk free rate is 6%, and the market risk premium is 11%. The cost of equity is estimated at
18%. Using the CAPM, 18% = 6% + 11%(Beta). Thus, beta = 1.09.
5. b
Using the discounted cash flow approach on the cash flows we calculated in Question 1:
Value  13 /1.18  16 /1.182  21/1.183   23  223.7  / 1.184  $162.5 million
Chapter 7
Stock Price Behavior and Market Efficiency
Concept Questions
1. The market is not weak-form efficient.
2. Unlike gambling, the stock market is a positive sum game; everybody can win. Also, speculators
provide liquidity to markets and thus help promote efficiency.
3. The efficient markets paradigm only says, within the bounds of increasingly strong assumptions about
the information processing of investors, that assets are fairly priced. An implication of this is that, on
average, the typical market participant cannot earn abnormal profits from a particular trading strategy.
However, that does not mean that a few particular investors cannot outperform the market over a
particular investment horizon. Certain investors who do well for a period of time get a lot of attention
from the financial press, but the scores of investors who do not do well over the same period of time
generally get considerably less attention.
4.
a. If the market is not weak form efficient, then this information could be acted on and a profit
could be earned from following the price trend. Under 2, 3, and 4, this information is fully
impounded in the current price and no abnormal profit opportunity exists.
b. Under 2, if the market is not semistrong form efficient, then this information could be used to
buy the stock ―cheap‖ before the rest of the market discovers the financial statement anomaly.
Since 2 is stronger than 1, both imply a profit opportunity exists; under 3 and 4, this information
is fully impounded in the current price and no profit opportunity exists.
c. Under 3, if the market is not strong form efficient, then this information could be used as a
profitable trading strategy, by noting the buying activity of the insiders as a signal that the stock
is underpriced or that good news is imminent. Since 1 and 2 are weaker than 3, all three imply a
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profit opportunity. Under 4, the information doesn’t signal a profit opportunity for traders;
pertinent information the manager-insiders may have is fully reflected in the current share price.
d. Despite the fact that this information is obviously less open to the public and a clearer signal of
imminent price gains than is the scenario in part c, the conclusions remain the same. If the
market is strong form efficient, a profit opportunity does not exist. A scenario such as this one is
the most obvious evidence against strong form market efficiency; the fact that such insider
trading is also illegal should convince you of this fact.
5. Taken at face value, this fact suggests that markets have become more efficient. The increasing ease
with which information is available over the internet lends strength to this conclusion. On the other
hand, during this particular period, large-cap growth stocks were the top performers. Value-weighted
indexes such as the S&P 500 are naturally concentrated in such stocks, thus making them especially
hard to beat during this period. So, it may be that the dismal record compiled by the pros is just a
matter of bad luck or benchmark error.
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6. It is likely the market has a better estimate of the stock price, assuming it is semistrong form efficient.
However, semistrong form efficiency only states that you cannot easily profit from publicly available
information. If financial statements are not available, the market can still price stocks based upon the
available public information, limited though it may be. Therefore, it may have been difficult to
examine the limited public information and make an extra return.
7. Beating the market during any year is entirely possible. If you are able to consistently beat the market,
it may shed doubt on market efficiency unless you are taking more risk than the market as a whole or
are lucky. Thus, before any conclusion is made, we would want to control for the amount of risk in
your portfolio.
8.
a.
False. Market efficiency implies that prices reflect all available information, but it does not
imply certain knowledge. Many pieces of information that are available and reflected in prices
are fairly uncertain. Efficiency of markets does not eliminate that uncertainty and therefore
does not imply perfect forecasting ability.
b.
True. Market efficiency exists when prices reflect all available information. To be efficient in
the weak form, the market must incorporate all historical data into prices. Under the
semistrong form of the hypothesis, the market incorporates all publicly-available information
in addition to the historical data. In strong form efficient markets, prices reflect all publicly
and privately available information.
c.
False. Market efficiency implies that market participants are rational. Rational people will
immediately act upon new information and will bid prices up or down to reflect that
information.
d.
False. In efficient markets, prices reflect all available information. Thus, prices will fluctuate
whenever new information becomes available.
e.
True. Competition among investors results in the rapid transmission of new market
information. In efficient markets, prices immediately reflect new information as investors bid
the stock price up or down.
9. Yes, historical information is also public information; weak form efficiency is a subset of semistrong
form efficiency.
10. Ignoring trading costs, on average, such investors merely earn what the market offers; the trades all
have zero NPV. If trading costs exist, then these investors lose by the amount of the costs.
11.
a.
Aerotech’s stock price should rise immediately after the announcement of the positive news.
b.
Only scenario ii indicates market efficiency. In that case, the price of the stock rises
immediately to the level that reflects the new information, eliminating all possibility of
abnormal returns. In the other two scenarios, there are periods of time during which an
investor could trade on the information and earn abnormal returns.
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12. False. The stock price would have adjusted before the founder’s death only if investors had perfect
forecasting ability. The 12.5 percent increase in the stock price after the founder’s death indicates that
either the market did not anticipate the death or that the market had anticipated it imperfectly.
However, the market reacted immediately to the new information, implying efficiency. It is
interesting that the stock price rose after the announcement of the founder’s death. This price
behavior indicates that the market felt he was a liability to the firm.
13. The announcement should not deter investors from buying UPC’s stock. If the market is semistrong
form efficient, the stock price will have already reflected the present value of the payments that UPC
must make. The expected return after the announcement should still be equal to the expected return
before the announcement. UPC’s current stockholders bear the burden of the loss, since the stock
price falls on the announcement. After the announcement, the expected return moves back to its
original level.
14. The market is generally considered to be efficient up to the semistrong form. Therefore, no systematic
profit can be made by trading on publicly-available information. Although illegal, the lead engineer
of the device can profit from purchasing the firm’s stock before the news release on the
implementation of the new technology. The price should immediately and fully adjust to the new
information in the article. Thus, no abnormal return can be expected from purchasing after the
publication of the article.
15. Under the semistrong form of market efficiency, the stock price should stay the same. The accounting
system changes are publicly available information. Investors would identify no changes in either the
firm’s current or its future cash flows. Thus, the stock price will not change after the announcement of
increased earnings.
16. Because the number of subscribers has increased dramatically, the time it takes for information in the
newsletter to be reflected in prices has shortened. With shorter adjustment periods, it becomes
impossible to earn abnormal returns with the information provided by Durkin. If Durkin is using only
publicly-available information in its newsletter, its ability to pick stocks is inconsistent with the
efficient markets hypothesis. Under the semistrong form of market efficiency, all publicly-available
information should be reflected in stock prices. The use of private information for trading purposes is
illegal.
17. You should not agree with your broker. The performance ratings of the small manufacturing firms
were published and became public information. Prices should adjust immediately to the information,
thus preventing future abnormal returns.
18. Stock prices should immediately and fully rise to reflect the announcement. Thus, one cannot expect
abnormal returns following the announcement.
19.
a.
No. Earnings information is in the public domain and reflected in the current stock price.
b.
Possibly. If the rumors were publicly disseminated, the prices would have already adjusted for
the possibility of a merger. If the rumor is information that you received from an insider, you
could earn abnormal returns, although trading on that information is illegal.
c.
No. The information is already public, and thus, already reflected in the stock price.
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20. The statement is false because every investor has a different risk preference. Although the expected
return from every well-diversified portfolio is the same after adjusting for risk, investors still need to
choose funds that are consistent with their particular risk level.
21. At the time of the announcement, the price of the stock should immediately decrease to reflect the
negative information.
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22. In an efficient market, the cumulative abnormal return (CAR) for Prospectors would rise substantially
at the announcement of a new discovery. The CAR falls slightly on any day when no discovery is
announced. There is a small positive probability that there will be a discovery on any given day. If
there is no discovery on a particular day, the price should fall slightly because the good event did not
occur. The substantial price increases on the rare days of discovery should balance the small declines
on the other days, leaving CARs that are horizontal over time.
Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this
solutions manual, rounding may appear to have occurred. However, the final answer for each problem is
found without rounding during any step in the problem.
Core Questions
1. To find the cumulative abnormal returns, we chart the abnormal returns for the days preceding and
following the announcement. The abnormal return is calculated by subtracting the market return from
the stock’s return on a particular day, Ri – RM . Calculate the cumulative average abnormal return by
adding each abnormal return to the previous day’s abnormal return.
Days from
Announcement
−5
−4
−3
−2
−1
0
1
2
3
4
5
Daily
Abnormal
Return
−0.1
0.1
−0.1
0.1
−0.2
1.9
0.0
−0.2
0.1
0.2
−0.1
Cumulative
Abnormal
Return
−0.1
0.0
−0.1
0.0
−0.2
1.7
1.7
1.5
1.6
1.8
1.7
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Given that the battle with the current CEO was acrimonious, it must be assumed that investors felt
his performance was poor, so we would expect the stock price to increase. The CAR supports the
efficient markets hypothesis. The CAR increases on the day of the announcement, and then remains
relatively flat following the announcement.
2. The diagram does not support the efficient markets hypothesis. The CAR should remain relatively flat
following the announcements. The diagram reveals that the CAR rose in the first month, only to drift
down to lower levels during later months. Such movement violates the semistrong form of the
efficient markets hypothesis because an investor could earn abnormal profits while the stock price
gradually decreased.
3.
a.
Supports. The CAR remained constant after the event at Time 0. This result is consistent with
market efficiency, because prices adjust immediately to reflect the new information. Drops in
CAR prior to an event can easily occur in an efficient capital market. For example, consider a
sample of forced removals of the CEO. Since any CEO is more likely to be fired following
bad rather than good stock performance, CARs are likely to be negative prior to removal.
Because the firing of the CEO is announced at Time 0, one cannot use this information to
trade profitably before the announcement. Thus, price drops prior to an event are neither
consistent nor inconsistent with the efficient markets hypothesis.
b.
Rejects. Because the CAR increases after the event date, one can profit by buying after the
event. This possibility is inconsistent with the efficient markets hypothesis.
c.
Supports. The CAR does not fluctuate after the announcement at Time 0. While the CAR was
rising before the event, insider information would be needed for profitable trading. Thus, the
graph is consistent with the semistrong form of efficient markets.
d.
Supports. The diagram indicates that the information announced at Time 0 was of no value.
There appears to be a slight drop in the CAR prior to the event day. Similar to part a, such
movement is neither consistent nor inconsistent with the efficient markets hypothesis (EMH).
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Movements at the event date are neither consistent nor inconsistent with the efficient markets
hypothesis.
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4. Once the verdict is reached, the diagram shows that the CAR continues to decline after the court
decision, allowing investors to earn abnormal returns. The CAR should remain constant, on average,
even if an appeal is in progress, because no new information about the company is being revealed.
Thus, the diagram is not consistent with the efficient markets hypothesis (EMH).
Intermediate Questions
5. To find the cumulative abnormal returns, we chart the abnormal returns for each of the three
companies for the days preceding and following the announcement. The abnormal return is calculated
by subtracting the market return from a stock’s return on a day, Ri – RM . Group the returns by the
number of days before or after the announcement for each respective company. Calculate the
cumulative average abnormal return by adding each abnormal return to the previous day’s abnormal
return.
Abnormal
returns
 Ri – R-M 
Days from
Average
Cumulative
announcement
Ross
Westerfield Jordan
Sum
abnormal return average residual
–4
−0.2
−0.2
0.2
−0.2
−0.1
−0.1
–3
0.2
−0.1
0.6
0.7
0.2
0.2
–2
0.2
−0.2
0.4
0.4
0.1
0.3
–1
0.2
0.2
−0.4
0.0
0.0
0.3
0
3.2
0.2
1.9
5.3
1.8
2.1
1
0.2
0.1
0.0
0.3
0.1
2.2
2
−0.1
0.0
0.1
0.0
0.0
2.2
3
−0.2
0.1
−0.2
−0.3
−0.1
2.1
4
−0.1
−0.1
−0.4
−0.6
−0.2
1.9
The market reacts favorably to the announcements. Moreover, the market reacts only on the day of
the announcement. Before and after the event, the cumulative abnormal returns are relatively flat.
This behavior is consistent with market efficiency.
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Spreadsheet Problem
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Chapter 8
Behavioral Finance and the Psychology of Investing
Concept Questions
1.
There are three trends at work at all times: primary, secondary, and tertiary. For a market timer, the
secondary, or short-run trend, might be the most important, but, for most investors, it is the primary,
or long-run trend that matters.
2.
A support area is a price or level below which a stock price or market index is not likely to drop. A
resistance area is a price or level above which a stock price or market index is not likely to rise.
3.
Mental accounting is when investors treat each investment separately as opposed to considering the
overall wealth of their portfolios. This bias may induce investors to sell winners too early and keep
losers too long.
4.
Plan participants often use the 1/n heuristic for their asset allocation. So, if someone allocates evenly
across all choices, the asset class with the most choices will receive the largest allocation.
5.
Men are generally more overconfident than women. This leads to excessive trading, which generally
results in lower returns.
6.
The illusion of knowledge suggests that you believe the information you hold is better than that held
by other investors. Therefore, you become overconfident and believe your investment choices are
better.
7.
At the time the theory was developed, large companies in the U.S. were either involved in the
manufacturing of goods or the transportation of them (primarily railroads). The basic idea behind the
Dow theory is that these activities are fundamentally related, so the two averages must move in the
same direction over time.
8.
The least likely limit to arbitrage is firm-specific risk. For example, in the 3Com/Palm case, the
stocks are perfect substitutes after accounting for the exchange ratio. An investor could invest in a
risk neutral portfolio by purchasing the underpriced asset and selling the overpriced asset. When the
prices of the assets revert to an equilibrium, the positions could be closed.
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9.
A contrarian investor goes against the crowd. For example, when investors are bullish, a contrarian
would argue the market is overbought and short sell. Conversely, when investors are pessimistic, a
contrarian would begin purchasing stocks.
10. Consider support and resistance lines. If it is agreed the resistance line is $90, what would a rational
investor do when the stock price reaches $89 (or some other suitable close price)? The investor
would sell the stock. This means the new resistance line is $89. Now, an investor would sell at $88.
This logic implies the support and resistance lines would collapse on each other.
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11. An up gap, where the low stock price today is higher than the high stock price from the previous day,
is a bullish signal. A down gap, where the high price today is lower than the low price from the
previous day is a bearish signal. Of course, gap traders also believe that the stock must eventually
―cover the gap,‖ that is, trade in the price range the gap missed.
12. As long as it is a fair coin the probability in both cases is 50 percent as coins have no memory.
Although many believe the probability of flipping a tail would be greater given the long run of
heads, this is an example of the gambler’s fallacy.
13. Prospect theory argues that investors are willing to take more risk to avoid the loss of a dollar than
they are to make a dollar profit. Also, if an investor has the choice between a sure gain and a gamble
that could increase or decrease the sure gain, the investor is likely to choose the sure gain. The focus
on gains and losses, combined with the tendency of investors to be risk-averse with regard to gains,
but risk-taking when it comes to losses, is the essence of prospect theory. A fully rational investor
(in an economic sense) is presumed to only care about his or her overall wealth, not the gains and
losses associated with individual pieces of that wealth.
14. Frame dependence is the argument that an investor’s choice is dependent on the way the question is
posed. An investor can frame a decision problem in broad terms (like wealth) or in narrow terms
(like gains and losses). Broad and narrow frames often lead the investor to make different choices.
While it is human nature to use a narrow frame (like gains and losses), doing so can lead to irrational
decisions. Using broad frames, like overall wealth, results in better investment decisions.
15. A noise trader is someone whose trades are not based on information or financially meaningful
analysis. Noise traders could, in principle, act together to worsen a mispricing in the short-run. Noise
trader risk is important because the worsening of a mispricing could force the arbitrageur to liquidate
early and sustain steep losses.
Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this
solutions manual, rounding may appear to have occurred. However, the final answer for each problem is
found without rounding during any step in the problem.
Core Questions
1.
Monday
Tuesday
Wednesday
Thursday
Friday
Adv./Dec.
232
705
230
1,958
73
Cumulative
232
937
1,167
3,125
3,198
Monday = 1,634 – 1,402 = 232
Tuesday = 1,876 – 1,171 = 705
Wednesday = 1,640 – 1,410 = 230
Thursday = 2,495 – 537 = 1,958
Friday = 1,532 – 1,459 = 73
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2.
Arms ratio
Monday
Tuesday
Wednesday
Thursday
Friday
.967
.760
1.343
.730
1.029
Monday = (684,997 ∕ 1,402) (825,503 ∕ 1,634) = 0.967
Tuesday = (440,665 ∕ 1,171) (928,360 ∕ 1,876) = 0.760
Wednesday = (719,592 ∕ 1,410) (623,369 ∕ 1,640) = 1.343
Thursday = (173,003 ∕ 537) (1,101,332 ∕ 2,495) = 0.730
Friday = (498,585 ∕ 1,459) (508,790 ∕ 1,532) = 1.029
3.
March
April
May
June
July
August
September
October
November
December
Penn
Teller
$174.35
183.08
190.88
199.00
207.90
214.08
217.99
214.99
207.34
192.97
$600.17
581.42
553.29
526.50
546.36
550.34
553.23
549.55
569.02
612.64
Penn
Teller
$177.24
189.62
194.33
201.10
215.38
215.28
215.91
214.31
199.63
181.94
$593.47
560.56
539.53
517.43
574.94
552.29
527.46
570.91
589.90
627.23
Penn
Teller
$175.80
185.80
191.25
$596.82
570.46
549.74
4.
March
April
May
June
July
August
September
October
November
December
5.
March
April
May
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June
July
August
September
October
November
December
Penn
Teller
197.87
210.19
212.71
214.47
213.99
203.14
188.12
528.06
565.88
553.42
534.23
563.43
581.41
613.66
6.
MSI
1
2
3
4
5
.5207
.5620
.6116
.5868
.6446
If the MSI is used as a contrarian indicator, since the indicator is headed upward, the market
appears to be headed downward.
7.
Price
$70.12
$70.14
$70.13
$70.09
$70.05
$70.07
$70.03
Up/Down
Price times
Volume
Positive Money
Flow
+
–
–
–
+
–
133,266
98,182
126,162
147,105
189,189
210,090
133,266
Negative Money
Flow
Net Money
Flow
98,182
224,344
371,449
322,455
581,539
Money flow at
the end of the day
–$259,084
In this case, the money flow is a bearish signal.
8.
4/1/2022
4/2/2022
4/3/2022
4/4/2022
4/5/2022
4/8/2022
4/9/2022
Simple
-
2,869.28
2,873.34
2,881.84
2,889.30
2,888.90
Exponential
-
2,867.21
2,871.34
2,876.71
2,887.40
2,892.98
2,883.13
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4/10/2022
4/11/2022
4/12/2022
Simple
Exponential
2,887.39
2,884.91
2,894.65
2,886.52
2,887.72
2,900.85
The reason to calculate the moving average on an index is the same as for an individual stock. It
can give an indication of whether the market as a whole is moving upward or downward
compared to its recent past. If the index closed below the 3-day moving average, it would be a
sell indicator.
9.
There appears to be a support level at about $25. The resistance level may be about $30, although the
stock did break through for a period. So, it may have short-term resistance at $30 and longer-term
resistance at $34. A support level is a level below which the stock or market is unlikely to go. A
resistance level is a level above which the stock or market is likely to rise.
10.
Adv./Dec.
Cumulative
Arms ratio
2,011
1,790
172
1,375
641
2,011
3,801
3,973
5,348
5,989
.545
.836
1.081
.904
.998
Monday
Tuesday
Wednesday
Thursday
Friday
Advance/Decline: Monday = 2,530 – 519 = 2,011
Arms ratio: Monday = (111,203 ∕ 519) ∕ (995,111 ∕ 2,530) = 0.545
11.
Price
$61.85
$61.81
$61.82
$61.85
$61.84
$61.87
$61.88
$61.92
$61.91
$61.93
Up/Down
−
+
+
−
+
+
+
−
+
Price times
Volume
Positive Money
Flow
$61,810
Negative Money
Flow
Net Money
Flow
$61,810
86,548
80,405
49,472
68,057
86,632
37,152
74,292
99,088
$86,548
166,953
111,282
235,010
321,642
358,794
185,574
457,882
Money flow at
the end of the day
$272,308
Since the price was relatively stable and the money flow was positive, this is likely a bullish
signal.
Intermediate Questions
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12. Primary support = $45 – [($45 – 32)(.382)] = $40.03
Secondary support = $45 – [($45 – 32)(.618)] = $36.97
13.
Day
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
3-day
−
−
39.60
40.07
40.71
41.10
41.00
40.98
40.76
40.33
39.96
39.90
40.27
40.65
40.84
5-day
−
−
−
−
40.22
40.49
40.78
41.04
40.91
40.55
40.36
40.25
40.13
40.29
40.55
Date
1
2
3
4
5
6
3-day
−
−
39.73
40.61
41.02
41.02
5-day
−
−
−
−
40.81
40.95
14.
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Date
7
8
9
10
11
12
13
14
15
3-day
40.84
41.05
40.60
39.83
39.99
40.12
40.41
40.94
40.81
5-day
40.82
41.05
40.60
39.83
39.99
40.12
40.41
40.94
40.81
15.
Week
1
2
3
4
Put/Call Ratio
1.1490
1.1234
1.1069
1.0965
The put/call ratio is a measure of investor sentiment about the future direction of the market. Puts
are a bet that the market (or stock) will move down and calls are a bet the market (or stock) will
move upwards. The put/call ratio is the number of down bets divided by the number of up bets. A
ratio greater than one indicates more investors believe the market (or stock) will move down than
the number of investors who believe the market will move up. It is a bearish signal. From these
numbers, it appears more investors believe the market will move down in the future. Of course,
there are caveats. First, the put/call ratio can be used as a contrarian indicator. Second, even
though a large number of calls may indicate that investors believe the stock (or market) will
increase in value, options are a derivative asset. So, there is another investor selling the call for a
premium who also believes he will make money on the transaction.
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16.
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17.
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CFA Exam Review by Kaplan Schweser
1. a
Tom believes that, on the basis of his five-year record, he can continue to outperform a
benchmark. His record could be due to luck and/or he may not be reporting his shortcomings.
2. c
As an overconfident investor, Higgins will tend to underestimate risk and overestimate the impact
of an event, which will likely lead to a negative surprise in the future.
3. a
Because she dislikes losses so much, she is willing to take more risk to make up the losses in her
portfolio.
4. c
Jack believes that because a firm’s environmental policy is good, the firm’s stock will be a good
investment. He ignores valuation.
5. c
These investors will use their experiences, inferences, and heuristics to form decisions, while
ignoring fundamental characteristics.
Chapter 9
Interest Rates
Concept Questions
1.
Short-term rates have ranged between zero and 14 percent. Long-term rates have fluctuated between
about two and 13 percent. Long-term rates, which are less volatile, have historically been in the four65
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to-five percent range (the 1960 – 1980 experience is the exception). Short-term rates have about the
same typical values, but more volatility (and lower rates in the unusual 1930 – 1960 period).
2.
A pure discount security is a financial instrument that promises a single fixed payment (the face
value) in the future with no other payments in between. Such a security sells at a discount relative to
its face value, hence the name. Treasury bills and commercial paper are two examples.
3.
The Fed funds rate is set in a very active market by banks borrowing and lending from each other.
The discount rate is set by the Fed at whatever level the Fed feels is appropriate. The Fed funds rate
changes all the time; the discount rate only changes when the Fed decides; the Fed funds rate is
therefore much more volatile. The Fed funds market is much more active. Banks usually borrow
from the Fed only as a last resort, which is the primary reason for the Fed’s discount rate-based
lending.
4.
Both are pure discount money market instruments. T-bills, of course, are issued by the government;
while commercial paper is issued by corporations. The primary difference is that commercial paper
has default risk, so it offers a higher interest rate.
5.
SOFR is the Secured Overnight Financing Rate, which is a broad measure of the cost of borrowing
cash overnight collateralized by Treasury securities. It recently replaced LIBOR, which is the
London Interbank Offered Rate. It is the interest rate offered by major London banks for dollardenominated deposits. Interest rates on loans are often quoted on a LIBOR-plus (or now SOFR-plus)
basis, so these rates are important, fundamental rates in business lending, among other things.
6.
Such rates are much easier to compute by hand; they predate (by hundreds of years or more)
computing machinery.
7.
Each STRIPS represents a particular piece of a Treasury note or bond. The three types of Treasury
STRIPS that are traded are coupon payments on a note or bond, the final principal payment on a
Treasury note, and the final principal payment on a Treasury bond.
8.
We observe nominal rates almost exclusively. Which one is more relevant actually depends on the
investor and, more particularly, what the proceeds from the investment will be used for. If the
proceeds are needed to make payments that are fixed in nominal terms (like a loan repayment,
perhaps), then nominal rates are more important. If the proceeds are needed to purchase real goods
(like groceries) and services, then real rates are more important.
9.
This statement is true if it is referring to the coupon rate. However, since the accrued principal
changes with inflation, the dollar amount of the coupon (even though it is a fixed percentage) will
change. So, it is false with regard to the dollar amount of the coupon.
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10. CFATM Institute suggested answer:
a. The pure expectations theory states the term structure of interest rates is explained entirely by
interest rate expectations. The theory assumes that forward rates of interest embodied in the term
structure are unbiased estimates of expected future spot rates of interest. Thus, the pure
expectations theory would account for a declining yield curve by arguing that interest rates are
expected to fall in the future rather than rise. Investors are indifferent to holding (1) a short-term
bond at a higher rate to be rolled over at a lower expected future short-term rate, and (2) a longerterm bond at a rate between the higher short-term rate and the lower expected future short-term
rate.
b. Liquidity preference theory (maturity preference) states that the term structure is a combination of
future interest rate expectations and an uncertainty ―risk‖ or uncertainty yield ―premium.‖ The
longer the maturity of a bond, the greater the perceived risk (in terms of fluctuations of value) to
the investor, who accordingly prefers to lend short term and thus requires a premium to lend
longer term. This yield ―premium‖ is added to the longer-term interest rates to compensate
investors for their additional risk. Theoretically, liquidity preference could account for a
downward slope if future expected rates were lower than current rates by an amount greater than
their respective term risk premium. Liquidity preference theory is consistent with any shape of
the term structure but suggests and upward bias or ―tilt‖ to any term structure shape given by
unbiased expectations.
c. Market segmentation theory states that the term structure results from different market
participants establishing different yield equilibriums between buyers and sellers of funds at
different maturity preferences. Market segmentation theory can account for any term structure
shape because of the different supply/demand conditions posted at maturity ranges. Borrowers
and lenders have preferred maturity ranges, based largely on institutional characteristics, and the
yield curve is the average of these different suppliers’ and demanders’ maturity preferences.
These maturity preferences are essentially fixed; that is, the participants do not tend to move
between or among maturity ranges, so different supply and demand conditions exist across the
maturity spectrum. In each maturity range, a higher demand for funds (supply of bonds) relative
to the supply of funds will drive bond prices down, and rates up, in that maturity range. A
downward sloping yield curve, in the context of market segmentation, indicates that a larger
supply of short-term debt relative to demand has led to lower short-term bond prices and/or a
small supply of long-term debt relative to demand has led to higher long-term bond prices. Either
set of supply/demand conditions works to drive long-term rates lower and short-term rates higher.
Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this
solutions manual, rounding may appear to have occurred. However, the final answer for each problem is
found without rounding during any step in the problem.
Core Question
1.
Price  $100 / 1  .035 / 2 
2.
Price  $100, 000 / 1  .044 / 2   $73, 737.34
Quoted price  $73, 737.34 / $1, 000  73.737
2(10)
 $70.68
2(7)
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3.
YTM  2  100 / 90.875 

1/ ( 2  5 )
– 1  .0192, or 1.92%

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4.
YTM  2  100 ƒ 70.485 

5.
8.9% – 2.1% ≈ 6.8%
6.
11.6% – 7.6% ≈ 4.0%
7.
P  $1, 000, 000[1– .0115  56 / 360 ]  $998, 211.11
8.
y  365 .0115  / 360 –  56 .0115   .01168, or 1.168%
9.
P  $1, 000, 000[1– .0218 112 / 360 ]  $993, 217.78
10.
y  365 .0218  / 360 – 112 .0218    .02225, or 2.225%
1/ ( 2  4 )
– 1  .0894, or 8.94%

Intermediate Questions
11. 99.012  100  1 –  64/360   DY  ; discount yield = .05558
bond equivalent yield  365 .05558   / 360 –  64 .05558    .05691
EAR  1  .05691 /  365 / 64  
365/64
– 1  .05826
12. P  100 [1– .0248  55 / 360 ]  .99621 , or 99.621% of par
y  366 .0248   / 360 –  55 .0248    .02531
Note, 2024 is a leap year so there are 366 days used in the calculation of the bond equivalent yield.
13. 1.0315  1   APR  90 / 365  
365/90
; APR = bond equivalent yield = .03113, or 3.113%
discount yield  360 .03113  / 365   90 .03113   .03047 , or 3.047%
14. The quoted yield of each of the STRIPS is.
Feb 23 STRIP:
97.123  100 / 1   y / 2   ;
y = .02941, or 2.941 %
Feb 24 STRIP:
94.770  100 / 1   y / 2   ;
y = .02704, or 2.704 %
Feb 25 STRIP:
92.424  100 / 1   y / 2   ;
y = .02643, or 2.643 %
Feb 26 STRIP:
90.066  100 / 1   y / 2   ;
y = .02633, or 2.633%
Feb 27 STRIP:
87.528  100 / 1   y / 2   ;
y = .02682, or 2.682%
Feb 28 STRIP:
85.410  100 / 1   y / 2   ;
y = .02646, or 2.646%
2
4
6
8
10
12
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Note that the term structure is somewhat downward sloping; the expectations hypothesis then
implies that this reflects market expectations of falling interest rates in the future.
15. EAR  1  .027040 / 2   – 1  .027223 , or 2.7223%
2
16. 1  .02704 / 2    1  .02941 / 2  
4
2
1  f  ; f  .02483, or 2.483%  EAR
1,1
1,1
P1  100 / 1.02483  .975773, or 97.5773%
The implied 1-year forward rate is smaller than the current 1-year spot rate, reflecting the
expectation that interest rates will go down in the future. Hence, for downward-sloping term
structures, the implied forward rate curve lies below the spot rate curve.
17.
f1,5  100  85.410 / 97.123  87.940  % of par 
87.940  100 ƒ (1  f1,5 )5 ; f1,5  .02604, or 2.604%
f3,2  100  87.528 / 94.424   94.703
94.703  100 / (1  f3,2 )2 ; f3,2  .02759, or 2.759%
18. Feb23 STRIPS:
P *  100 / 1  .02941  .0005  / 2   .970752, or 97.0752% of par
2
%P   97.0752 – 97.123 / 97.123  – .00049, or – .049%
Feb25 STRIPS:
P *  100 / 1  .02643  .0005  / 2   .922873, or 92.2873% of par
6
%P   92.2873 – 92.424  / 92.424  – .00148, or – .148%
Feb26 STRIPS:
P *  100/ 1  .02646  .0005  / 2   .851575, or 85.1575% of par
12
%P  85.1575 – 85.41 / 85.41  – .00296, or – .296%
For equal changes in yield, the longer the maturity, the greater the percentage price change. Hence,
for parallel yield curve shifts, the price volatility is greater for longer-term instruments.
Feb23 STRIPS:
97.123 – .50  100 / 1   y * / 2   ;
2
y *  .03465, or 3.465%
%y   3.465% – 2.941%  /2.941%   17.83%
Feb25 STRIPS:
92.424 – .50  100 / 1   y * /2   ’; y *  .02827, or 2.827%
6
%y   2.827% – 2.643%  / 2.643%   6.93%
Feb28 STRIPS:
85.41 – .50  100 / 1   y * /2   ;
12
y *  .02745, or 2.745%
y   2.745% – 2.646%  / 2.646%   3.75%
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For equal changes in price, the absolute yield volatility is greater the shorter the maturity; the effect
is magnified for percentage yield volatility when the yield curve is upward sloping, because yields
(the divisor) are smaller for short maturities. Because of this, note that for sharply downward sloping
yield curves, it’s possible for shorter maturity instruments to have less percentage yield volatility,
but greater absolute yield volatility, than slightly longer maturity instruments.
19. First 6 months
Accrued principal = $1,000(1.02) = $1,020.00
Payment  $1, 020 .01/ 2   $5.10
Second 6 months
Accrued principal = $1,020(1.03) = $1,050.60
Payment  $1, 050.60 .01/ 2   $5.25
Third 6 months
Accrued principal = $1,050.60(1.01) = $1,061.11
Payment  $1, 061.11.01/ 2   $5.31
Fourth 6 months
Accrued principal = $1,061.11(1.02) = $1,082.33
Payment  $1, 082.33 .01/ 2   $5.41
20. Approximate real rate = 1.64% – .70% ≈ 0.94%
Real interest rates are not observable because they do not correspond to any traded asset (at least not
until very recently in the U.S.); hence, they must be inferred from nominal interest rates (which do
correspond to traded assets), and from estimated inflation data. Real interest rate estimates are
therefore only as good as (1) the inflation estimates used in the Fisher relation and (2) the degree to
which the Fisher relation itself actually describes the behavior of economic agents.
21.
f1,1  1.0492 /1.043 – 1  .0550, or 5.50%
1/1
f1,2  1.0563 /1.043
– 1  .0626, or 6.26%
f1,3  1.0644 /1.043
– 1  .0711, or 7.11%
1/2
1/3
22.
f 2,1  1.0563 /1.0492 – 1  .0701, or 7.01%
f3,1  1.0644 /1.0563 – 1  .0884, or 8.84%
23. I1  r1 – 2%  4.30% – 2%  .0230, or 2.30%
I 2  f1,1 – 2%  5.50% – 2%  .0350, or 3.50%
I3  f2,1 – 2%  7.01% – 2%  .0501, or 5.01%
I 4  f3,1 – 2%  8.84% – 2%  .0684, or 6.84%
Spreadsheet Problems
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CFA Exam Review by Kaplan Schweser
1. a
Under the expectations theory, forward rates exclusively represent expected future spot rates.
Thus, the entire term structure at a given time reflects expectations of future short-term spot rates.
2. b
Greater demand for short-term securities could explain an upward sloping curve according to the
market segmentations theory, as it suggests that the rate of interest for a particular maturity is
determined solely by demand and supply for that maturity.
3. c
The two-year spot rate is 5.75%, and the one-year is 5.25%. So, the following must hold:
1.0575  1.0525 1  i 
2
So, i = 6.25%
4. a
For a steepening to occur, in every case, the short-term yield decreases relative to the long-term
yield. Therefore, the price of short-term Treasury securities increases relative to long-term
securities.
Chapter 10
Bond Prices and Yields
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Concept Questions
1.
Premium (par, discount) bonds are bonds that sell for more than (the same as, less than) their face or
par value.
2.
The face value is normally $1,000 per bond. The coupon is expressed as a percentage of face value
(the coupon rate), so the annual dollar coupon is calculated by multiplying the coupon rate by
$1,000. Coupons are normally paid semi-annually; the semi-annual coupon is equal to the annual
coupon divided by two.
3.
The coupon rate is the annual dollar coupon expressed as a percentage of face value. The current
yield is the annual dollar coupon divided by the current price. If a bond’s price rises, the coupon rate
won’t change, but the current yield will fall.
4.
Interest rate risk refers to the fact that bond prices fluctuate as interest rates change. Lower coupon
and longer maturity bonds have greater interest rate risk.
5.
For a premium bond, the coupon rate is higher than the yield. The reason is that the bond sells at a
premium because it offers a coupon rate that is high relative to current market required yields. The
reverse is true for a discount bond: it sells at a discount because its coupon rate is too low.
6.
A bond’s promised yield is an indicator of what an investor can expect to earn if (1) all of the bond’s
promised payments are made and (2) market conditions do not change. This second condition
implies that coupon payments are reinvested at the promised yield (i.e., YTM) and the bond is sold
or redeemed at its expected value. The realized yield is the actual, after-the-fact return the investor
receives. The realized yield is more relevant, of course, but it is not knowable ahead of time. A
bond’s calculated yield to maturity is the promised yield.
7.
The yield to maturity is the required rate of return on a bond expressed as a nominal annual interest
rate. For noncallable bonds, the yield to maturity and required rate of return are interchangeable
terms. Unlike YTM and required return, the coupon rate is not used as the interest rate in bond cash
flow valuation, but is a fixed percentage of par over the life of the bond used to set the coupon
payment amount. For the example given, the coupon rate on the bond is still 10 percent, and the
YTM is 8 percent.
8.
Since the yield increased, the price of the bond will decrease. This can be explained in two ways.
First, any new bonds will have a 15 percent coupon rate in order to sell at par since that is the market
interest rate. Investors will pay less for a 9 percent coupon bond since they can buy a bond with a 15
percent coupon rate. Second, the decrease in price is a function of the time value of money. The
price of the bond is the present value of the coupon payments plus the present value of the principal.
In any present value calculation, the present value declines when the interest rate increases.
9.
a.
Bond price is the present value term when valuing the cash flows from a bond; YTM is
the interest rate used in valuing the cash flows from a bond. They have an inverse
relationship.
b.
If the coupon rate is higher than the required return on a bond, the bond will sell at a
premium, since it provides periodic income in the form of coupon payments in excess of
that required by investors on other similar bonds. If the coupon rate is lower than the
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required return on a bond, the bond will sell at a discount, since it provides insufficient
coupon payments compared to that required by investors on other similar bonds. For
premium bonds, the coupon rate exceeds the YTM; and for discount bonds, the YTM
exceeds the coupon rate. For bonds selling at par, the YTM is equal to the coupon rate.
c.
Current yield is defined as the annual coupon payment divided by the current bond price.
For premium bonds, the current yield exceeds the YTM; for discount bonds the current
yield is less than the YTM; and for bonds selling at par value, the current yield is equal to
the YTM. In all cases, the current yield plus the expected one-period capital gains yield of
the bond must be equal to the required return.
10. A premium bond is one with a relatively high coupon, and, in particular, a coupon that is higher than
current market yields. These are precisely the bonds that the issuer would like to call, so a yield to
call is probably a better indicator of what is likely to happen than the yield to maturity (the opposite
is true for discount bonds). It is also the case that the yield to call is likely to be lower than the yield
to maturity for a premium bond, but this can depend on the call price. A better convention would be
to report the yield to maturity or yield to call, whichever is smaller.
Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this
solutions manual, rounding may appear to have occurred. However, the final answer for each problem is
found without rounding during any step in the problem.
Also note that we have written out solutions using formulas; however, students should consult Section
10.3 in the book for a detailed example on how to compute price and yield using a financial calculator.
This can easily be done for each problem as we have identified the relevant input variables in each
formula.
Core Questions
Note that all questions can be solved more easily using a financial calculator. To do so, the coupon =
PMT, the par value = FV, the number of payments (or periods) = n, the semiannual yield  I/Y , and the
price = PV.
1.
P = $35(PVIFA4.55%,24 ) + $1,000(PVIF4.55%,24 ) = $848.55
2.
P = $1,086 = $20(PVIFAR%,28 ) + $1,000(PVIFR%,28 ); R = 1.616%, YTM = 3.23%
current yield = $40.00/$1,086 = .0368, or 3.68%
3.
P = $41(PVIFA3.7%,18 ) + $1,000  PVIF3.7%,18  = $1,051.89
4.
P = $36(PVIFA3.0%,50 ) + $1,000(PVIF3.0%,50 ) = $1,154.38
5.
P = $902.30 = $30(PVIFA R%,24 ) + $1,000  PVIFR%,24  ; R = 3.616%, YTM = 7.23%
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6.
P = $1,047 = $41 PVIFA R%,24  + $1,000(PVIFR%,24 ) ; R = 3.798%, YTM = 7.60%
7.
P = $928 = $37.50(PVIFAR%,18 ) + $1,000(PVIFR%,18 ) ; R = 4.334%; YTM = 8.67%
8.
YTM   $1, 000 / $417 

9.
1/20
YTC   $500 / $417  – 1  2  .0182, or 1.82%


1/40
– 1  2  .0442, or 4.42%

1/20
10. YTC   $550 / $417  – 1  2  .0279, or 2.79%


Intermediate Questions

11. P  $938  $C PVIFA 3.75%,20
  $1, 000(PVIFA
3.75%,20
); C  $33.04
coupon rate = 2(.03304) = .0661, or 6.61%
12. P  $31(PVIFA3.7%,18 )  $1, 000(PVIF3.7%,18 )  $922.16
13. P  $1,080  $37.50(PVIFAR%,46 )  $1,000( PVIFR %,46 ); R  3.403%; YTM  6.81%
14. Assuming a $1,000 par value, the original price of the bond was $1, 000 /1.0340  $306.56 . Two
years later, the bond has 18 years to maturity and the same price, so the new yield to maturity must
be  $1, 000 / $306.56 
1/36

– 1  2  .0668 , or 6.68%. Thus, rates have risen, which has kept

the bond price from rising.
15. If held to maturity, a zero-coupon bond will always have a realized yield equal to its original yield to
maturity, which in this case is 6 percent.
16. P : P0  $40(PVIFA3%,30 )  $1, 000(PVIF3%,30 )  $1,196.00
P1  $40(PVIFA3%,28 )  $1,000(PVIF3%,28 )  $1,187.64
P5  $40(PVIFA3%,20 )  $1,000(PVIF3%,20 )  $1,148.77
P10  $40(PVIFA3%,10 )  $1,000(PVIF3%,10 )  $1,085.30
P14  $40(PVIFA3%,2 )  $1,000(PVIF3%,2 )  $1,019.13
P15  $1, 000
D : P0  $40(PVIFA5%,30 )  $1,000(PVIF5%,30 )  $846.28
P1  $40(PVIFA5%,28 )  $1,000(PVIF5%,28 )  $851.02
P5  $40(PVIFA5%,20 )  $1, 000  PVIF5%,20   $875.38
P10  $40(PVIFA5%,10 )  $1,000(PVIF5%,10 )  $922.78
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P14  $40(PVIFA5%,2 )  $1,000(PVIF5%,2 )  $981.41
P15  $1, 000
All else held equal, the premium over par value for a premium bond declines as maturity is
approached, and the discount from par value for a discount bond declines as maturity is
approached. This is sometimes called the ―pull to par.‖
17. If both bonds sell at par, the initial YTM on both bonds is the coupon rate, 6 percent. If the YTM
suddenly rises to 8 percent, then:
PA  $30(PVIFA4%,10 )  $1,000(PVIF4%,10 )  $918.89
PB  $30(PVIFA4%,30 )  $1,000(PVIF4%,30 )  $827.08
PA %   $918.89 – $1, 000  / $1, 000  – .0811, or – 8.11%
PB %   $827.08 – $1, 000  / $1, 000  – .1729, or –17.29%
If the YTM suddenly falls to 4 percent, then:
PA  $30(PVIFA 2%,10 )  $1, 000  PVIF2%,10   $1, 089.83
PB  $30(PVIFA2%,30 )  $1,000(PVIF2%,30 )  $1, 223.96
PA %   $1, 089.83 – $1, 000  / $1, 000   .0898, or 8.98%
PB %   $1, 223.96 – $1, 000  / $1, 000   .2240, or 22.40%
All else the same, the longer the maturity of a bond, the greater is its price sensitivity to changes in
interest rates.
18. Initially, at a YTM of 7 percent, the prices of the two bonds are:
PJ  $20(PVIFA3.5%,20 )  $1, 000(PVIF3.5%,20 )  $786.81
PK  $40(PVIFA3.5%,20 )  $1,000(PVIF3.5%,20 )  $1,071.06
If the YTM rises from 7 percent to 9 percent:
PJ  $20(PVIFA4.5%,20 )  $1, 000(PVIF4.5%,20 )  $674.80
PK  $40(PVIFA4.5%,20 )  $1, 000(PVIF4.5%,20 )  $934.96
PJ   $674.80 – $786.81 / $786.81  – .1424, or –14.24%
PK   $934.96 – $1, 071.06  / $1, 071.06  – .1271, or –12.71%
If the YTM declines from 7 percent to 5 percent:
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PJ  $20(PVIFA2.5%,20 )  $1, 000(PVIF2.5%,20 )  $922.05
PK  $40(PVIFA 2.5%,20 )  $1, 000  PVIF2.5%,20   $1, 233.84
PJ   $922.05 – $786.81 / $786.81   .1719, or 17.19%
PK   $1, 233.84 – $1, 071.06  / $1, 071.06   .1520, or 15.20%
All else the same, the lower the coupon rate on a bond, the greater is its price sensitivity to changes
in interest rates.
19. Current yield  .0740  $80 / P0 ; P0  $80 / .0740  $1,081.08
P0  $1, 081.08  $40[ (1 – 1/1.034 
Nx2
) / .034 ]  $1, 000 /1.034 Nx2
N = 9.20 years
20. The maturity is indeterminate; a bond selling at par can have any maturity length.
21.
a.
P0  $1,080  $30(PVIFAR%,20 )  $1,000(PVIFR%,20 );R  2.487%, YTM  4.97%
This is the rate of return you expect to earn on your investment when you purchase the bond.
b.
Price when sold  $30(PVIFA3.487%,16 )  $1,000(PVIF3.487%,16 )  $940.99
Future value of reinvested interest payments  $30  FVIFA 2.487%,4   $124.55
Realized return   $940.99 – $1, 080  $124.55 / $1, 080  – .0134, or –1.34%
This is a total return over the two year period. If we want an annual number we would calculate
the interest rate that equates the cost ($1,080) with the total value accrued ($940.99 + $124.55)
over the two year period. In this case, I = −0.67%
The realized yield is less than the expected yield when the bond was purchased because interest
rates have increased by 2 percent; bond prices fall when yields rise. Further, this realized yield is
for the full period, while the YTM is a yearly estimate.
22. The yield to call can be computed as:
P  $1,080  $50(PVIFAR%,20 )  $1,100(PVIFR%,20 ); R  4.688%, YTC  9.38%
Since the bond sells at a premium to par value, you know the coupon rate must be greater than
the yield. Thus, if interest rates remain at current levels, the bond issuer will likely call the bonds
to refinance (at a lower coupon rate) at the earliest possible time, which is the date when call
protection ends. The yield computed to this date is the YTC, and it will always be less than the
YTM for premium bonds with a zero call premium. In the present example:
P = $1,080 = $50(PVIFAR%,50 ) + $1,000(PVIFR%,50 ); R = 4.589%, YTM = 9.18%
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where if the bond is held until maturity, no call premium must be paid. Note that using the same
analysis, a break-even call premium can also be computed:
P = $1,080 = $50  PVIFA 4.59%,20  +  $1,000 + X  (PVIF4.59%,20 ); X = $66.20
Thus, if interest rates remain unchanged, the bond will not be called if the call premium is
greater than $66.20.
23. P = $1,025.30 = $35(PVIFAR%,10 ) + $1,000(PVIFR%,10 ) ; R = 3.20%, YTM = 6.40%



Duration = 1.0320/.0640  – [ 1.0320 + 5 .07 – .0640  / .0640 + .07 1.032010 – 1 

Duration = 4.314 years
Modified duration = 4.314/ 1.0320  = 4.180 years
24. Estimated percent change in price = –4.180 .02  = –.08361 = (P1 /P0 ) – 1
so P1 = 1 – .08361 $1,025.30  = $939.58




Actual P1 = $35 PVIFA 4.2%,10 + $1,000 PVIF4.2%,12 = $943.78
25. Dollar value of an 01 = 4.18 × $102.53 × .0001 = .0429
For a $1,000 face value, this implies a change in selling price of $0.4286.
26. P = $1,065 = $37.50(PVIFAR%,16 ) + $1,000(PVIFR%,16 ); R = 3.224%, YTM = 6.447%


Duration = 1.03224/.06447  – 1.03224 + 8  .075 – .06447   / .06447 + .075 1.0322416 – 1 


Duration = 6.223 years
Modified duration = 6.223/ 1.03224  = 6.029 years
Dollar value of an 01 = 6.029 × $106.5 × .0001 = .0642
For a $1,000 face value, this implies a change in selling price of $0.642
Yield value of a 32nd = 1/  32 × .0642  = .487 basis points


 


 
27. Duration = 1.045/.09  – 1.045 + 10 .08 – .09   / .09 + .08 1.04520 – 1  = 6.954 years

Modified duration = 6.954/ 1.045  = 6.655 years
28. Duration = 1.035/.07  – 1.035 + 10  .08 – .07   / .07 + .08 1.03520 – 1  = 7.178 years

Modified duration = 7.178/ 1.035  = 6.935 years
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For an option free bond, at a lower YTM, the duration is higher.

 

29. Duration = 1.035/.07  – 1.035 + 19 .08 – .07   / .07 + .08 1.03538 – 1  = 10.498 years

Modified duration = 10.498/ 1.035  = 10.143 years
30. Initial price = $40(PVIFA3.5%,38 ) + $1,000(PVIF3.5%,38 ) = $1,104.21
If interest rates rise .25%:
Estimated percent change in price = –10.143 .0025 = –.02536 = (P1 /P0 ) – 1
so P1 = 1 – .02536  $1,104.21 = $1,076.21
Actual P1 = $40(PVIFA3.625%,38 ) + $1,000(PVIF3.625%,38 ) = $1,076.71
If interest rates rise 1%:
Estimated percent change in price = –10.143 .01 = –.1014 = (P1 /P0 ) – 1
so P1 = 1 – .1014  $1,104.21 = $992.21
Actual P1 = $40(PVIFA4.0%,38 ) + $1,000(PVIF4.0%,38 ) = $1,000.00
If interest rates rise 2%:
Estimated percent change in price = –10.143 .02  = –.2029 = (P1 /P0 ) – 1
so P1 = 1 – .2029  $1,104.21 = $880.21
Actual P1 = $40(PVIFA4.5%,38 ) + $1,000(PVIF4.5%,38 ) = $909.75
If interest rates rise 5%:
Estimated percent change in price = –10.143 .05 = –.5071 = (P1 /P0 ) – 1
so P1 = 1 – .5071 $1,104.21 = $544.22
Actual P1 = $40(PVIFA6.0%,38 ) + $1,000(PVIF6.0%,38 ) = $703.08
While duration gives an effective estimate for small interest rate changes, duration does not produce
a good estimate of the price change for large interest rate changes.
31. Zero coupon YTM = $949 = $1,000/ 1 + r  ; r = 5.37%
Two year spot rate: $1,020 = $75/ 1 + .0537  + $1,075/ 1 + r2  ; r2 = 6.44%
2
Three
year
spot
rate:
$1,029 = $85/ 1 + .0537  + $85/ 1 + .0644  + $1,085/ 1 + r2  ; r3 = 7.50%
2
3
32. P = $65/ 1 + .0420  + $65/ 1 + .0450  + $65/ 1 + .0490  + $1,065/ 1 + .0510  = $1,051.06
2
3
4
P = $1,051.06 = $65(PVIFAR%,4 ) + $1,000(PVIFR%,4 ); YTM = 5.06%
Spreadsheet Problems
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CFA Exam Review by Kaplan Schweser
1. c
Shortening portfolio duration makes the value of the portfolio less sensitive to interest rate
changes. So, if interest rates increase, the value of the portfolio will decrease less.
2. b
The estimated percentage price change = −3.5851 × 1% = −3.5851%
At a starting price of $100, this is a drop of −$3.59
3. a
The estimated percentage price change = −6.9848 × 1% = −6.9848%
At a starting price of $107.18, this is a drop of −$7.49
4. a
Since long-term interest rates are expected to increase more than short-term rates, bond prices are
expected to decrease more than note prices. By short-selling bonds and buying notes, the portfolio
manager can profit from the difference in the relative price changes.
Chapter 11
Diversification and Risky Asset Allocation
Concept Questions
1.
Based on market history, the average annual standard deviation of return for a single, randomly
chosen stock is about 50 percent. The average annual standard deviation for an equally-weighted
portfolio of many stocks (at least 30-50 randomly selected stocks) is about 20 percent.
2.
If the returns on two stocks are highly correlated, they have a strong tendency to move up and down
together. If they have no correlation, there is no particular connection between the two. If they are
negatively correlated, they tend to move in opposite directions.
3.
An efficient portfolio is one that has the highest return for its level of risk. Said differently, it is the
portfolio with the lowest risk for a given level of return.
4.
True. Remember, portfolio return is a weighted average of individual returns.
5.
False. Remember the principle of diversification—correlation matters. This statement is true,
however, if the correlation between the two stocks is exactly +1.
6.
The common answer might be that over time volatility cancels out; however, this is incorrect and is
an example of the time diversification fallacy. The more appropriate response is that younger
investors have a greater ability to modify their work flow, time, etc. to offset the loss. Older
investors are less able to withstand a large one-time loss.
7.
An investment with high volatility could actually reduce the risk of the overall portfolio if its
correlation to the existing assets is very low.
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8.
The importance of the minimum variance portfolio is that it determines the lower bound of the
efficient frontier. While there are portfolios on the investment opportunity set to the right and below
the minimum variance portfolio, they are inefficient. That is, there is a portfolio with the same level
of risk and a higher return. No rational investor would ever invest in a portfolio below the minimum
variance portfolio.
9.
False. Individual assets can lie on the efficient frontier depending on its expected return, standard
deviation, and correlation with all other assets.
10. If two assets have zero correlation and the same standard deviation, then evaluating the general
expression for the minimum variance portfolio shows that x = ½; in other words, an equallyweighted portfolio is minimum variance.
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Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this
solutions manual, rounding may appear to have occurred. However, the final answer for each problem is
found without rounding during any step in the problem.
Core Questions
1.
.25(–.08) + .5(.13) + .25(.23) = .1025, or 10.25%
2.
.25  –.08 – .1025   .5 .13 – .1025   .25 .23 – .1025   .01277;σ  11.30%
3.
2
2
2
1/ 3 –.08  1/ 3.13  1/ 3.23  .0933, or 9.33%
2
2
2
1/ 3 –.08 – .0933  1/ 3.13 – .0933  1/ 3.23 – .0933  .01669;σ  12.92%
4.
Calculating
Expected
Returns
(1)
State of
Economy
Bust
Boom
5.
(1)
State
of Economy
(2)
Probability of
State of
Economy
.40
.60
Roll
Ross
(3)
(4)
Return
Product
if State (2) × (3)
Occurs
–10%
–.0400
28%
.1680
E(R) =
.1280, or
12.80%
(5)
(6)
Return if Product
State
(2) × (5)
Occurs
21%
.0840
8%
.0480
E(R) =
.1320, or
13.20%
(2)
Probability of
State of
Economy
(3)
Return Deviation
from Expected Return
(4)
Squared
Return
Deviation
Roll
Bust
Boom
.40
.60
–.2280
.1520
.0520
.0231
σ2 
.0208
.0139
.0347
Ross
Bust
Boom
.40
.60
.0780
–.0520
.0061
.0027
.0024
.0016
.0041
σ2 
(5)
Product
(2) × (4)
Taking square roots, the standard deviations are 18.62% and 6.37%.
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6.
Expected
Portfolio
Return
(1)
State of
Economy
(2)
Probability of
State of
Economy
(3)
Portfolio Return if State Occurs
(4)
Product
(2) × (3)
Bust
.40
.55(–10%) + .45(21%) = 3.95%
.0158
Boom
.60
.55(28%) + .45(8%) = 19.00%
.1140
E  RP  =
7.
Calculating
Portfolio
Variance
(1)
State of
Economy
Bust
Boom
8.
(2)
Probability of
State of Economy
.40
(3)
Portfolio Return
if State Occurs
.10
.60
.15
.1298, or
12.98%
(4)
Squared Deviation from
Expected Return
.0008
.0004
(5)
Product
(2) × (4)
.00034
.00023
σ2 P 
.00056
σP 
2.38%
E  RA   .3 .04   .4 .09   .3 .12   .0840, or 8.40%
E  RB   .3  –.20   .4 .13  .3 .33  .0910, or 9.10%
σ A 2  .3 .04 – .0840   .4 .09 – .0840   .3 .12 – .0840   .000984;σ A  .000984
2
2
1/2
2
σ B 2  .3  –.2 – .0910   .4 .13 – .0910   .3 .33 – .0910   .043149;σ B  .043149
2
9.
2
2
1/2
 .2077
a. boom: E  Rp  .25 .18   .50 .48   .25 .33  .3675
good: E  Rp  .25 .11  .50 .18   .25 .15   .1550
poor: E  Rp   .25 .05   .50  –.09   .25  –.05   – .0450
bust:
E  Rp  .25  –.03  .50  –.32   .25  –.09   – .1900
E  Rp  .10 .3675   .30 .1550   .40  –.0450   .20  –.1900   .0273
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 .0314
b.
σ p 2  .10 .3675 – .0273  .30 .1550 – .0273  .40  –.0450 – .0273  .20  –.1900 – .0273
2
2
σ p 2  .02800;σ p  .02800
1/2
2
2
 .1673
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10. Notice that we have historical information here, so we calculate the sample average and sample
standard deviation (using n – 1) just like we did in Chapter 1. Notice also that the portfolio has less
risk than either asset.
Annual Returns
on Stocks A and
B
Year
2018
2019
2020
2021
2022
Stock A
11%
37%
–21%
26%
13%
Stock B
21%
–38%
48%
16%
24%
Portfolio AB
17.00%
–8.00%
20.40%
20.00%
19.60%
Avg return
Std deviation
13.20%
21.82%
14.20%
31.67%
13.80%
12.26%
Intermediate Questions
11. Boom: .35(15%) + .45(18%) + .20(20%) = 17.35%
Bust: .35(10%) + .45(0%) + .20(–10%) = 1.50%
E  RP   .40 .1735   .60 .0150   .0784, or 7.84%
σ 2P  .40 .1735 – .0784   .60 .0150 – .0784   .00603;σ P  7.76%
2
2
12. E  RP   .50 .14   .50 .10   .1200, or 12.00%
σ 2P  .502 .422   .502 .312   2 .50 .50 .42 .31.10   .07464;σ P  27.32%
 
   2 .50 .50 .42 .311.0   .13323;σ  36.50%
σ  .50 .42   .50 .31   2 .50 .50 .42 .31 0.0   .06813;σ  26.10%
σ  .50 .42   .50 .31   2 .50 .50 .42 .31 1.0   .00303;σ  5.50%
13. σ 2P  .502 .422  .502 .312
2
2
2
2
2
2
2
2
2
P
P
P
2
P
P
As the correlation becomes smaller, the standard deviation of the portfolio decreases. In the extreme,
with a correlation of –1, this means that as one asset has a higher than expected return, the other
asset has a lower than expected return. The extra returns, whether positive or negative, will offset
each other resulting in smoother portfolio return with less variance.
.312 - .42  .31  .10
 .33709; w Down  1 – .33709   .66291
14. w 3 Doors 
.422  .312 - 2  .42  .31  .10
E  RP   .33709 .14   .66291.10   .1135, or 11.35%
σ 2P  .337092 .422   .662912 .312   2 .33709 .66291.42 .31.10   .06809
σ P  26.09%
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15.
Risk and
Return
with
Stocks and
Bonds
Portfolio
Weights
Stocks
1.00
0.80
0.60
0.40
0.20
0.00
16. w D 
Bonds
0.00
0.20
0.40
0.60
0.80
1.00
Expected
Standard
Return
12.00%
11.00%
10.00%
9.00%
8.00%
7.00%
Deviation
21.00%
17.67%
14.77%
12.60%
11.58%
12.00%
.422 – .31  .42  –.10
 .6345; w I  1 – .6345   .3655
.312  .422 – 2  .31  .42  –.10
17. E  RP   .6345 .13  .3655 .16   .1410, or 14.10%
σ 2P  .63452 .312   .36552 .422   2 .6345 .3655 .31.42  –.10   .0562
σ P  23.71%
.182 - .28  .18  .40
 .1737; w L  1 – .1737   .8263
.282  .182 - 2  .28  .18  .40
E  RP   .1737 .10   .8263 .07   .0752, or 7.52%
18. w K 
σ 2P  .1737 2 .282   .82632 .182   2 .1737 .8263.28 .18 .40   .03027
σ P  17.40%
.57 2 - .42  .57  .25
 .6946; w Wildcat  1 – .6946   .3054
.422  .57 2 - 2  .57  .42  .25
E  RP   .6946 .14   .3054 .12   .1339, or 13.39%
19. w Bruin 
σ 2P  .69462 .422   .30542 .57 2   2 .6946 .3054 .42 .57 .25   .14080
σP  37.52%
20. E(R) = .45(12%) + .25(16%) + .30(13%) = 13.30%
σ 2P  .452 .412  .252 .582  .302 .482  2 .45 .25 .58 .41.30   2 .45 .30 .41.48 .20  






2(.25)(.30)(.58)(.48)(.05) = 0.10457
σ P  32.34%
21. w J 
.192 - .54  .19  .50
 – .0675; w S  1 –  –.0675    1.0675
.542  .192 - 2  .54  .19  .50
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σ 2P   –.06752 .542   1.06752 .192   2 .54 .19  –.0675 1.0675 .50   .03507
σ P  .03507 
1/2
 .1873, or 18.73%
E  RP   – .0675 .13  1.0675 .10   .0980, or 9.80%
Even though it is possible to mathematically calculate the standard deviation and expected return of
a portfolio with a negative weight, an explicit assumption is that no asset can have a negative weight.
The reason this portfolio has a negative weight in one asset is the relatively high correlation between
the two assets. If you look at the investment opportunity sets in the chapter, you will notice that as
the correlation decreases, the investment opportunity set bends further backwards. However, for a
portfolio with a correlation of +1, there is no minimum variance portfolio with a variance lower than
the lowest variance asset. This implies there is some necessary level of correlation to make the
minimum variance portfolio have a variance lower than the lowest variance asset. The formula to
determine if there is a minimum variance portfolio with a variance less than the lowest variance asset
is:
.19
 min
 .3519  .50 so there is no minimum variance portfolio with a
  . In this case,
.54
 max
variance lower than the lowest variance asset assuming non-negative asset weights.
22. Look at  2P :
σ2P = (x A × σA + x B× σB )2
= x 2A   A2  x 2B   B2  2  x A  x B   A   B  1 , which is precisely the expression
for the variance on a two-asset portfolio when the correlation is +1.
23. Look at  2P :
σ2P = (x A × σA – x B× σB )2
= x 2A   A2  x B2   B2  2  x A  x B   A   B  (-1) ,
which
expression for the variance on a two-asset portfolio when the correlation is –1.
is
precisely
the
24. From the previous question, with a correlation of –1:
σp = x A ×σA – x B×σB
= x ×σ A – 1 – x  ×σ B
Set this to equal zero and solve for x to get:
0 = x × σ A – 1 – x  × σ B
x = σ B /(σ A + σ B )
This is the weight on the first asset.
25. Let  stand for the correlation, then:
σ2P  x 2A   A2  x 2B   B2  2  x A  x B   A   B  
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= x 2 × σ A 2 + 1 – x  × σ B2 + 2 × x × 1 – x  × σ A × σ B × r
2
Take the derivative with respect to x and set equal to zero:
dσ p 2 /dx = 2 × x × σ A 2 – 2 × 1 – x  × σ B2 + 2 × σ A × σ B × r– 4 × x × σ A × σB × r = 0
Solve for x to get the expression in the text.
26.
CFA Exam Review by Kaplan Schweser
1. b
Increasing return may not be appropriate if the risk level increases more than the return. Focusing
on assets that help diversify the existing portfolio, while maintaining return, will result in a more
efficient portfolio.
2. a
11% = (.9 × 10%) + (.1 × 20%)
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3. b
14.1% = sqrt[(.1)(.1)(16)(16) + (.9)(.9)(16)(16) + 2(.1)(.9)(16)(16)(−0.23)]
4. c
9.7% = (.9 × 10%) + (.05 × 10%) + (.05 × 4%)
5. c
Since the beta of Beta Naught is zero, its correlation with any of the other funds is zero. Thus, the
lowest standard deviation will be achieved with the fund that has the lowest standard deviation.
Since Hi Rise and Quality Commodity have the same standard deviation, which is less than New
Horizon, either of them would produce the same result.
Chapter 12
Return, Risk, and the Security Market Line
Concept Questions
1.
Some of the risk in holding any asset is unique to the asset in question. By investing in a variety of
assets, this unique portion of the total risk can be almost completely eliminated at little cost. On the
other hand, there are some risks that affect all investments. This portion of the total risk of an asset
cannot be costlessly eliminated. In other words, systematic risk can be controlled, but only by a
costly reduction in expected returns.
2.
If the market expected the growth rate in the coming year to be 2 percent, then there would be no
change in security prices if this expectation had been fully anticipated and priced. However, if the
market had been expecting a growth rate different than 2 percent and the expectation was
incorporated into security prices, then the government's announcement would most likely cause
security prices in general to change; prices would drop if the anticipated growth rate had been more
than 2 percent, and prices would rise if the anticipated growth rate had been less than 2 percent.
3.
a.
b.
c.
d.
e.
f.
systematic
unsystematic
both; probably mostly systematic
unsystematic
unsystematic
systematic
a.
An unexpected, systematic event occurred; market prices in general will most likely
decline.
No unexpected event occurred; company price will most likely stay constant.
No unexpected, systematic event occurred; market prices in general will most likely stay
constant.
An unexpected, unsystematic event occurred; company price will most likely decline.
No unexpected, systematic event occurred unless the outcome was a surprise; market
prices in general will most likely stay constant.
4.
b.
c.
d.
e.
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5.
False. Expected returns depend on systematic risk, not total risk.
6.
Earnings contain information about recent sales and costs. This information is useful for projecting
future growth rates and cash flows. Thus, unexpectedly low earnings lead market participants to
reduce estimates of future growth rates and cash flows; price drops are the result. The reverse is
often true for unexpectedly high earnings.
7.
Yes. It is possible, in theory, for a risky asset to have a beta of zero. Such an asset’s return is
uncorrelated with the overall market. Based on the CAPM, this asset’s expected return would be
equal to the risk-free rate. It is also possible to have a negative beta; the return would be less than the
risk-free rate. A negative beta asset would carry a negative risk premium because of its value as a
diversification instrument. A negative beta asset can be created by shorting an asset with a positive
beta. A portfolio with a zero beta can always be created by combining long and short positions.
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8.
The rule is always ―buy low, sell high.‖ In this case, we buy the undervalued asset and sell (short)
the overvalued one. It does not matter whether the two securities are incorrectly valued with regard
to some third security; all that matters is their relative value. In other words, the trade will be
profitable if the relative misvaluation disappears; however, there is no guarantee that the relative
misvaluation will disappear, so the profits are not certain.
9.
If every asset has the same reward-to-risk ratio, the implication is that every asset provides the same
risk premium for each unit of risk. In other words, the only way to increase your return (reward) is to
accept more risk. Investors will only take more risk if the reward is higher, and a constant reward-torisk ratio ensures this will happen. We would expect every asset in a liquid, well-functioning market
to have the same reward-to-risk ratio due to competition and investor risk aversion. If an asset has a
reward-to-risk ratio that is lower than all other assets, investors will avoid that asset, thereby driving
the price down, increasing the expected return and the reward-to-risk ratio. Similarly, if an asset has
a reward-to-risk ratio that is higher than other assets, investors will flock to the asset, increasing the
price, and decreasing the expected return and the reward-to-risk ratio.
10.
a. Systematic risk refers to fluctuations in asset prices caused by macroeconomic factors that are
common to all risky assets; hence systematic risk is often referred to as market risk. Examples of
systematic risk include the business cycle, inflation, monetary policy, and technological changes.
Firm-specific risk refers to fluctuations in asset prices caused by factors that are independent of the
market such as industry characteristics or firm characteristics. Examples of firm-specific risk include
litigation, patents, management, and financial leverage.
b. Trudy should explain to the client that picking only the top five best ideas would most likely
result in the client holding a much riskier portfolio. The total risk of the portfolio, or portfolio
variance, is the combination of systematic risk and firm-specific risk. i.) The systematic component
depends on the sensitivity of the individual assets to market movements as measured by beta.
Assuming the portfolio is well-diversified, the number of assets will not affect the systematic risk
component of portfolio variance. The portfolio beta depends on the individual security betas and the
portfolio weights of those securities. ii.) On the other hand, the components of the firm-specific risk
(sometimes called nonsystematic risk) are not perfectly positively correlated with each other and as
more assets are added to the portfolio those additional assets tend to reduce portfolio risk. Hence,
increasing the number of securities in a portfolio reduces firm-specific risk. For example, a patent
expiring for one company would not affect the other securities in the portfolio. An increase in oil
prices might hurt an airline stock but aid an energy stock. As the number of randomly selected
securities increases, the total risk (variance) of the portfolio approaches its systematic variance.
Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this
solutions manual, rounding may appear to have occurred. However, the final answer for each problem is
found without rounding during any step in the problem.
Core Questions
1.
E  Ri   .132  .035  .075βi ;βi  1.29
2.
E  Ri   .08  .03   E  Rmkt  – .03 .60  ; E  Rmkt   .1133
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3.
E  Ri   .12  Rf  .10 – Rf 1.40  ; Rf  .05
4.
E  R i   .11  .045  .80  MRP  ; MRP  .0813
5.
β P  .10 1.4   .25 .6   .50 1.5   .15 .9   1.175
6.
Portfolio value = 400($60) + 500($85) + 900($25) = $89,000
x A  400  $60  / $89, 000  .2697
x B  500  $85  / $89, 000  .4775
x C  900  $25  / $89, 000  .2528
β P  .2697 .8  .4775 1.2   .2528 .7   .97
7.
β P  1.0  1/ 3  0   1/ 3 1.20   1/ 3(β X );β X  1.80
8.
E  Ri   .03  .11 – .03.85  .0980
9.
E  Ri   .055  .12 – .055 1.2   .1330
Dividend yield  $0.80 / $35  .0229
Capital gains yield = .1330 − .0229 = .1101
Price next year = $35(1 + .1101) = $38.86
10.
a.
E  RP   .09  .04  / 2  .0650
b. β P  0.5  x S  0.9   1 – x S  0  ; x S  .5 / .9  .5556; x rf  1 – .5556  .4444
c.
E  RP   .08  .09x S  .04 1 – x S  ; x S  .80;β p  .80  0.9   .20  0   .72
d. β P  1.8  x S  0.9   1 – x S  0  ; x S  1.8 / .9  2.00; x rf  1 – 2.00  –1.00
The portfolio is invested 200% in the stock and −100% in the risk-free asset. This represents
borrowing at the risk-free rate to buy more of the stock.
Intermediate Questions
11. β P  x W 1.1  1 – x W  0   1.1x W
E  RW   .12  .04  MRP 1.10  ; MRP  .08 /1.10  .0727
E  RP   .04  .0727βP ; slope of line  MRP  .0727; E  RP   .04  .0727βP  .04  .0727 1.1x W 
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xW
E  rp 
βp
xW
E  rp 
βp
0%
4.00%
.00
100%
12.00%
1.10
25
6.00%
.28
125
14.00%
1.38
50
8.00%
.55
150
16.00%
1.65
75
10.00%
.83
12. E  Rii   .05  .07βi
.13  E  RY   .05  .07 1.05  .1235 ;
Y plots above the SML and is undervalued.
Reward-to-risk ratio Y  .13 – .05  /1.05  .0762
.09  E  RZ   .05  .07  0.70   .0990 ;
Z plots below the SML and is overvalued.
reward-to-risk ratio Z  .09 – .05 / .70  .0571
13.
.13 – Rf  /1.05  .09 – Rf  / 0.70 ; Rf  .01, or 1.00%
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14.
E  R  – R  / β  E  R  – R  / β
β / β  E  R  – R  / E  R  – R 
A
A
f
A
B
A
B
f
f
B
B
f
15. Here we have the expected return and beta for two assets. We can express the returns of the two
assets using CAPM. If the CAPM is true, then the security market line holds as well, which means
all assets have the same risk premium. Setting the risk premiums of the assets equal to each other
and solving for the risk-free rate, we find:
.123 – Rf  /1.05  .118 – Rf  / .90
.90 .123 – Rf   1.05 .118 – Rf 
Rf  .0880, or 8.80%
Now using CAPM to find the expected return on the market with both stocks, we find:
.1230  .0880  1.05  RM – .0880 
.118  .0880  .9  RM – .0880 
RM  .1213, or 12.13%
RM  .1213, or 12.13%
16. From
the
βi  Corr  Ri , RM   (σi / σ M ) .
chapter,
Also,
Corr  Ri , RM   Cov  Ri , RM  / (σi  σ M ) . Substituting this second result into the expression for
β i produces the desired result.
17. The relevant calculations can be summarized as follows:
Return
deviation
s
Returns
Year
2018
2019
2020
2021
2022
Totals
Security
8%
−18%
21%
38%
16%
65%
Market
5%
−14%
15%
21%
7%
34%
Average returns:
Security:
Market:
65 / 5  13.00%
34 / 5  6.80%
Security
−5.00%
−31.00%
8.00%
25.00%
3.00%
Product
of
deviation
s
Squared
deviatio
ns
Market
−1.80%
−20.80%
8.20%
14.20%
0.20%
Security
.00250
.09610
.00640
.06250
.00090
.16840
Market
.00032
.04326
.00672
.02016
.00000
.07048
.00090
.06448
.00656
.03550
.00006
.10750
Variances:
Standard deviations:
.16840 / 4  .04210
.07048 / 4  .01762
 .04210  20.52%
 .01762  13.27%
Covariance  Cov  Ri , RM   .10750 / 4  .02688
Correlation = Corr  Ri , RM   .02688 / .2052  .1327   .99
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Beta  β  .99  20.52 /13.27   1.53
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18. E  Rp   .13  w X .31  w Y .20   1 – w X – w Y .07 
β p  .7  w X 1.80   w Y 1.3  1 – w X – w Y  0 
solving these two equations in two unknowns gives w X  – .16667, w Y  .76923
w Rf  .39744
amount of stock Y to buy = .76923 ($100,000) = $76,923
19. E  RI   .30 .05   .40 .19   .30 .13  .1300; .1300  .05  .08β I ,β I  1.00
σ 2I  .30 .05 – .1300   .40 .19 – .1300   .30 .13 – .1300   .00336;
2
2
2
σ I  .00336
1/2
 .0580
E  RII   .30  –.18  .40 .14   .30 .29   .0890; .0890  .05  .08β II ,β II  .49
σ 2II  .30  –.18 – .0890   .40 .14 – .0890   .30 .29 – .0890   .03487;
2
2
2
σ II  .03487 
1/2
Although stock II has more total risk than I, it has much less systematic risk, since its beta is much
smaller than I’s. Thus, I has more systematic risk, and II has more unsystematic and more total risk.
Since unsystematic risk can be diversified away, I is actually the ―riskier‖ stock despite the lack of
volatility in its returns. Stock I will have a higher risk premium and a greater expected return.
20. E(R) = .05 + 1.15[.13 − .05] = 14.20%
Year
Unexpected
Returns
R − E(R)
RM – E  RM 
2018
2019
2020
2021
2022
−4.20%
−3.20%
−22.20%
−20.20%
13.80%
−1.00%
−5.00%
−24.00%
1.00%
−6.00%
Systematic
Portion
Unsystematic
Portion
β   RM – E  RM  
R – E  R  – β   RM  E  RM  
−1.15%
−5.75%
−27.60%
1.15%
−6.90%
−3.05%
2.55%
5.40%
−21.35%
20.70%
21. Furhman Labs: E(R) = 4.0% + 1.2(11.5% − 4.0%) = 13.00%
Garten Testing: E(R) = 4.0% + .9(11.5% − 4.0%) = 10.75%
Undervalued
Overvalued
*Supporting calculations
Furhman: Forecast − Required = 13.75% − 13.00% = 0.75%
Garten: Forecast − Required = 10.50% − 10.75% = −0.25%
Undervalued
Overvalued
If the forecast return is less (greater) than the required rate of return, the security is overvalued
(undervalued).
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 .1867
Spreadsheet Problem
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CFA Exam Review by Kaplan Schweser
1. a
Required return = 7% + 7%(1.3) = 16.1%
Since the required return is greater than the expected return (15.5%), then we should sell.
2. c
Beta  .88  58% / 35%   1.46
3. a
Montana’s required return = 7% + 7%(1.5) = 17.5%. Since this required return is higher than the
expected return (15%), Montana should not be purchased. Even though its expected return is the
highest, it is not enough to compensate for the risk.
Texas’expected return is less than required, so it should not be purchased. Ohio’s expected return
is greater than its required return, so it should be purchased.
4. b
Since the security market line runs from the risk-free rate through the market return, holding the
risk-free rate constant and decreasing the market risk premium (slope of line) will cause the
security market line to become flatter.
Chapter 13
Performance Evaluation and Risk Management
Concept Questions
1.
The Sharpe ratio is calculated as a portfolio’s risk premium, or excess return, divided by the standard
deviation of the portfolio’s return. The Treynor ratio is the portfolio risk premium divided by the
portfolio’s beta coefficient. So, the Sharpe ratio concentrates on total risk, while the Treynor focuses
on systematic risk.
2.
A common weakness of both the Jensen alpha and the Treynor ratio is that both require an estimate
of beta, which can differ a lot depending on the source, which in turn can lead to a mismeasurement
of risk adjusted return.
3.
Jensen’s alpha is the difference between a stock’s or a portfolio’s actual return and that which is
predicted by the CAPM. A positive alpha implies abnormal returns above the SML line (as drawn
using the CAPM).
4.
An advantage of the Sharpe ratio is that a beta estimate is not required; however, the Sharpe ratio is
not appropriate when evaluating individual stocks because it uses total risk rather than systematic
risk.
5.
To determine significance, one might use the t-statistics or p-values from a regression estimate.
Beyond this, the information ratio will identify whether the abnormal return is heavily impacted by
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volatility in the estimate (i.e., a high tracking error). Also, a high R-squared will give some degree of
confidence to the alpha estimate. Lastly, adherence to GIPS standards may give confidence to the
estimate of one firm over another.
6.
A Sharpe-optimal portfolio is the portfolio with the highest possible Sharpe ratio given the available
investments. This portfolio has the characteristic of having the highest possible return for the least
amount of risk.
7.
The Sharpe ratio uses total deviation from the mean, while the Sortino ratio uses only returns that are
less than the mean (i.e., upside volatility is ignored). Thus, the Sortino ratio only penalizes the
investment (or manager) for undesirable volatility and thus expresses a fund’s excess return relative
to downside risk only.
8.
After establishing the desired probability (x), the VaR statistic provides the minimum loss you would
receive x% of the time. As an example, given:
Prob(R  −.20) = 5%
we would expect at least a 20% loss in one out of twenty periods (5% of the time).
9.
This is equivalent to saying that 5% of the time the minimum loss is 20%, similar to the previous
answer.
10. For sector funds or investments that only cover a portion of the market (e.g., value or growth), a
more specific index may provide a better standard for judging performance.
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Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this
solutions manual, rounding may appear to have occurred. However, the final answer for each problem is
found without rounding during any step in the problem.
Core Questions
1.
54%  2 / 12 = 22.05%
2.
8.60% / 1 / 12  29.79%
3.
Portfolio
X
Y
Z
Market
4.
Sharpe ratio
.27586
.29167
.28571
.31579
Treynor ratio
.0640
.0636
.0533
.0600
Jensen's alpha
.50%
.40%
−.50%
.00%
X Jensen  0.12  0.04   0.10  0.04  1.25  0.0050, or 0.50%
Information ratio = Jensen’s Alpha ÷ Tracking Error = 0.50% ÷ 9.20% = 0.0543
5.
R-squared gives the percentage of the fund’s return driven by the market, which is:
.752  56.25%
6.
TE  2.1% / .50  4.2%
7.
Prob(R  .12 − 1.645(.30) = 5%
Prob(R  −.3735) = 5%
8.
Prob(R  .18 /12  – 1.96 .44 1/12  )  2.5%
1/2
Prob(R  −.2339) = 2.5%
9.
E  R   .12  .18  / 2  .15
  (.52  .302  .52  .442 )1/2  .2663
Prob(R  .15 /12  – 1.96 .26631/12  )  2.5%
1/2
Prob(R  −.1382) = 2.5%
10. For a portfolio with two investments having zero correlation, the Sharpe ratio would be calculated as
follows:
x E(R S )  x B E(R B ) - R f
Sharpe ratio  S
(x S2 S2  x 2B B2 )1/2
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11. Sharpe ratio 
[.5 
2
2
2
S  .5

.5E(R S )  .5E(R B ) - R f
2
1/2
B  .2(.5)(.5)( S )( B )(Corr(RS , R B ))]


12. Any portfolio of the two securities will also have the same expected return.
E(R ) - R
E(R ) - R
Sharpe ratio  2 2 S 2 2f 1/2  2 2 B 2 2f 1/2
(x S S  x B B )
(x S S  x B B )
13. Prob(R  .11 − 2.326(.54)) = 1%
Prob(R  −1.1462) = 1%
This number does not make sense since it is impossible to lose more than 100% in a stock.
14. Prob(R  .11 + 2.326(.54)) = 1%
Prob(R  + 1.3662) = 1%
While this is a large return, it is possible, and even plausible. Since it is not possible for a stock to
lose more than 100% but it is possible for a stock to gain more than 100%, stock returns are not truly
normal.
15. E  R   .10  .18  / 2  .1400
  .52 .262   .52 .622   2 .5 .5 .26 .62 .5  
1/2
 .3915
Prob(R  .1400 /12  – 1.645 .3915 1 / 12  )  5%
1/2
Prob(R  −.1742) = 5%
16. E  R   .10  .18  / 2  .1400
  .52 .262   .52 .622   2 .5 .5 .26 .62  –.5  
1/2
 .2696
Prob(R  .1400 /12  – 1.645 .2696 1/12  )  5%
1/2
Prob(R  −.1164) = 5%
17. E(R) = .14
  [.3332 .302   .3332 .402   .3332 .502   2 .333.333 .30 .40  0  
2 .333.333.30 .50  0   2 .333.333.40 .50  0 ]1/2  .2357
Prob(R  .14 − 2.326(.2357)) = 1%
Prob(R  −.4083) = 1%
  – .15 – .05.29 .48.25 / {.12 – .05 .48   .15 – .05 .29 
2
18. w A  .12 – .05  .48
2
2
− (.12 − .05 + .15 − .05)[(.29)(.48)(.25)]}
w A  .6792
w B  .3208
E  R P   .6792 .12   .3208 .15   .1296
  .67922 .292   .32082 .482   2 .6792 .3208 .29 .48 .25  
1/2
 .2787
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Sharpe ratio  .1296 – .05 / .2787  .2857
Prob(R  .1296 − 1.960(.2787)) = 2.5%
Prob(R  −.4166) = 2.5%
19. Sharpe  .0546  .0240  / .1505  .2034
Treynor  .0546  .0240  / .88  .0350
20. First find the average returns of the fund, the market and the risk free rate, which are 5.46%, 1.96%,
and 2.40%, respectively. The deviations for the fund and the market returns are 15.05% and 16.68%,
respectively.
Next find the excess return over the risk free rate, as well as the difference between the fund and
market returns.
2018
2019
2020
2021
2022
Fund Excess
−16.20%
22.10%
10.40%
2.20%
−3.20%
Market Excess
−25.50%
16.50%
7.40%
3.60%
−4.20%
Difference
9.30%
5.60%
3.00%
−1.40%
1.00%
The correlation between the fund and the market is .97.
So, the fund beta  0.97 15.05% /16.68%   0.88
Jensen’s alpha  .0546 – .0240  .0196  .0240 .88    .0345 , or 3.45%
For the information ratio, we need the average of the differences in return and the tracking error .
The average return difference is 3.50% and the standard deviation of the difference in returns is 4.14.
So, the information ratio  3.50% / 4.14%  .8321
21. First find the squared differences between the fund’s return each year and its average return,
including only those where the yearly return is less than the average. Divide by n-1 to find the
variance, and take the square root to find the (downside) standard deviation. Repeat this for the
market.
Sortino  fund   .0546  .0240  / .1035  0.2957
Sortino  market   .0196  .0240  / .1328   0.0331
Since the fund has a higher Sortino than the market, it would be considered to have had ―good‖
performance on a relative, risk-adjusted basis.
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Spreadsheet Problem
22. The Solver inputs are:
based on the following spreadsheet.
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23.
CFA Exam Review by Kaplan Schweser
1. a
Miranda  .102 – .02  / .37  .2216
S&P 500   .225 – .02  / .44   .5568
2. c
Miranda  .102 – .02  / 1.10  .0745
S&P 500   .225 – .02  / 1.00   .2450
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3. b
alpha = .102 − [.02 + (−.225 − .02)1.10] = .3515
Chapter 14
Futures Contracts
Concept Questions
1.
a.
b.
c.
d.
Two are visible in Figure 14.1; wheat futures are traded on the Chicago Board of Trade (CBT)
and the Kansas City Board of Trade (KC). The CBT and KC are both part of the CME Group.
There are at least three others, the Minneapolis Grain Exchange, the Winnipeg Commodity
Exchange (WPG) and the MidAmerica Commodity Exchange (MCE), not shown in Figure
14.1. Of these, the largest trading activity occurs in Chicago.
There are 100 troy oz. per contract, for a total of 1,000 troy oz. on ten contracts. It is traded on
the COMEX division of the New York Mercantile Exchange.
At 5,000 bushels per contract, you must deliver 100,000 bushels.
Of the two contracts listed, the July contract has the largest open interest.
2. Long hedge; i.e., buy corn futures. If corn prices do rise, then the futures position will show a profit,
offsetting the losses from higher corn prices when they are purchased.
3. Short the index futures. If the S&P 500 index subsequently declines in a market sell-off, the futures
position will show a profit, offsetting the losses on the portfolio of stocks.
4. Sell the futures. If interest rates rise, causing the value of the bonds to be less at the time of sale, the
corresponding futures hedge will show a profit.
5. Buy yen futures. If the value of the dollar depreciates relative to the yen in the intervening four
months, then the dollar/yen exchange rate will rise, and the payment required by the importer in
dollars will rise. A long yen futures position would profit from the dollar's depreciation and offset the
importer's higher invoice cost.
6. Sell crude oil futures. Price declines in the oil market would be offset by a gain on the short position.
7. Sell T-bond futures. Bond price declines in the market would be offset by a gain on the short position.
8. It is true. Each contract has a buyer and a seller, a long and a short. One side can only profit at the
expense of the other. Including commissions, futures contracts, like most derivative assets, are
actually negative sum gains. This doesn’t make them inappropriate tools, it just means that, on
average and before commissions, they are a break-even proposition.
9. In reality, two factors make stock index arbitrage more difficult than it might appear. First, the
dividend yield on the index depends on the dividends that will be paid over the life of the contract;
this is not known with complete certainty and must, therefore, be estimated. Second, buying or selling
the entire index is feasible, but index staleness (discussed in our first stock market chapter) is an
issue; the current up-to-the-second price of the index is not known because not all components will
have just traded. Of course, trading costs must be considered as well.
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Thus, there is some risk in that the inputs used to determine the correct futures price may be incorrect,
and what appears to be a profitable trade may not be. Program traders usually establish bounds,
meaning that no trade is undertaken unless a deviation from parity exceeds a preset amount. Setting
the bounds is itself an issue. If they are set too narrow, then the risks described above exist. If they are
set too wide, other traders will step in sooner and eliminate the profit opportunity.
10. There are two similarities. 1) You are selling an asset today that you do not currently own (you may
expect to own the asset in the future, say a wheat harvest). 2) Both contracts have an initial margin
and a maintenance margin.
There are several major differences between a futures contract and short selling a stock. 1) With a
futures contract, you are agreeing to a price at a specific date in the future. The price at settlement
may be above or below the agreed upon price. In short selling the stock, you are selling at the current
price and the price in the future is not set. 2) In a futures contract, the maturity date is determined
when the contract is sold. A short stock sale can theoretically extend to infinity. 3) The cash flows
from the short sale are different. In a futures contract, cash for the sale of a futures contract is not
exchanged until the settlement of the contract. At the settlement date, you will receive the cash for the
sale. In a short stock sale, you receive the cash for the sale of the stock today (although your broker
may not allow you access to the cash). When you close the short stock position, you must pay cash to
purchase the stock.
Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this
solutions manual, rounding may appear to have occurred. However, the final answer for each problem is
found without rounding during any step in the problem.
Core Questions
1.
a. The settle price is 232.40 cents per pound. One contract is valued as the contract size times the
per unit price, so 37,500 × $2.3240 = $87,150.00.
b. The settle price is $4.2522 per gallon. The value of a position in 10 contracts is 10 × 42,000 ×
$4.2522= $1,785,924.00.
c. The index futures price was down 335 for the day, or 5 × −$335 = −$1,675. For a position in 25
contracts, this represents a change in value of 25 × −$1,675= −$41,875, which would represent a
loss to a long position in the futures contract and a gain to a short position in the futures contract.
d. The contract price closed up .41 cents for the day ($.0041), so a short position would have had a
loss of 10 × 60,000 × $0.0041 = -$2,460.
2.
The contract settled down 31.50 cents, so a long position loses: 20 × 5,000 × −$.315 = −$31,500.
3.
The contract settled down 3.25 cents, so a short position gains: 15 × 5,000 × $.0325 = $2,437.50.
4.
The
5.
The total open interest on the June 2022 Japanese Yen is 229,461 contracts. Each contract has a long
and a short, so the open interest represents either the number of long positions or the number of short
positions. Each contract calls for the delivery of ¥12,500,000, and the settle price on the contract is
contract
settled
down
5.2/32nds,
30  $100, 000   5.2 / 32  /100  $4,875 .
so
a
short
position
gains:
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$.7645 per 100 yen, or $.7645 /100  ¥12,500,000  $95,562.50 . With 229,461 contracts, the
total dollar value is about $21,927,866,812.50.
6.
F6/12  $16.40 1  .03
7.
$94.90  S 1  .045 
8.
$42.95  $42.60 1  R 
9.
F4/12  $49.24 1  .054 – .015 
6/12
2/12
 $16.64
; S  $94.21
4/12
; R  .0249
10. $27.18  S 1  .025 – .0125 
4/12
6/12
 $49.87
; S  $27.01
Intermediate Questions
11. If the contract settles down, a long position loses money. The loss per contract is: 42,000 × $.04 =
$1,680, so when the account is marked-to-market and settled at the end of the trading day, your
balance per contract is $6,720, which is less than the maintenance margin, so you will receive a
margin call. The minimum price change for a margin call is $1,200 = 42,000 × X, or X = $.02857 =
2.857 cents per gallon.
12. Establish your account at an initial margin of 10 × $12,000 = $120,000. Your maintenance margin is
10 × $11,200 = $112,000. The initial value of the position is 10 × 100 × $1,300 = $1,300,000.
Day 1:
New position value = 10 × 100 × $1,295 = $1,295,000, for a loss of
$5,000. Your margin account balance is now $115,000, which is not
below the maintenance margin level, so no margin deposit is required.
Day 2:
New position value = 10 × 100 × $1,290 = $1,290,000, for loss of
$5,000. Your margin account balance is now $110,000. You must meet a
margin call of $10,000, bringing your margin back to $120,000.
Day 3:
New position value = 10 × 100 × $1,305 = $1,305,000, for a gain of
$15,000. Your margin account balance is now $135,000.
Day 4:
New position value = 10 × 100 × $1,315 = $1,315,000, for a gain of
$10,000. Your margin account balance is now $145,000.
Your total profit is $1,315,000 − $1,300,000 = $15,000.
13. Establish your account at an initial margin of 15 × $7,425 = $111,375. Your maintenance margin is
15 × $6,500 = $97,500. The initial value of the position is 15 × 42,000 × $2.085 = $1,313,550.
Day 1:
New position value = 15 × 42,000 × $2.071 = $1,304,730, for a gain of
$8,820. Your margin account balance is $120,195.
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Day 2:
New position value = 15 × 42,000 × $2.099 = $1,322,370, for a loss of
$17,640. Your margin account balance is now $102,555, which is not
below the maintenance margin level, so no margin deposit is required.
Day 3:
New position value = 15 × 42,000 × $2.118 = $1,334,340, for a loss of
$11,970. Your margin account balance is now $90,585. You must meet a
margin call of $20,790, bringing your margin back to $111,375.
Day 4:
New position value = 15 × 42,000 × $2.146 = $1,351,980, for a loss of
$17,640. Your margin account balance is now $93,735. You must meet a
margin call of $17,640, bringing your margin back to $111,375.
Your total profit is $1,313,550 − $1,351,980 = −$38,430
14. 20 × 1,000 × ($118.87 − $116.50) = $47,400.00
15. −15 × 62,500 × ($1.2500 − $1.2590) = $8,437.50
16. Parity implies that F  4,920 1  .06 – .02 
1/2
 5, 017.44 . Thus, if the futures price is
actually at 4,952, the futures are underpriced and you should sell the index and buy the futures.
17. Since you are long the asset (stocks), to create a hedge, you would short the futures contract. The
number of futures contracts to short is:
Number of contracts  1.15  $175, 000, 000  / 1, 450  $500   277.59 , or about 278
contracts.
However, the Midcap 400 futures might not be liquid enough to handle such a large hedge. Also,
when the contract expires it will be necessary to ―roll‖ the hedge into a subsequent contract month.
18. 2, 281.55  2, 270.42 1  X 
6/12
; X  .0098, or 0.98%
19. 2,399.25  2,370.48 1  .05 – d 
1/2
; d  .0256, or 2.56%
20. DF  6.7   3 /12   6.95 years
Contracts to sell   5.1  $500, 000, 000  /  6.95  1.02  $100, 000   3,597.12 ,
or
about 3,597 contracts.
21. DF  6.2  85 / 365   6.43 years
Contracts to sell  8.4  $400, 000, 000  /  6.43  1.02  $100, 000   5,120.75 ,
or
about 5,121 contracts.
22. F  $48.15 1  .04 
5/12
 $48.94 ; the futures contract is underpriced
Opening transactions now:
Buy the futures
Sell the stock short
Lend $48.15 at 4% for 5 months
Total cash flow
$0
$48.15
−$48.15
$.00
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Closing transactions:
Accept delivery on the futures
Cover the short position
Collect the loan
Total cash flow
23. F  $53.87 1  .05 
6/12
−$48.56
$0
+$48.94
$.38
 $55.20 ; the futures contract is overpriced
Opening transactions now:
Sell the futures
Buy the stock
Borrow $53.87 at 5% for 6 months
Total cash flow
$0
−$53.87
+$53.87
$.00
Closing transactions:
Deliver the futures
Sell the stock
Repay the loan
Total cash flow
+$55.94
$0
−$55.20
$.74
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CFA Exam Review by Kaplan Schweser
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1. a
The day the freight cars are sold, Jackson is effectively long Euros, so the optimal solution is to
sell (short) Euro futures contracts in exchange for $18, 750, 000   €15, 000, 000 / €.80 / $  .
2. b
Jackson wants to ―lock in‖ the price of $6,390,977   C$8,500, 000 / C$1.33 / $  for the
Canadian dollars by buying Canadian dollars with a futures contract.
3. a
Being long the currency means holding or expecting to receive a foreign currency; therefore, to
hedge this exposure, you need to sell futures contracts (deliver foreign currency and receive
domestic currency at the expiration of the contract).
Chapter 15
Stock Options
Concept Questions
1.
Assuming American-style exercise rights, a call option confers the right, without the obligation, to
buy an asset at a given price on or before a given date. An American-style put option confers the
right, without the obligation, to sell an asset at a given price on or before a given date. Europeanstyle options are the same except that exercise can only occur at maturity. One reason you would buy
a call option is that you expect the price of the asset to increase. Similarly, you would buy a put
option if you expect the price of the asset to decrease. In both cases, other reasons exist, but these are
the basic ones. A call option has unlimited potential profit, while a put option has limited potential
profit; the underlying asset's price cannot be less than zero.
2.
a.
b.
c.
d.
The buyer of a call option pays money for the right to buy....
The buyer of a put option pays money for the right to sell....
The seller of a call option receives money for the obligation to sell....
The seller of a put option receives money for the obligation to buy....
3.
In general, the break-even stock price for a call purchase is the exercise price plus the premium paid.
For stock prices higher than this, the purchaser realizes a profit. For a put purchase, it’s the strike
price less the premium. For stock prices lower than this, the purchaser realizes a profit.
4.
If you buy a put option on a stock that you already own, you guarantee that you can sell the stock for
the strike price on the put. Thus, you have, in effect, insured yourself against stock price declines
beyond this point. This is the protective put strategy.
5.
The intrinsic value of a call option is MAX{0, S − K}. It is the value of the option if it were
exercised immediately.
6.
The intrinsic value of a put option at expiration is MAX{0, K − S}. By definition, the intrinsic value
of an option is its value if it were exercised immediately.
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7.
The call is selling for less than its intrinsic value; an arbitrage opportunity exists. Buy the call for
$10, exercise the call by paying $35 in return for a share of stock, and sell the stock for $50. You've
made a riskless $5 profit.
8.
42 contracts were traded, 25 calls and 17 puts; this represents options on 4,200 shares of Milson
stock.
9.
The calls are in the money. The intrinsic value of the calls is $4.
10. The puts are out of the money. The intrinsic value of the puts is $0.
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11. The March call and the October put are mispriced. The call is mispriced because it is selling for less
than its intrinsic value. The arbitrage is to buy the call for $3.50, exercise it and pay $55 for a share
of stock, and sell the stock for $59 for a riskless profit of $.50. The October put is mispriced because
it sells for less than the July put. To take advantage of this, sell the July put for $3.63 and buy the
October put for $3.25, for a cash inflow of $.38. The exposure of the short position is completely
covered by the long position in the October put, with a positive cash inflow today.
To prevent arbitrage from occurring, the March call would need to sell for at least $4.00, and the
October put would need to sell for more than the July put, i.e., greater than $3.63.
12. The covered put would represent writing put options on the stock. This strategy is analogous to a
covered call because the upside potential of the underlying position (which in the case of a short sale
would be a decline in the stock price) is capped in exchange for the receipt of the option premium for
certain.
The protective call would represent the purchase of call options as a form of insurance for the short
sale position. If the stock price rises, then losses incurred on the short sale are offset, or insured, by
gains on the call options; however, if the stock price falls, which represents a profit to the short
seller, then only the purchase price of the option is lost.
13. The call is worth more. To see this, we can rearrange the put-call parity condition as follows:
C – P  S – K / 1  r 
T
If the options are at the money, S = K, then the right-hand side of this expression is equal to the
stock price minus the present value of the strike price. This is necessarily positive. Intuitively, if both
options are at the money, the call option offers a much bigger potential payoff (since it is
theoretically unlimited), so it’s worth more.
14. Looking at the previous answer, if the call and put have the same price (i.e., C − P = 0), it must be
that the stock price is equal to the present value of the strike price (i.e., K > S), so the put is in the
money.
15. A stock can be replicated by a long call (to capture the upside gains), a short put (to reflect the
downside losses), and a T-bill (to capture the time-value component–the ―wait‖ factor).
Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this
solutions manual, rounding may appear to have occurred. However, the final answer for each problem is
found without rounding during any step in the problem.
Core Questions
1.
Your options are worth $64 − $60 = $4 each, or $400 per contract. With eight contracts, the total
value is $3,200. Your net profit is $3,200 less the $2,400 (8 contracts at $300 each) you invested, or
$800.
2.
Your options are worth $45 − $39 = $6 each, or $600 per contract. With five contracts, the total
value is $3,000. Your net profit is $3,000 less the $1,500 (5 contracts at $300 each) you invested, or
$1,500.
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3.
The stock costs $50 per share, so if you invest $97,500, you’ll get 1,950 shares. The option premium
is $1.95, so an option contract costs $195. If you invest $97,500, you’ll get $97,500 / $195  500
contracts. If the stock is selling for $60 in 90 days, your payoff on the stock is $10 per share, or
$19,500 total. The percentage gain is $19,500 / $97,500  .2000 , or 20.00%. Your options are
worth $10 per share, or $1,000 per contract. However, you have 500 contracts, so your options are
worth $500,000 in all. Since you paid $97,500 for the 50 contracts, your profit is $402,500. Your
percentage gain is a pleasant $402,500 / $97,500  4.1282 , or 412.82%.
If the stock is selling for $50, your profit is $0 on the stock, so your percentage return is 0%.
Your option is worthless (why?); the percentage loss is −100%. If the stock is selling for $40, verify
that your percentage loss on the stock is −20.00% and your loss on the option is again −100%.
4.
50 contracts at $1,068 per contract = $53,400
5.
Stock price = $105.70: option value = 50(100)($105.70 − $100) = $28,500
Stock price = $101.60: option value = 50(100)($101.60 − $100) = $8,000
6.
Initial cost = 30(100)($4.90) = $14,700; maximum gain = 30(100)($100) − $14,700 = $285,300.
Terminal value = 30(100)($100 − $84.60) = $46,200; net gain = $46,200 − $14,700 = $31,500
7.
Stock price = $90:
Initial revenue = 30(100)($10.10) = $30,300
Terminal value = 30(100)($90 − $100) = −$30,000
Net gain = −$30,000 + $30,300 = $300
Stock price = $110: net gain = $30,300.
The break-even stock price is the $100 exercise price less the premium of $10.10, or $89.90. For
terminal stock prices above $89.90, the premium received more than offsets any loss, so the writer of
the put option makes a net profit (ignoring commissions and the effects of the time value of money).
8.
P  C – S  K / 1  r 
T
P  $3 – $66  $65 / 1  .05 
6/12
P = $.43
9.
S  C – P  K / 1  r 
T
S  $8 – $6  $80 / 1  .04 
5/12
S = $80.70
10. C  S  P – K / 1  r 
T
C  $51  $3.20 – $50 / 1  .05 
2/12
C = $4.60
Intermediate Questions
11. Div  $1.45 / 1  .04 
2/12
 $1.44
P  C – S  Div  K / 1  r 
T
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P  $3.90 – $47  $1.44  $45 / 1  .04 
5/12
P = $2.61
12. Div  $2.10 / 1  .06 
3/12
 $2.07
S  C – P  Div  K / 1  r 
T
S  $4.60 – $7.20  $2.07  $60 / 1  .06 
3/12
S = $58.60
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13. Div  $1.40 / 1  .05 
2/12
 $1.39
C  S  P – Div – K / 1  r 
T
C  $83  $8.30 – $1.39 – $80 / 1  .05 
7/12
C = $12.16
14. You get to keep the premium in all cases. For 10 contracts and a $2.75 premium, that’s $2,750. If the
stock price is $40 or $50, the options expire worthless, so your net profit is $2,750. If the stock price
is $60, you lose $10 per share on each of 1,000 shares, or $10,000 in all. You still have the premium,
so your net loss is $7,250.
15. You get to keep the premium in all cases. For 15 contracts and a $2.40 premium, that’s $3,600. If the
stock price is $45 or $55, the options expire worthless, so your net profit is $3,600. If the stock price
is $35, you lose $10 per share on each of 1,500 shares, or $15,000 in all. You still have the premium,
so your net loss is $11,400.
16. The contract costs $1,400. At maturity, an in-the-money SPX option is worth 100 times the
difference between the S&P index and the strike, or $1,800 in this case. Your net profit is $400.
17.
Stock price
$50.00
$55.00
$60.00
$65.00
$70.00
Short profit
$10.00
$5.00
$0
−$5.00
−$10.00
Short put
payoff
−$10.00
−$5.00
$0
$0
$0
Short
put profit
−$8.20
−$3.20
$1.80
$1.80
$1.80
Net profit
$1.80
$1.80
$1.80
−$3.20
−$8.20
Stock price
$60
$65
$70
$75
$80
Short profit
$10
$5
$0
−$5
−$10
Call payoff
$0
$0
$0
$5
$10
Call profit
−$3.40
−$3.40
−$3.40
$1.60
$6.60
Net profit
$6.60
$1.60
−$3.40
−$3.40
−$3.40
Stock price
$70
$75
$80
$85
$90
Short profit
$10
$5
$0
−$5
−$10
Short
Put payoff
−$10
−$5
$0
$0
$0
Protective
Call payoff
$0
$0
$0
$5
$10
Total payoff
$0
$0
$0
$0
$0
Stock price
$70
$75
Put payoff
−$10
−$5
Call payoff
$0
$0
Total payoff
−$10
−$5
18.
19.
20.
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Stock price
$80
$85
$90
Put payoff
$0
$0
$0
Call payoff
$0
$5
$10
Total payoff
$0
$5
$10
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21. Cost of strategy = $4.20 + $2.80 = $7.00
Stock price
$65
$70
$75
$80
$85
Call payoff
$0
$0
$0
$5
$10
Put payoff
$10
$5
$0
$0
$0
Total payoff
$10
$5
$0
$5
$10
Total profit
$3.00
−$2.00
−$7.00
−$2.00
$3.00
Breakeven prices = $75 ± $7.00 = $82.00 and $68.00
22.
Index level
4050
4100
4150
4200
4250
Long call
payoff
0
0
25
75
125
Short call
payoff
0
0
0
−50
−100
Total payoff
0
0
25
25
25
Index level
4000
4050
4100
4150
4200
Long put
payoff
100
50
0
0
0
Short put
payoff
−125
−75
−25
0
0
Total payoff
−25
−25
−25
0
0
Index level
4000
4050
4100
4150
4200
Long call
payoff
0
0
0
50
100
Short put
payoff
−100
−50
0
0
0
Total payoff
−100
−50
0
50
100
Index level
3900
3950
4000
4050
4100
4150
4200
Long call
payoff (1300)
0
0
0
50
100
150
200
Long call
payoff (1500)
0
0
0
0
0
0
0
Short call (2)
payoff (1400)
0
0
0
0
0
−100
−200
23.
24.
25.
Total payoff
0
0
0
50
100
50
0
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26. Total cost = $8.60 + $6.75 = $15.35
Stock price
Long call payoff
Long put payoff
$80
$0
$20.00
$85
$0
$15.00
$90
$0
$10.00
$95
$0
$5.00
$100
$0
$0
$105
$0
$0
$110
$0
$0
$115
$5.00
$0
$120
$10.00
$0
$125
$15.00
$0
$130
$20.00
$0
Total payoff
$20.00
$15.00
$10.00
$5.00
$0
$0
$0
$5.00
$10.00
$15.00
$20.00
Total profit
$4.65
−$.35
−$5.35
−$10.35
−$15.35
−$15.35
−$15.35
−$10.35
−$5.35
−$.35
$4.65
27. Total cost = $4.55 − $1.24 = $3.31
Stock price
Long call payoff
$15.00
$0
$17.00
$0
$20.00
$0
$21.00
$1.00
$22.00
$2.00
$23.00
$3.00
$24.00
$4.00
$25.00
$5.00
$28.00
$8.00
$30.00
$10.00
Total payoff
$0
$0
$0
$1.00
$2.00
$3.00
$4.00
$5.00
$5.00
$5.00
Total profit
−$3.31
−$3.31
−$3.31
−$2.31
−$1.31
−$0.31
$.69
$1.69
$1.69
$1.69
Short call payoff
$0
$0
$0
$0
$0
$0
$0
$0
−$3.00
−$5.00
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28. Total cost = $0.45 − $1.64 = −$1.19
Stock price
Long put payoff
Short put payoff
$15.00
$5.00
−$10.00
$17.00
$3.00
−$8.00
$20.00
$0
−$5.00
$21.00
$0
−$4.00
$22.00
$0
−$3.00
$23.00
$0
−$2.00
$24.00
$0
−$1.00
$25.00
$0
$0
$28.00
$0
$0
$30.00
$0
$0
Total payoff
−$5.00
−$5.00
−$5.00
−$4.00
−$3.00
−$2.00
−$1.00
$0
$0
$0
Total profit
−$3.81
−$3.81
−$3.81
−$2.81
−$1.81
−$.81
$.19
$1.19
$1.19
$1.19
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Spreadsheet Problems
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CFA Exam Review by Kaplan Schweser
1. b
Put-call parity states: S  Vp  Vc  Xe –rt
So, Vp  $7.38  $100e
.07 (.5)
– $100  $3.94
(Note the use of continuous, as opposed to discrete, compounding.)
2. a
An increase in the dividend implies that the underlying stock price will decrease (or not increase
as much). So, the value of the call option will decline since IVcall  MAX  S  X, 0 
3. b
Put-call parity states: S + Vp = Vc + Xe –rt
 .07(.5)
So, Vp  14.84  100e
– 110  1.40
Chapter 16
Option Valuation
Concept Questions
1.
The six factors are the stock price, strike price, time to expiration, risk-free interest rate, stock price
volatility, and dividend yield.
2.
Increasing the time to expiration increases the value of an option. The reason is that the option gives
the holder the right to buy or sell. The longer the holder has that right, the more time there is for the
option to increase in value. For example, imagine an out-of-the-money option that is about to expire.
Because the option is essentially worthless, increasing the time to expiration obviously would
increase its value.
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3.
An increase in volatility acts to increase both put and call values because greater volatility increases
the possibility of favorable in-the-money payoffs, while the downside is still limited to the amount of
the premium paid. This is referred to as asymmetric payoffs.
4.
An increase in dividend yield reduces call values and increases put values. The reason is that, all else
the same, dividend payments decrease stock prices. To give an extreme example, consider a
company that sells all its assets, pays off its debts, and then pays out the remaining cash in a final,
liquidating dividend. The stock price would fall to zero, which is great for put holders, but not so
great for call holders.
5.
Interest rate increases are good for calls and bad for puts. The reason is that if a call is exercised in
the future, we have to pay a fixed amount at that time. The higher the interest rate, the lower is the
present value of that fixed amount. The reverse is true for puts in that we receive a fixed amount.
6.
The time value of both a call option and a put option is the difference between the price of the option
and the intrinsic value. For both types of options, as maturity increases, the time value increases
since you have a longer time to realize a price increase (decrease). A call option is more sensitive to
the maturity of the contract.
7.
An option’s delta tells us the (approximate) dollar change in the option’s value that will result from a
change in the stock price. If a call sells for $5.00 with a delta of .60, a $1 stock price increase will
add approximately $.60 to the option price, increasing it to $5.60.
8.
Vesting refers to the date at which an option can be exercised. For example, if the option has a 4year vesting period, it cannot be exercised for 4 years. Vesting is beneficial for the company because
it can be a ―golden handcuff.‖ Employees with valuable stock options, or options that can be
valuable in the future, are less likely to leave because of the actual or potential value of the employee
stock options.
9.
There are two possible benefits. First, awarding employee stock options may better align the interests
of the employees with the interests of the stockholders, lowering agency costs. Second, if the
company has little cash available to pay top employees, employee stock options may help attract
qualified employees for less pay.
10. The fact that employee stock options are not tradeable decreases their value relative to tradeable
stock options. An option always has value until it is exercised or expires. The ability to sell an option
is in itself an option; therefore, it must have some value.
Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this
solutions manual, rounding may appear to have occurred. However, the final answer for each problem is
found without rounding during any step in the problem.
Core Questions
1.
ln(84/80)  (.04  .422 / 2)  135 / 365
d1 
 .3766
.42  135 / 365
d 2  .3766 – .42  .1212
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The standard normal probabilities are:
N  d1   .6468
N  d 2   .5482
Calculating the price of the call option yields:
C   $84  .6468  –  $80  e –.04  135/365  .5482   $11.11
2.
ln(81 / 90)  (.03  .50 2 / 2)  60 / 365
d1 
 – .3 9 4 0
.50  60 / 365
d 2  – .3940 – .50  – .5968
The standard normal probabilities are:
N  d1   .3468
N  d 2   .2753
Calculating the price of the call option yields:
C   $81  .3468  –  $90  e –.03  60/365  .2753  $3.43
3.
ln(73 / 75)  (.05  .37 2 / 2)  100 / 365
 .0280
.37  100 / 365
d 2  .0280 – .37   .1657
d1 
The standard normal probabilities are:
N  d1   .5112
N  d 2   .4342
Calculating the price of the call option yields:
C   $73  .5112  –  $75  e –.05  100/365  .4342   $5.19
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4.
ln(63 / 60)  (.04 – .02  .432 / 2)  45 / 365
 .4150
.43  45 / 365
d 2  .4150 – .43  .2640
d1 
The standard normal probabilities are:
N  d1   .6609
N  d 2   .6041
Calculating the price of the call option yields:
C   $63  e –.02  45/365  .6609  –  $60  e –.04  45/365  .6041  $5.47
5.
ln(44 / 40)  (.041 - .025  .452 / 2)  65 / 365
 .6119
.45  65 / 365
d 2  .6119 – .45  .4220
d1 
The standard normal probabilities are:
N  d1   .7297
N  d 2   .6635
Calculating the price of the call option yields:
C   $44  e –.025  65/365  .7297  –  $40  e –.041  65/365  .6635  $5.62
6.
ln(68 / 70)  (.06  .412 / 2)  45 / 365
  .0780
.41  45 / 365
d 2  –.0780 – .41  – .2220
d1 
The standard normal probabilities are:
N  d1   .4689
N  d 2   .4122
N  – d1   .5311
N  – d 2   .5878
Calculating the price of the put option yields:
P   $70  e –.06  45/365  .5878 –  $68  .5311  $4.73
7.
ln(42 / 35)  (.05  .472 / 2)  140 / 365
 .8378
.47  140 / 365
d2  .8378 – .47  .5467
d1 
The standard normal probabilities are:
N  d1   .7989
N  d 2   .7077
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N  – d1   .2011
N  – d 2   .2923
Calculating the price of the put option yields:
P   $35  e –.05  140/365  .2923 –  $42  .2011  $1.59
8.
ln(67 / 80)  (.03  .302 / 2)  60 / 365
 – 1.3566
.30  60 / 365
d 2  –1.3566 – .30  –1.4782
d1 
The standard normal probabilities are:
N  d1   .0875
N  d 2   .0697
N  – d1   .9125
N  – d 2   .9303
Calculating the price of the put option yields:
P   $80  e –.03  60/365  .9303 –  $67  .9125   $12.92
9.
Number of option contracts = –
Portfolio beta  Portfolio value
Option delta  Option contract value
Number of option contracts  – 1.07  $300M  / .62  4, 030  $100    –1, 285  contracts to write 
10. You can either buy put options or sell call options. In either case, gains or losses on your stock
portfolio will be offset by gains or losses on your option contracts. To calculate the number of
contracts needed to hedge a $300 million portfolio with a beta of 1.15 using an option contract value
of $405,000 (100 times the index) and a delta of .50, we use the formula from the chapter:
Number of option contracts = –
Portfolio beta  Portfolio value
Option delta  Option contract value
Filling in the numbers, we need to write 1.15  $300M  / .5  $405, 000   –1, 704 call
contracts.
11. Up price = $45(1.15) = $51.75
Down price = $45(.87) = $39.15
Value of call in up price = Max($51.75 – 50, 0) = $1.75
Value of call in down price = Max($39.15 – 50, 0) = $0
C u - Cd
$1.75 - 0

 .1389
Su - Sd
$51.75 - 39.15
Su (1  r - u)  C u
(.1389)($45)(1  .025  1.15)  $1.75
Call 

 $.95
1 r
1  .025
Delta 
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12. Up price = $74(1.2) = $88.80
Down price = $74(.8) = $59.20
Value of call in up price = Max($88.80 – 75, 0) = $13.80
Value of call in down price = Max($59.20 – 75, 0) = $0
C u - Cd
$13.80 - 0

 .4662
Su - Sd
$88.80 - 59.20
Su (1  r - u)  Cu
(.4662)($74)(1  .042  1.20)  $13.80
Call 

 $8.01
1 r
1  .042
Delta 
13. Up price = $58(1.13) = $65.54
Down price = $58(.88) = $51.04
Value of call in up price = Max($65.54 – 55, 0) = $10.54
Value of call in down price = Max($51.04 – 55, 0) = $0
C u - Cd
$10.54 - 0

 .7269
Su - Sd
$65.54 - 51.04
Su (1  r - u)  Cu
(.7269)($58)(1  .03  1.13)  $10.54
Call 

 $6.14
1 r
1  .03
Delta 
Using put-call parity:
P  S0  C  K / 1  r 
P  $6.14  $55 /1.03 – $58
P = $1.54
Intermediate Questions
14. K = 0, so C = S = $70
15.  = 0, so d1 and d 2 go to +∞, so N  d1  and N  d 2  go to 1.
C   $68  1 –  $60  e –.05  6/12  1  $9.48
16. for  = ∞, d1 goes to +∞ so N  d1  goes to 1, and d 2 goes to –∞ so N  d 2  goes to 0; C = S = $55
ln(20.72/23.15)  (.043  .292 /2)  3.5
 .3443
17. d1 
.29  3.5
d2  .3443 – .29  – .1983
These standard normal probabilities are given:
N  d1   .6347
N  d 2   .4214
Calculating the price of the employee stock options yields:
ESO   $20.72  .6347  –  $23.15  e –.043  3.5  .4214 
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ESO = $4.76
18. This is a hedging problem in which you wish to hedge one option position with another. Your
employee stock option (ESO) position represents 10,000 shares, and you need to know how many
put option contracts are required to establish the hedge. First, we need to calculate deltas for both
options.
Using values from the previous answer, the ESO delta is:
ESO  Call  Delta  N  d1   .6347
For the put option, we get this value for d1 :
d1 
ln(20.72 / 22.50)  (.043  .292 / 2)  .25
 – .4217
.29  .25
These standard normal probabilities are given:
N  d1   .3366
N  – d1   .6634
Put option Delta  – N  – d1   – .6634
The number of put option contracts is then calculated as:
Number of option contracts  –
ESO delta 10,000
.6347  10,000
–
Put option delta  100
-.6634  100
Performing the calculation yields 95.67, or about 96, put option contracts.
19. After the volatility shift, we need to recalculate deltas for both options. The new value of d1 for the
ESO is:
d1 
ln(20.72/23.15)  (.043  .452 /2)  3.5
 0.4680
.45  3.5
In turn, the new ESO delta is:
ESO  Call  Delta  N  d1   0.6801
For the put option, we obtain this value for d1 :
d1 
ln(20.72/22.50)  (.043  .452 /2)  .25
 – .2060
.45  .25
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Put option Delta  – N  – d1   – .5816
The new number of contracts required is:
Number of option contracts = –
.680110, 000
.5816 100
Which yields 116.93, or about 117, put option contracts.
20. The stock price in one period will be:
Su  $60 1.15  $69.00
Sd  $60  0.87   $52.20
In two periods, the stock price will be:
Suu  $60 1.15 1.15   $79.35
Sud  $60 1.15 .87   $60.03
Sdd  $60  0.87 .87   $45.41
The call value for each node is:
Value of call Suu  Max ($79.35 – 60, 0)  $19.35
Value of call Sud = Max ($60.03 – 60, 0)  $.03
Value of call Sdd  Max ($45.41– 60, 0)  $0
The delta of the up and down moves will be:
Delta u 
C u - Cd
Su - Sd

$19.35 - 0.03
 1.000
$79.35 - 60.03
Delta d 
C u - Cd
Su - Sd

$0.03 - 0
 .0021
$60.03 - 45.41
So the call value after an up move will be:
Callu 
Su (1  r - u)  Cuu
1 r

(1.00)($69)(1  .032  1.15)  $19.35
 $10.86
1  .032
The value of a call with a first down move is $0 since it will always be worthless. The delta today is:
Delta 
C u - Cd
Su - Sd

$10.86 - 0.02
 .6455
$69.00 - 52.20
So, the value of a call today is:
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Call 
S(1  r - u)  C u
1 r

(.6455)($60)(1  .032  1.15)  $10.86
 $6.10
1  .032
21. The stock price in one period will be:
Su  $35 1.18   $41.30
Sd  $35 .85   $29.75
In two periods, the stock price will be:
Suu  $35 1.18 1.18   $48.73
Suu  $35 1.18 .85   $35.11
Sdd  $35 .85 .85   $25.29
The call value for each node is:
Value of call Suu  Max ($48.73 – 40, 0)  $8.73
Value of call Sud = Max ($35.11– 40, 0)  $0
Value of call Sdd = Max ($25.29 – 40, 0)  $0
The delta of the up and down moves will be:
Delta u 
C u - Cd
Su - Sd

$8.73 - 0
 .6408
$48.73 - 35.11
Delta d 
C u - Cd
Su - Sd

$0 - 0
 0
$35.11 - 25.29
So, the call value after an up move will be:
Callu 
Su (1  r - u)  Cuu
1 r

(.6408)($41.30)(1  .03  1.18)  $8.73
 $4.63
1  .03
The value of a call with a first down move is $0 since it will always be worthless. The delta today is:
Delta 
C u - Cd
Su - Sd

$4.63 - 0
 .4005
$41.30-29.75
So, the value of call today is:
Call 
S (1  r - u)  Cu
1 r

(.4005)($35)(1  .03  1.18)  $4.63
 $2.45
1  .03
Using put-call parity:
P  S0  C  K / 1  r 
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P  $2.45  $40 /1.03 – $35
P = $6.28
22. Notice that the call option is currently out-of-the-money, as the stock price of $78 is below the
exercise price of $80. Further, note that the ―up‖ move is a factor less than one, meaning that the
stock price is expected to fall on both the ―up‖ and down moves. Thus, if the stock’s price will be
less than it is today, then the option will always be out of the money, so its value is zero.
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Spreadsheet Answers
CFA Exam Review by Kaplan Schweser
1. c
ln(100 / 100)  (.07  .202 / 2)  1
 .4500
.20  1
d 2  .4500 – .20  .2500
d1 
The standard normal probabilities are:
N  d1   .6736
N  d 2   .5987
Calculating the price of the call option yields:
C   $100  .6736  –  $100  e –.07  1  .5987   $11.54
2. a
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Put-call parity states: S + Vp = Vc + Xe-rt
So, Vp  11.54  100e
.07 (1)
– 100  4.78
3. b
Due to the limited potential downside loss, changes in volatility positively affect option value for
both calls and puts.
4. b
The correct value is the delta of the put option.
Chapter 17
Alternative Investments
Concept Questions
1. Based on the principle of diversification, combining investments results in diversifiable (or asset
specific) risk being eliminated. This reduction is most pronounced when combining assets with low
correlation. This is the case with most alternative investments.
2. To be classified as an accredited investor in the United States, the person must have at least $1
million in net investible assets or have an income of at least $200,000 ($300,000 if married) in each
of the last two years. In addition, institutional investors such as pensions and endowments could also
be considered accredited. Due to the liquidity (and other risks) associated with alternative
investments, the government often limits participation to those who are able to withstand significant
losses.
3. Hedge funds and private equity funds invest in assets and in ways that are not standard. So, it is
difficult to compare them to more traditional indexes such as the S&P500. Moreover, there are no
standard indexes for these areas. So, investors are only able to compare the performance across funds
in the same general category.
4. When a hedge fund has a high-water mark, the manager will only receive performance fees when the
fund’s value is higher than its previous highest value. Should the investment drop in value in a given
period, then the manager must bring it back above the previous high-water mark before she can
receive performance fees again.
5. A fund of funds has two possible advantages. First, it provides diversification across categories and/or
managers. Second, they may also be able to improve the identification and selection of the best funds
to include. The primary disadvantage is the addition of another layer of fees.
6. A clawback provision requires the general partner (i.e., fund manager) to return capital in a case
where an early investment is favorable (therefore generating carried interest), only to be followed by
a series of poor investments. The clawback effectively causes general partners to withhold any payout
of carried interest until the fund is liquidated, or near liquidation.
7. With preferred stock, the fund may be able to specify a dividend that must be paid out each year, or
preferred stock may be used to provide some protection in the event of bankruptcy. The most critical
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aspect, however, is probably the conversion feature. This feature enables the venture capital fund to
retain upside return potential if the venture is successful. Thus, convertible preferred stock offers the
ability to enhance downside protection without forgoing upside return—the best of both worlds.
8. Contango in the futures market means that the futures price is higher than the spot price. When we
roll a contract in which we are long, we end up selling the current contract at a lower price than what
we pay to roll into the longer contract. Thus, each time we roll a contract we incur a loss, i.e. the roll
cost. So, it is possible that a commodity’s price remains flat, yet we sustain a loss on our investment if
we are using futures contracts to mimic the underlying commodity return.
9. Spot positions in commodities are essentially cash transactions. Since futures contracts trade via
margin, thereby creating leverage, futures are much more volatile. However, futures also require
lower upfront costs, and they also eliminate storage costs that would be incurred on spot holdings.
10. Since ETNs are effectively debt instruments of the fund issuer, investors are actually subject to
default risk. Further, many ETNs use futures contracts to mimic returns of underlying commodities,
which implies the existence of a roll cost.
11. A primary benefit of blockchain technology is less expensive, faster settlements for transactions.
What may have taken days, can now take place in a matter of minutes, all in a secure, private
transaction. All details of bitcoin ownership are encrypted, so owners, buyers, and sellers are all
anonymous. This anonymity is appealing to people wishing to protect their privacy for legitimate
reasons, but of course it is also appealing to people who wish to hide money from, e.g., tax collectors.
Blockchain technology can also be used for more than just transferring value. The ability to document
ownership has led to whole new classes of assets.
12. Among the major risks associated with cryptocurrency is volatility in prices. This is particularly
pronounced since there is no standard way to assign a true value to cryptocurrencies. Beyond this,
cryptocurrency is often held in a digital wallet, and losing the wallet means losing the currency.
Core Questions
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this
solutions manual, rounding may appear to have occurred. However, the final answer for each problem is
found without rounding during any step in the problem.
1. Dollar return = $10,000,000(.25) = $2,500,000
Fee = $2,500,000(.2) = $500,000
2. Value of 3 Hammer shares = 3($15) = $45
Buy 3 Hammer for $45 and short 1 Arm for $50. At the buyout, you will receive 1 share of Arm for
your 3 Hammer shares, which you can use to cover the short. You net $5 in arbitrage profit.
3. The management fee is paid on committed capital
Fee = $1,000,000,000(.02) = $20,000,000
4. Return above the hurdle = 18% − 6% = 12%
Carried interest = $10,000,000(.12)(.2) = $240,000
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5.
Multiple  18.6 / 2.9  6.41x
6. Margin = $4,500(25) = $112,500
7.
Margin percent  $4,500 /  5, 000  $15    .0600, or 6.00%
Leverage  1/ .06  16.67x
Cash return on silver   $17 – $15 / $15  .1333, or 13.33%
Levered return = 13.33%(16.67) = 222%
Alternatively, we could calculate the return as:
($17 − $15)(5,000) = $10,000
Return %  $10, 000 / $4,500  2.22, or 222%
8.
F  $3.17 1.03
9.
Value  $425, 000 / .15  $2,833,333
6/12
 $3.217
10. Value = NOI/rate
So, rate = NOI/Value  $945,000 / $5, 250,000  .180, or 18.0%
Intermediate Questions
11. Management fee = $25,000,000(.02) = $500,000
Amount invested = $25,000,000 − $500,000 = $24,500,000
End of year balance = $24,500,000(1.14) = $27,930,000
Performance fee = ($27,930,000 − $25,000,000)(.2) = $586,000 (note, at this point, the high-water
mark is the original investment of $25,000,000)
Balance after performance fee = $27,930,000 − $586,000 = $27,344,000
Investor return   $27,344, 000 – $25, 000, 000  / $25, 000, 000  .0938, or 9.38%
12. Year 1:
Management fee = $750,000(.02) = $15,000
Since there is a loss in Year 1, there is no performance fee.
Ending Year 1 balance = ($750,000 − $15,000)(.9) = $661,500
Year 2:
Management fee = $661,500(.02) = $13,230
Ending Year 2 balance (pre-fee) = ($661,500 − $13,230)(1.2) = $777,924
Performance fee = ($777,924 − $750,000)(.2) = $5,585 (note, at this point, the high-water mark is the
original investment of $750,000)
13. Multiples:
$96 / $20  4.80
$165.6 / $36  4.6
$50 / $30  5.0
Average = 4.80
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Price estimate = $28(4.80) = $134.40 million
14. Required FV of investment  $12 1.45   $76.92
5
Percentage of exit value  $76.92 / $380  .2024, or 20.24%
15. Margin percent  $5,500 / 1, 000  $55    .1000, or 10.00%
Leverage  1/ .10  10x
Cash return on oil   $56.25 – $55  / $55  .0227, or 2.27%
Levered return = 2.27%(10) = 22.7%
Alternatively, we could calculate the return as:
($56.25 − $55)(1,000) = $1,250
Return %  $1, 250 / $5,500  .227, or 22.7%
At the lower price of oil:
Cash return on oil   $54 – $55  / $55  – 0182, or –1.82%
Levered return = −1.82%(10) = −18.2%
16. NOI = $894,000(1 − .035) − $426,000 = $436,710
Valuation  $436, 710 / .16  $2, 729, 438
17. Price estimate = $125,000 + 1,500($35) + 2($8,000) − 5($6,000) = $163,500
18. Value = NOI/rate
So, rate = NOI/Value
Cap rates for comparables:
$2.2 / $13.75  .160, or 16.0%
$3.6 / $22.22  .162, or 16.2%
$2.7 / $16.46  .164, or 16.4%
Average = .162, or 16.2%
Value estimate  $3.1/ .162  $19.13 million
Spreadsheet Questions
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CFA Exam Review by Kaplan Schweser
1. a
Fund of funds charge their own fee, which adds an additional layer relative to those charged by
the underlying funds.
2. b
She is able to accept increased volatility.
3. a
Hedge funds lack performance comparisons and are generally more opaque.
4. b
While hedge funds have limited comparative data, individual companies would be even more
opaque.
Chapter 18
Corporate Bonds
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Concept Questions
1.
A bond refunding is a call in which an outstanding issue is replaced with a lower coupon issue. The
point is to replace a relatively high coupon issue with a lower coupon issue. All bond refundings
involve a call, but not all calls involve a refunding. For example, an issue may be called, but not
replaced.
2.
Call protection refers to the period during which the bond is not callable, typically five to ten years
for a corporate bond. The call premium is the amount above par that the issuer must pay to call the
bond; it generally declines to zero through time.
3.
A put bond gives the owner the right to force the issuer to buy the bond back, typically either at face
value or according to a preset price schedule. Obviously, the put feature is very desirable from the
owner’s perspective, but not the issuer’s.
4.
All else the same, a callable bond will have a higher yield (because buyers don’t like call features
and, therefore, demand a higher return); a putable bond will have a lower yield (because buyers like
put features).
5.
The advantage is that the coupon adjusts up when interest rates rise, so the bond’s price won’t fall (at
least not nearly as much as it would have). It cuts both ways, however. The coupon will fall if
interest rates decline, so the owner will not experience the price gains that otherwise would have
occurred.
6.
Some examples of embedded options in bonds are: 1) Put bonds have a put option feature that gives
the bondholder the right to sell the bond back to the issuer at a preset price. The put feature makes
the bond more valuable to the bondholder, so a put bond has a higher price than a comparable nonputable bond. 2) Convertible bonds have a call option feature that gives the bondholder the right to
buy stock from the issuer at a preset price. The call option makes the bond more valuable to the
bondholder, so a convertible bond has a higher price than a comparable non-convertible bond. 3)
Callable bonds have a call option feature that gives the issuer the right to buy the bonds back from
the bondholder at a preset price. The call feature makes the bond less valuable to the bondholder, so
a callable bond has a lower price than a comparable non-callable bond.
7.
The critical distinction lies in their credit ratings when they were first issued. Original issue junk
refers to a bond that had a credit rating below investment grade when it was first issued. A fallen
angel had a credit rating of investment grade when it was first issued, but has since fallen to below
investment grade.
8.
Because of the negative convexity effect, callable bonds cannot rise in value as far as noncallable
bonds, so they do have less interest rate sensitivity. Also, a callable bond may ―mature‖ sooner than
an otherwise identical noncallable issue (because it is called), so this shorter effective maturity also
means less interest rate sensitivity. Unfortunately, the smaller interest rate sensitivity is almost all on
the upside, so it is not a good thing.
9.
A refunding provision restricts the ability of an issuer to call their bonds. Such a provision specifies
that the issuer cannot call their bonds for the purpose of refunding their debt with a new bond issue.
Since this is the most common reason that bonds are called (i.e., for a refunding), a bond issue with a
refunding provision is far less likely to be called by its issuer than a comparable callable bond
without a refunding provision.
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10. T-bills are pure discount, zero-coupon instruments with original maturities of one year or less. Tbonds are straight coupon bonds with original maturities greater than ten years. A small number of
previously issued T-bonds are callable.
11. Agencies have slightly more credit risk. They are subject to state taxes, they have a variety of call
features, and they are less liquid (and have wider spreads). These factors translate into a somewhat
higher yield. Agencies offer a wider variety of maturities and bond types as well. Pricing structure
may also differ, as Treasuries have updated to decimal pricing, while agencies are following the
historical convention of pricing in increments of 32nds of one percent.
12. Treasuries are subject to federal taxes, but not state and local taxes. Munis are tax-exempt at the
federal level. They are usually exempt at the state level only within the issuing state. Munis can have
significantly greater default risk, and they are, for the most part, much less liquid. Munis are
generally callable, whereas most Treasuries are not.
13. A general obligation (GO) muni is backed by the full faith and credit (i.e., the taxing power) of the
issuer. A revenue bond is backed only by the revenue produced from a specific project or activity.
14. To a certain extent, it’s an apples and oranges issue. Munis are much less liquid, have greater default
risk, are generally callable fairly early in their lives, and may be subject to state taxes if a capital gain
is realized. These factors increase muni yields. As a result, when critical tax rates are calculated, they
are likely to be too low. A better approach is to compare munis to corporate bonds with similar
features and risks. An even better approach is to compare taxable and nontaxable munis.
15. It is true. The reason is that Treasuries are callable at par. Referring back to Chapter 10, if two
premium bonds have the same price and the same coupon rate, but different maturities (i.e., the call
date and the final maturity date), the one with the shorter maturity has the lower yield. This has to be
true because of the ―pull to par,‖ i.e., the fact that for a given yield a premium bond’s price will
decline as maturity approaches.
Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this
solutions manual, rounding may appear to have occurred. However, the final answer for each problem is
found without rounding during any step in the problem.
While we show calculations using equations, many from this chapter are more easily completed using a
financial calculator. Each input, however, is easily identified from the equations we provide.
Core Questions
1.
$1,000 / 45  $22.22
2.
$1,000 / $58  17.24
3.
36 × $42 = $1,512
4.
120% − 4 × 2% = 112%
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5.
P  $1,070  $30  PVIFA3.45%,10   $1000  PVF3.45%,10   CP  PVF3.45%,10  ; CP  $150.94
6.
The minimum value is the larger of the conversion value or the intrinsic bond value. The conversion
value is 25 × $49 = $1,225. To calculate the intrinsic bond value, note that we have a face value of
$1,000 (by assumption), a semiannual coupon of $25, an annual yield of 4 percent (2 percent per
half-year), and 10 years to maturity (20 half-years). Using the standard bond pricing formula from
our previous chapter, the bond’s price if it were not convertible is $1,081.76. Thus, this convertible
bond will sell for at least (if not more than) $1,225.
7.
You can convert or tender the bond (i.e., surrender the bond in exchange for the call price). If you
convert, you get stock worth 20 × $72 = $1,440. If you tender, you get $1,080 (108 percent of par).
It’s a no-brainer: convert.
8.
$10,000 / 1  .052 / 2   $5, 400.87
9.
$7,693  $10,000 / 1  R  ; R  1.468%; YTM  1.468%  2  2.94%
24
18
10. Bonds available for competitive bids = $60B − $8B = $52 billion
Beginning with the highest bid ($9,430), we get $9B + $10B + $8B + $11B + $14B = $52 billion, so
the competitive bid price is $9,405. All bids above this will be accepted, along with the $8B
noncompetitive bids. The amount raised is  $9,405 / $10,000   $60B  $56.43 billion. Note that
if the competitive bids are for a larger value than is available, there will be an allocation.
11. $67.50(PVIFA1.95%,20 )  $5,000(PVIF1.95%,20 )  $4,507.08
12. $4,920  $155(PVIFA R %,14 )  $5,000(PVIFR %,14 ); R  3.244%, YTM  6.49%
13. $5,640  $142.50(PVIFA R %,20 )  $5,000 1.10  (PVIFR %,20 ); R  2.429%, YTC  4.86%
14. 6.50%(1 − .35) = 4.23%
15. 1 – .047 / .064  .2656, or 26.56%
Intermediate Questions
16. You must buy at the asked yield of 2.73%. This implies a price of:
$1,000  1 – .0273  152 / 360   $988.473 per $1,000 purchased.
17. You must sell at the bid yield of 2.75%. This implies a price of:
$1,000  1 – .0275  152 / 360   $988.389 . Thus, the dollar spread is $988.473 − $988.389 =
$.084 per $1,000 of bonds.
18. The minimum face value is $1,000. You must pay the ask price of 102.375 percent of face. This
amounts to $1,023.75.
19. $994.375  $23(PVIFA R %,60 )  $1,000(PVIFR %,60 ); R  2.317%, YTM  4.63%
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20. Conversion value = $32 × 25 = $800; Conversion price = $1,050 / 25  $42.00
21. An increase in the stock’s price volatility increases the bond price. The conversion option on the
stock becomes more valuable. An increase in interest rate volatility decreases the bond value. The
chance of the bond being called increases, causing the value of the call option on the bond to become
more valuable, thereby pushing down the value of the bond.
22. Conversion price  $960 / 25  $38.40
One  year bond return   $1,080  $60 – $960  / $960  .1875, or 18.75%
One  year stock return   $54 – $42  / $42  .2857, or 28.57%
23. The two components are the straight bond value (its value as a bond) and the option value (the value
associated with the potential conversion into equity).
The increase in equity price does not affect the straight value of the Sands’ convertible but does
increase the option component value significantly, because the conversion option becomes deep inthe-money when the equity price is compared to the convertible’s conversion price.
Spreadsheet Problems
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CFA Exam Review by Kaplan Schweser
1. c
The call option value is the difference between the value of the callable bond and the value of the
otherwise equivalent non-callable bond ($100.83 − $98.79 = $2.04).
2. a
All option values increase when the volatility of the underlying asset increases. This is due to the
asymmetric payoff of options.
3. c
Since the bond has a fixed coupon, it becomes relatively less attractive to investors when interest
rates increase. Its cash flows are now discounted at a higher discount rate, which reduces the
value of the bond. This is true for both callable and non-callable bonds.
Chapter 19
Projecting Cash Flow and Earnings
Concept Questions
1.
The 10K and 10Q are reports public firms must file with the SEC. They contain, among other things,
financial statements including balance sheets, income statements, and cash flow statements. The
easiest way to retrieve them is online from EDGAR.
2.
The reason is that, ultimately, sales are the driving force behind a business. A firm’s assets,
employees, and, in fact, just about every aspect of its operations and financing exist to directly or
indirectly support sales. Put differently, a firm’s future need for things like capital assets, employees,
inventory, and financing are determined by its future sales level.
3.
They are current in the sense that they are expected to convert to cash (or otherwise be used up)
within the next 12 months. Operating assets are current because they consist of current assets other
than cash.
4.
Earnings per share are equal to net income divided by the number of shares outstanding. Net income
is sometimes called ―total earnings.‖ There are some issues concerning how to measure shares
outstanding, but these go beyond the scope of this chapter.
5.
Depreciation is a ―noncash item‖ because the depreciation deduction does not literally represent a
cash outflow. It is instead purely an accounting entry.
6.
It is the cash generated by ordinary business activity, meaning the everyday, routine functioning of
the business.
7.
ROE is a better measure of the company’s performance. ROE shows the percentage return for the
year earned on shareholder investment. Since the goal of a company is to maximize shareholder
wealth, this ratio shows the company’s performance in achieving this goal over the period. ROA
would be a better measure if the focus was purely operating efficiency.
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8.
The retained earnings number on the income statement is the amount retained that year. The number
on the balance sheet is the cumulative amount from all previous years. Put differently, the income
statement number is the increment or addition to the balance sheet number.
9.
Gross margin is gross profit divided by sales, where gross profit is sales less cost of goods sold.
Operating margin is operating profit divided by sales, where operating profit is equal to gross profit
less operating expenses. Thus, the difference is that operating margin considers both costs of goods
sold and operating expenses. It indicates how much of each sales dollar is left after accounting for
costs of goods sold (gross margin) and, additionally, for operating expenses (operating margin).
Generally speaking, larger values are better.
10. Gross margin will generally be larger since operating margin deducts additional expenses beyond
cost of goods sold. Both can be negative. Also, gross margin can be positive while operating margin
is negative, but not the other way around.
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Core Questions
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this
solutions manual, rounding may appear to have occurred. However, the final answer for each problem is
found without rounding during any step in the problem.
1.
Sales
Cost of goods sold
Gross profit
Operating expense
Operating income
Investment income
Investment expense
Pretax income
Income taxes
Net income
Dividends
Retained earnings
2.
Cash
Operating assets
Fixed assets
Investments
Other assets
Total assets
3.
$318,000
164,000
$154,000
71,000
$83,000
1,200
7,400
$76,800
16,128
$60,672
$3,200
$57,472
$21,000
64,000
150,000
32,000
36,000
$303,000
Current liabilities
Long-term debt
Other liabilities
$42,000
102,000
11,000
Stockholder equity
Total liabilities and equity
148,000
$303,000
Gross margin  $154,000 / $318,000  .4843, or 48.43%
Operating margin  $83,000 / $318,000  .2610, or 26.10%
ROA  $60,672 / $303,000  .2002, or 20.02%
ROE  $60,672 / $148,000  .4099, or 40.99%
4.
BVPS  $148,000 / 17,000  $8.71
EPS  $60,672 / 17,000  $3.57
CFPS   $60,672  $15,000  / 17,000  $4.45
5.
Price  book  $48 / $8.71  5.51
Price  earnings  $48 / $3.57  13.45
Price  cash flow  $48 / $4.45  10.78
6.
An increase of sales to $6,240 is an increase of:
Sales increase   $6, 240 – $4,800  / $4,800
Sales increase = .30, or 30%
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Assuming costs and assets increase proportionally, the pro forma financial statements will look like
this:
Pro forma
Pro forma
income
balance sheet
statement
Sales
$ 6,240 Assets
Costs
Net income
$ 18,460 Debt
4,134
$ 2,106 Total
$ 9,900
Equity
6,406
$ 18,460 Total
$ 16,306
If no dividends are paid, the equity account will increase by the net income, so:
Equity = $4,300 + $2,106
Equity = $6,406
So, the EFN is:
EFN = Total assets − Total liabilities and equity
EFN = $18,460 − $16,306 = $2,154
7.
Depreciation per share  $310,000 / 140,000  $2.21
Operating cash flow per share = $1.64 + $2.21 = $3.85
Price  cash flow  $43 / $3.85  11.16
8.
EPS  $98,000 / 28,000  $3.50
9.
Total dividends = $1.28 × 75,000 = $96,000
Addition to Retained Earnings = $520,000 − $96,000 = $424,000
10.
Net income
Dep and amort.
Operating cash flow
Net property purchases
Purchase of equipment
Investing cash flow
Issue / Redeem Stock
Issue / Redeem LTD
Dividends paid
Financing cash flow
Net cash increase
$175
52
$227
$10
(70)
($60)
$7
(18)
(9)
($20)
$147
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11. An increase of sales to $31,625 is an increase of:
Sales increase   $31,625 – $27,500  / $27,500
Sales increase = .15, or 15%
Assuming costs and assets increase proportionally, the pro forma financial statements will look like
this:
Pro forma
income
statement
Sales
Costs
EBIT
Taxes (21%)
Net income
Pro forma
balance sheet
$31,625.00 Assets
22,367.50
9,257.50 Total
1,944.08
$ 7,313.43
$120,750.00 Debt
Equity
$120,750.00 Total
$ 43,000.00
68,335.85
$111,335.85
The payout ratio is constant, so the dividends paid this year is the payout ratio from last year times
net income, or:
Dividends   $850 / $6,359  $7,313.43
Dividends = $977.58
The addition to retained earnings is:
Addition to retained earnings = $7,313.43 − $977.58
Addition to retained earnings = $6,335.85
And, the new equity balance is:
Equity = $62,000 + $6,335.85
Equity = $68,335.85
So, the EFN is:
EFN = Total assets − Total liabilities and equity
EFN = $120,750 − $111,335.85
EFN = $9,414.15
Intermediate Questions
12. Gross margin is $1,900 / $7,800  .2436 , or 24.36%. Operating margin is $910 / $7,800  .1167 ,
or 11.67%.
13. Return on assets  ROA  is $530 / $4,030  .1315, or 13.15%.
Return on equity  ROE  is $530 / $1,710  .3099, or 30.99%.
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14. Note that, measured in thousands, there are 265 shares. Book value per share (BVPS) is thus
$1,710 / 265  $6.45 . Earnings per share (EPS) is $530 / 265  $2.00 (as shown on the income
statement). Cash flow per share (CFPS) is  $530  $175 / 265  $2.66 . The recent price per share
is $34.50, so the Price/Book ratio is 5.35; the Price/Earnings ratio is 17.25; and the Price/Cash flow
ratio is 12.97.
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15. With a 10% sales increase, sales will rise to $8,580. A constant gross margin is assumed, implying
that Cost of Goods Sold will also increase by 10%. A constant tax rate is used. Items in italics are
carried over unchanged. The pro forma income statement follows
Net sales
Cost of goods sold
Gross profit
Operating expense
Operating income
Other income
Net interest expense
Pretax income
Income tax
Net income
Earnings per share
Shares outstanding
Kiwi Fruit Company Pro Forma Income Statement
$8,580
(6,490)
$2,090
(990)
$1,100
70
(250)
$920
(252)
$668
$2.52
265,000
Next, we prepare the cash flow statement. Notice that we pick up the $668 net income from the pro
forma income statement. Items in italics are carried over unchanged. By assumption, no investments
occur, and no long-term debt is issued or redeemed.
Kiwi Fruit Company Pro Forma Cash Flow Statement
Net income
$668
Dep and amort.
175
Chg. in operating assets
(90)
Chg. In current liabilities
(120)
Operating cash flow
$633
Net additions to property
$0
Changes in other assets
0
Investing cash flow
$0
$0
Issue / Redeem LTD
Dividends paid
(220)
Financing cash flow
($220)
Net cash increase
$413
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Finally, we have the balance sheet. Cash rises by $413. Net cash flow is from the cash flow
statement. The $90 increase in Operating Assets and the $120 decrease in Current Liabilities are also
from the cash flow statement. The $175 reduction in Property, Plant, and Equipment is the amount
of the depreciation deduction shown on the cash flow statement. The increase in retained earnings is
equal to pro forma Net Income less pro forma Dividends.
Cash and equiv.
Operating assets
PP & E
Other assets
Total assets
Current liabilities
Long-term debt
Other liabilities
Total liabilities
Paid in capital
Retained earnings
Total equity
Total L&E
Kiwi Fruit Company Pro Forma Balance Sheet
$983
740
2,525
110
$4,358
$800
1,280
120
$2,200
$340
1,818
$2,158
$4,358
We should note that the assumptions made here could vary, so good analysts may (and will) come up
with different values.
16. Using the benchmarks from question 14, projected stock prices are:
BVPS  P / B  $8.14  5.35  $43.54
EPS  P / E  $2.52  17.25  $43.48
CFPS  P / CF  $3.18  12.97  $41.25
Thus, projected prices assuming a 10% sales increase are in the $41.25− $43.54 range.
17. Full capacity sales  $480,000 / .75
Full capacity sales = $640,000
The maximum sales growth is the full capacity sales divided by the current sales, so:
Maximum sales growth   $640,000 / $480,000  – 1
Maximum sales growth = .3333, or 33.33%
18. To find the new level of fixed assets, we need to find the current percentage of fixed assets to full
capacity sales. Doing so, we find:
Fixed assets / Full capacity sales  $420,000 / $640,000
Fixed assets / Full capacity sales  .6563
Next, we calculate the total dollar amount of fixed assets needed at the new sales figure.
Total fixed assets = .6563($695,000)
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Total fixed assets = $456,094
The new fixed assets necessary is the total fixed assets at the new sales figure minus the current level
of fixed assets.
New fixed assets = $456,093.75 − $420,000
New fixed assets = $36,093.75
Spreadsheet Problems
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CFA Exam Review by Kaplan Schweser
1. a
At the time of payment to the supplier, operating cash flow (OCF) decreases and CFF increases
by the amount of the payment, leaving total cash flow unaffected.
2. b
Securitizing accounts receivable is unsustainable because it accelerates future operating cash
flows into the current period. Since there is a gain, the firm could recognize it as a reduction in
operating expenses (instead of as revenue). It does not reclassify financing cash flow as operating
cash flow.
3. a
If VirtualCon delayed payment by 90 days instead of paying the suppliers on time, its CFO would
be higher in the intervening 90 days becaue it would not be reduced by the amount of the
payment. Its CFF would be lower because it would not be increased by the amount of the
payment.
Chapter 20
Global Economic Activity and Industry Analysis
Concept Questions
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1. If the economy was in recession, the Federal Reserve would likely undertake a loose monetary policy.
This may involve reducing the discount rate or conducting open market purchases.
2. Investors want to invest in assets that are appreciating. As such, an appreciating Australian dollar
would make an investment in Australia more attractive.
3. Top-down analysis begins with a broad choice of securities and attempts to narrow it down to a
smaller set. The filtering process typically begins with macroeconomic analysis to determine which
industries may be attractive. Subsequent analysis then revolves around industry and company specific
information.
4. Industrials would be more sensitive to the business cycle as spending on such items is driven by GDP
growth. Healthcare is less sensitive since it is not as dependent on GDP.
5. Consumer spending represents a majority of GDP. Thus, changes in consumer confidence, which
impact spending, may lead to changes in GDP.
6. If inflation increases, interest rates would likely follow. An increase in rates, all else equal, leads to a
reduction in bond prices, with long-term bonds being impacted to a greater degree. Thus, short-term
securities would be preferred. Another way to think about this is that with shorter term securities,
increasing rates can be captured as securities are rolled over. With longer term securities the investor
is stuck with a lower rate for an extended period.
7. A patent effectively acts as a barrier to entry, at least for a particular product. A patent expiration
thereby reduces barriers and increases competitiveness. As such, a patent expiration is usually
associated with lower prices and reduced profits for the affected areas.
8. Supply-side economists generally believe that lower taxes spur growth and thereby actually leads to
higher tax revenue. Thus, (b) would be consistent with supply side economics.
9. Inflation reduces purchasing power. Thus, if GDP (or wages) rises by 3%, but inflation is 5%, the
amount of goods one can buy is actually lower in real terms.
10. High governmental debt ―crowds out‖ the private sector. For example, if there is a fixed supply of
funds, an increase in government borrowing means less funds available for the private sector. Further,
this added demand for funds may increase interest rates, which creates an added cost for private firms
and individuals.
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Core Questions
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this
solutions manual, rounding may appear to have occurred. However, the final answer for each problem is
found without rounding during any step in the problem.
1.
Money multiplier  1 / .18  5.56
Maximum amount = $2 × 5.56 = $11.11 billion
If there is low demand for loanable funds or if banks choose to hold more than required, then the
amount will be lower.
2.
Money multiplier  300 / 60  5.00
Reserve requirement  1 / 5  .20, or 20%
3.
Inflation  125.6 / 123.9 – 1  .0137, or 1.37%
This value implies that the general price of goods has increased by 1.37% over the period. So, it
would take 1.37% more money to buy the same basket of goods.
4.
Beginning value  154.65 / 1.022  151.32
5.
Approximate real growth = 3.2% – 2.8% ≈ .4%
6.
Real  nominal / 1  inflation 
122.8  124.9 / 1  inflation 
Inflation = .071, or 1.71%
7.
Real GDP  $1, 425.68 / 1.043  $1,366.9 billion
8.
Unemployment rate  10 / 155  .0645, or 6.45%
Intermediate Questions
9.
2022 Inflation rate  196.8 / 190.3 – 1  .0342, or 3.42%
5  year average rate  196.8 / 174 
1/5
– 1  .0249, or 2.49%
10. Nominal 2021 GDP Growth  136.1 / 125.4 – 1  .0853, or 8.53%
Nominal 2022 GDP Growth  138.2 / 136.1 – 1  .0154, or 1.54%
11. 2021 Inflation rate  106.1.1 / 105.3 – 1  .0076, or .76%
2022 GDP Growth  106.4 / 106.1 – 1  .0028, or .28%
2021 Real GDP Growth = 8.53% – .76% = .0777, or 7.77%
2022 Real GDP Growth = 1.54% – .28% = .0126, or 1.26%
12. $1,500,000 / .0245  61, 224, 489.8 rupees
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13. Beginning yen = $125,000(84.28) = 10,535,000
Ending yen = 10,535,000(1.07) = 11,272,450
Ending dollars  11,272,450 / 82.56  $136,536.46
Total return   $136,536.46 / $125,000  – 1  .0923, or 9.23%
14. Beginning yen = $125,000(84.28) = 10,535,000
Ending yen = 10,535,000(1.07) = 11,272,450
Ending dollars  11,272,450 / 88.65  $127,156.80
Total return   $127,156.80 / $125,000  – 1  .0173, or 1.73%
The total return comes from the investment return and the exchange rate movement. In this case, the
yen depreciated, thereby offsetting some of the investment return that was earned.
15. Beginning pesos = $785,000(12.2) = 9,577,000
Ending pesos = 9,577,000(1.10) = 10,534,700
Ending dollars  10,534,700 / 12.5  $842,776
Total return   $842,776 / $785,000  – 1  .0736, or 7.36%
Spreadsheet Questions
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CFA Exam Review by Kaplan Schweser
1. a
If the French currency appreciates relative to the English currency, this will make the product
more expensive to the English customers.
2. a
The profit margins and number of firms in the industry is declining.
3. c
Consumers are switching to other products (1) and modes of purchase (2). Further, a large portion
of sales come from a small segment of the market (4).
4. b
Chapter 21
Mortgage-Backed Securities
Concept Questions
1.
Mortgage securitization benefits borrowers by reducing interest rates. Interest rates are reduced
because securitization increases liquidity in the mortgage market. More liquid mortgages have higher
prices and, hence, lower interest rates.
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2.
It benefits mortgage originators by allowing them to transfer the risk associated with holding
mortgages and instead focus on what they do best, originating mortgages. Also, and equally
important, by selling mortgages, originators obtain new funds to loan out.
3.
For the same rate and original balance, the 15-year mortgage will have higher payments because a
larger principal payment must be made each month to pay off the loan over a shorter time, even
though the interest component may be smaller.
4.
Only GNMA is a federal agency, and GNMA securities are backed by the full faith and credit of the
U.S. government. The other two, in principle, do not have this backing. As a practical matter,
however, the difference is slight.
5.
It means that timely payment of both principal and interest is guaranteed.
6.
Mortgages are prepaid because the underlying property is sold, interest rates fall, or the owner
otherwise wishes to refinance (perhaps to increase the loan balance as a way to obtain funds for other
purposes) or pay off the mortgage. When interest rates fall, prepayments accelerate. Larger drops
lead to sharp increases in prepayment rates.
7.
The call feature on a bond gives the borrower the right to buy the bond (i.e., pay off the debt) at a
fixed price. The right to prepay a mortgage gives the borrower the same right.
8.
Prepayments that result purely from interest drops are a risk; the mortgage investor will have to
reinvest at a lower rate. However, some mortgages are prepaid for other reasons, such as the sale of
the underlying property. This can happen even if interest rates have risen substantially; such a
prepayment benefits the mortgage investors. Thus, not all prepayments are bad, just those that result
in the need to reinvest at a lower rate.
9.
For a fully modified mortgage pool, all cash flows are guaranteed to be paid in a timely manner,
meaning that no cash flows will be paid out late. The guarantee does, however, allow cash flows to
be paid out early, which occurs in the case of defaults. When a default occurs, the remaining balance
on the defaulting mortgage is paid out immediately. Thus to a mortgage pool investor, a default
appears as a prepayment since in both cases an early payment of principal is realized.
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10. A collateralized mortgage obligation (CMO) is a mortgage-backed security with cash flows that are
divided into multiple securities. They exist because they provide a means of altering some of the less
desirable characteristics of MBSs, thereby increasing marketability to a broader class of investors.
More fundamentally, they exist because investment banks (the creators and marketers) have found
them to be a profitable product! The three best-known CMO structures are interest only/principal
only strips, sequential CMOs, and protected amortization class securities.
11. Every mortgage payment has an interest portion and a principal portion. IO and PO strips are very
simple CMOs; the interest and principal portions are separated into distinct payments. Holders of IO
strips receive all the interest paid; the principal goes to holders of PO strips. If interest rates change,
the IO strips (especially the longer dated ones) are vastly riskier. With PO strips, the only uncertainty
is when the principal is paid. All PO strips-holders will receive full payment. With an IO strip,
however, prepayment means that no future interest payments will be made, so the amount of interest
that will be received is unknown.
12. PO strips have greater interest rate risk if we define interest rate risk to mean losses associated with
interest rate increases and gains associated with interest rate decreases. When interest rates go up,
prepayments slow down, thereby postponing the time until principal is received. In this case, IO
strips can actually behave like ―inverse floaters.‖ Their value tends to rise when interest rates
increase. The reason is that slowing prepayments increases the interest that will be received by IO
strips-holders. However, the value of IO strips falls when interest rates decrease.
13. The A-tranche will essentially receive all of the payments, both principal and interest, until it is fully
paid off. The Z-tranche receives nothing until the A-tranche is paid off. After that, the Z-tranche
receives everything. The Z-tranche is much riskier because the size and timing of the payment is
more uncertain.
14. With a protected amortization class (PAC) CMO, payments are made to one group of investors
according to a set schedule. This means that the protected class investors have almost fully
predictable cash flows. After protected class investors are paid, all the remaining cash flow goes to
non-PAC investors, who hold PAC support or PAC companion bonds. In essence, one group of
investors receives fixed payments, the other group absorbs all (or virtually all) the uncertainty
created by prepayments.
15. Macaulay duration assumes fixed cash flows. With MBSs and CMOs, the payments depend on
prepayments, which in turn depend on interest rates. When prepayments pick up, duration falls, and
vice versa. Thus, no single measure is accurate. Effective duration attempts to account for the
possibility that mortgage pool cash flows can vary. Effective duration for a mortgage pool will
typically be based on a prepayment model that accounts for the effects of changing interest rates on
prepayments.
Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this
solutions manual, rounding may appear to have occurred. However, the final answer for each problem is
found without rounding during any step in the problem.
Core Questions
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
1.
$315,000 .049 / 12   / 1 – 1 / 1  .049 / 12 

2.
$1, 240 1 – 1 / 1  .045 / 12 

3.
$417,000 .052 / 12   / 1 – 1 / 1  .052 / 12 

4.
$1,500 1 – 1 / 1  .0525 / 12 

5.
1 – 1 – .07 
6.
7.
8.
9.

360


1/12
360

  $1,671.79


 / .045 / 12   $244,727.84
 
360
360

  $2, 289.79


 / .0525 / 12   $271,638.89
 
 .006029, or .6029%
00426  1 – 1 – CPR  ; CPR  .0499, or 4.99%
$107,680 – $52,973 = $54,707
360
Payment  $250,000 .054 / 12   / 1 – 1 / 1  .054 / 12    $1, 403.83


The interest in the first month is equal to the original loan amount ($250,000) multiplied by the
interest rate, .054 / 12  .0045 , or .45% per month. Thus, the interest amounts to $1,125. The
remaining $1,403.83 – $1,125 = $278.83 is principal. The interest allocation for the second payment
is $1,123.75, and the principal reduction is $280.08.
1/12



Payment  $140,000 .076 / 12   / 1 – 1 / 1  .076 / 12 


180

  $1,305.79


96
Balance  $1,305.79 1 – 1 / 1  .076 / 12   / .076 / 12   $93,710.71



10. Payment  $145,000 .061 / 12   / 1 – 1 / 1  .061 / 12 


Balance  $878.69 1 – 1 / 1  .061 / 12 

264

360
  $878.69


 / .061 / 12   $127,532.15

Intermediate Questions

11. Original payment  $160,000 .06 / 12   / 1 – 1 / 1  .06 / 12 


Balance  $959.28 1 – 1 / 1  .06 / 12 

300

360

  $959.28


 / .06 / 12   $148,886.97

New payment  $148,886.97 .05 / 12   / 1 – 1 / 1  .05 / 12 

Savings = $959.28 – $870.38 = $88.90

300
  $870.38


12. Original payment  $350,000 .0725 / 12   / 1 – 1 / 1  .0725 / 12 


Balance  $2,529.82 1 – 1 / 1  .0725 / 12 

180


  $2,529.82


 / .0725 / 12   $277,130.78

New payment  $277,130.78 .054 / 12   / 1 – 1 / 1  .054 / 12 

Savings = $2,529.82– $2,249.71 = $280.11
180

300
  $2, 249.71


13. Original payment  $230,000 .0690 / 12   / 1 – 1 / 1  .0690 / 12 

360
  $1,514.78


164
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
Balance  $1,514.78 1 – 1 / 1  .069 / 12 

300

 / .069 / 12   $216, 269.67


New payment   $216, 269.67  $2,500 .057 / 12   / 1 – 1 / 1  .057 / 12 

Savings = $1,514.78 – $1,369.69 = $145.09

14. Original payment  $220,000 .0720 / 12   / 1 – 1 / 1  .0720 / 12 


Balance  $1, 493.33 1 – 1 / 1  .0720 / 12 

240
360

300
  $1,369.69


  $1, 493.33


 / .0720 / 12   $189,666.02

$189,666.02  $3,500  $1, 493.33  PVIFA R %,240  ; R  .58%; APR  6.96%

15. Original payment  $120,000 .0795 / 12   / 1 – 1 / 1  .0795 / 12 


Balance  $876.34 1 – 1 / 1  .0795 / 12 

180

360
  $876.34


 / .0795 / 12   $91,978.17

$91,978.17  $2,000  $876.34  PVIFA R %,180  ; R  0.633%; APR  7.60%
16. For a seasoned 100 PSA mortgage, the CPR is 3 percent per year.
PSA 50 : CPR   50 / 100 .03  .0150, or 1.50%
PSA 200 : CPR   200 / 100 .03  .0600, or 6.00%
PSA 400 : CPR   400 / 100 .03  .1200, or 12.00%
These CPRs have two (more or less) equivalent interpretations. They are an estimate of the
probability that any given mortgage in the pool will prepay in a given year. A more useful
interpretation is that they are an estimate of the percentage of outstanding principal that will be
prepaid in a given year. In other words, if the odds of prepayment are 3 percent for any given
mortgage, then we expect that 3 percent of all mortgages will prepay, meaning that 3 percent of the
principal in a mortgage pool will be prepaid per year.
17. PSA 50 : SMM  1 – 1 – .015 
1/12
PSA 200 : SMM  1 – 1 – .06 
1/12
 .001259, or .1259%
 .005143, or .5143%
PSA 400 : SMM  1 – 1 – .12   .010596, or 1.0596%
Notice that the 400 PSA is not double 200; there’s a compound interest-type effect in the calculation.
The SMM estimates the probability of prepayment in a given month. Thus, with 50 PSA, it is
estimated that .1259 percent of mortgages will prepay in a given month.
1/12
Spreadsheet Problems
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166
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CFA Exam Review by Kaplan Schweser
1. a
CPRs are industry benchmarks. SMM is computed as follows:
SMM  1 – 1 – CPR 
1/12
2. c
A mortgage loan can be refinanced at any time. This is, in effect, a call option. The other two
characteristics are consistent with mortgage loans and not traditional corporate bonds.
3. b
This is just the weighted average of the mortgage rates. The contribution of each pool to the
WAC is found by multiplying the weight of the pool by its respective coupon. The WAC is then
found by adding all of the results together in the following manner:
.1961  8.25%  .2941  7.7%   .3431  6.9%   .1667  9.2%  7.78%
4. b
SMM  1 – 1 – CPR 
At 200 PSA, we must double the CPR. As such, the equation is:
SMM  1 – [1 – (2  3.2%)]1/12  .0055
1/12
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