CFA test

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Question #1 of 100 Question ID: 1261641
An investor believes there are three important factors that determine the expected
return for a common stock. The investor uses the following factor betas and factor
exposures.
Factors
Factor
Betas
Factor Exposures
1 0.7 1.5%
2 1.2 4.0%
3 −0.1 5.0%
If the risk-free rate is 3%, what is the expected return for this stock using the arbitrage
pricing theory (APT) model?
A) 5.35%.
B) 8.35%.
C) 9.50%.
D) 10.37%.
Explanation
E(R) = 0.03 + 0.7(0.015) + 1.2(0.04) − 0.1(0.05)
E(R) = 0.03 + 0.0105 + 0.048 − 0.005
E(R) = 0.0835
(Book 1, Module 6.2, LO 6.f)
Question #2 of 100 Question ID: 1261695
A $1,000 par corporate bond carries a coupon rate of 6%, pays coupons semiannually,
and has 10 coupon payments remaining to maturity. Market rates are currently 5%.
There are 90 days between settlement and the next coupon payment. The dirty and
clean prices of the bond, respectively, are closest to:
A) $1,043.76, $1,013.76.
B) $1,043.76, $1,028.76.
C) $1,056.73, $1,041.73.
D) $1,069.70, $1,054.70.
Explanation
The dirty price of the bond is calculated as N = 10; I/Y = 2.5; PMT = 30; FV = 1,000;
CPT → PV = 1,043.76. Adjusting the PV for the fact that there are only 90 days until
the receipt of the first coupon gives $1,043.76 × (1.025)90/180 = $1,056.73. Clean
price = dirty price − accrued interest = $1,056.73 − $30(90 / 180) = $1,041.73.
(Book 3, Module 43.1, LO 43.c)
Question #3 of 100 Question ID: 1261730
Which of the following statements regarding option "Greeks" is incorrect?
A) Vega is highest when options are at-the-money.
B) Forward instruments cannot be used to create gamma-neutral positions.
C)
D)
Rho is higher for at-the-money versus in-the-money options.
Gamma represents the expected change in delta for a change in the value of the
underlying instrument.
Explanation
In-the-money options are more sensitive to changes in rates (rho is higher) than out-
of-the-money options.
(Book 4, Module 60.3, LO 60.g)
Question #4 of 100 Question ID: 1261675
Firm X is looking to mitigate counterparty risk by centrally clearing trades through a
central counterparty (CCP). The firm is aware of the some of the potential benefits of
central clearing, but is concerned that the drawbacks have not been properly
considered by its risk management department. Which of the following definitions is
associated with the moral hazard problem of using a central counterparty?
A)
B)
C)
D)
CCPs are expected to be designated as systemically important entities. 
Counterparties are likely to over-trade products for which the CCP underestimates 
risk.
Losses arising from a counterparty’s default are spread across all central clearing 
members.
When margin calls are made, members have to liquidate su�cient assets to meet 
the margin calls.
Explanation
Given the role CCPs play in mandatory central clearing, CCPs are expected to be
designated as "systemically important" entities. As a result, the likelihood of
government support or bailout in a severe stress scenario is likely. This creates a
moral hazard problem because CCPs designated as systemically important could
potentially accept higher risk and may have less stringent risk management
governance knowing that a government bailout in a default scenario is likely.
(Book 3, Module 30.1, LO 30.c)
Question #5 of 100 Question ID: 1261688
An asset manager sells a March 2010 call on XYZ stock with an exercise price of $45
for a $3 premium. He also buys a March 2010 call on the same stock with an exercise
price of $40 for a $5 premium. Identify this option strategy and the maximum profit
and loss for the manager.
A) Bear call spread, maximum pro�t is $3, maximum loss is $2.
B) Bull call spread, maximum pro�t is $3, maximum loss is unlimited.
C) Bear call spread, maximum pro�t is unlimited, maximum loss is $2.
D) Bull call spread, maximum pro�t is $3, maximum loss is $2.
Explanation
Bull call spread, maximum profit is $3, maximum loss is $2.
In a bull call spread, the buyer of the spread purchases a call option with a low
exercise price, XL, and subsidizes the purchase price of the call by selling a call with
a high exercise price, XH.
The maximum profit will occur at any stock price over the high exercise price. For
example, at a stock price of $50: Maximum profit: 10 − 5 − 5 + 3 = $3.
The maximum loss will occur at any stock price below the low exercise price. For
example, at a stock price of $35: Maximum loss: 0 − 0 − 5 + 3 = −$2.
(Book 3, Module 38.2, LO 38.c)
Question #6 of 100 Question ID: 1261657
Based on a sample size of 100 and sample mean of $30, a risk analyst estimates a
95% confidence interval for the mean weekly soft drink expenditures of students at a
local college. His estimate of the confidence interval is $26.77 to $33.23. Since the
analyst knew the standard deviation beforehand, the confidence interval was based
on a standard deviation closest to:
A) 1.65.
B) 6.59.
C) 11.53.
D) 16.48.
Explanation
With a known variance, the 95% confidence interval is constructed as 
. So the analyst knew . Solving for σ
provides 16.48.
(Book 2, Module 17.1, LO 17.d)
Question #7 of 100 Question ID: 1261685
Consider a 1-year European call option with a strike price of $27.50 that is currently
valued at $4.10 on a $25 stock. The 1-year risk-free rate is 6% compounded annually.
Which of the following is closest to the value of the corresponding put option?
A) $0.00.
B) $4.95.
C) $5.00.
D) $5.04.
Explanation
Using put-call parity: p = c + X / (1 + r)T − S0 = 4.10 + [27.50 / (1.06)] − 25 = $5.04.
(Book 3, Module 37.2, LO 37.c)
Question #8 of 100 Question ID: 1261701
Which of the following statements comparing VaR with expected shortfall is true?
A)
B)
C)
D)
Expected shortfall is sub-additive while VaR is not.
Both VaR and expected shortfall measure the amount of capital an investor can 
expect to lose over a given time period and are, therefore, interchangeable as risk 
measures.
Both VaR and expected shortfall depend on the assumption of a normal distribution 
of returns.
VaR can vary according to the con�dence level selected, but expected shortfall will 
not.
Explanation
± 1.96x̄
σ
n−−√
33.23 = 30 + 1.96
σ
100
− −−√
VaR measures the expected amount of capital one can expect to lose within a given
confidence level over a given period of time. One of the problems with VaR is that it
does not provide information about the expected size of the loss beyond the VaR.
VaR is often complemented by the expected shortfall, which measures the expected
loss conditional on the loss exceeding the VaR. Note that since expected shortfall is
based on VaR, changing the confidence level may change both measures. A key
difference between the two measures is that VaR is not sub-additive, meaning that
the risk of two funds separately may be lower than the risk of a portfolio where the
two funds are combined. Violation of the subadditivity assumption is a problem with
VaR that does not exist with expected shortfall.
(Book 4, Module 45.2, LO 45.g)
Question #9 of 100 Question ID: 1261697
Cooper Industries (Cooper) is the pay-fixed counterparty in an interest rate swap. The
swap is based on a notional value of $2,000,000, and Cooper receives a floating rate
based on the 6-month Hong Kong Interbank Offered Rate (HIBOR). Cooper pays a
fixed rate of 7% semiannually. A swap payment has just been made. The swap has a
remaining life of 18 months, with pay dates at 6, 12, and 18 months. Spot HIBOR rates
are shown in the table below.
6-month HIBOR 6.5%
12-month HIBOR 6.8%
18-month HIBOR 7.5%
24-month HIBOR 7.7%
The value of the swap to Cooper is closest to:
A) $0.
B) $6,346.
C) $9,431.
D) $12,486.
Explanation
The fixed payments made by Cooper are (0.07 / 2) × $2,000,000 = $70,000. The
present value of the fixed payments
= ($70,000 / 1.0650.5) + ($70,000 / 1.0681) + [($70,000 + $2,000,000) /
(1.075)1.5]
= $67,830 + $65,543 + $1,857,196 = $1,990,569The value of the floating rate payments received by Cooper at the payment date is
the value of the notional principal, or $2,000,000. Recall that a swap payment has
just been made.
The value of the swap to Cooper is ($2,000,000 − $1,990,569) = $9,431.
(Book 3, Module 44.2, LO 44.g)
Question #10 of 100 Question ID: 1261645
Metallgesellschaft Refining and Marketing (MGRM) offered customers contracts to buy
fixed amounts of heating oil and gasoline at a fixed price over a 5- or 10-year period.
The customer contracts effectively gave MGRM a short position. MGRM hedged
exposure using a rolling hedge strategy. This strategy is best described as:
A)
B)
C)
D)
buying futures contracts of di�erent expirations and allowing them to expire in 
sequence.
buying futures contracts of di�erent expirations and closing out the position shortly 
before expiration.
using short-term futures to hedge a long-term risk exposure by replacing them with 
longer-term contracts shortly before they expire.
using short-term futures contracts with a larger notional value than the long-term 
risk they are meant to hedge.
Explanation
This strategy is called a stack-and-roll hedge and is designed to hedge long-term risk
exposures with short-term contracts. Using short-term futures contracts with a
larger notional value than the long-term risk they are meant to hedge could result in
"over hedging" depending on the hedge ratio.
(Book 1, Module 9.1, LO 9.a)
Question #11 of 100 Question ID: 1261723
Assume an investor holds a portfolio of bonds as follows:
$2,000,000 par value of 10-year bonds with a duration of 6.95 priced at 95.5000.
$3,000,000 par value of 15-year bonds with a duration of 9.77 priced at 88.6275.
$5,000,000 par value of 30-year bonds with a duration of 14.81 priced at
114.8750.
The duration of this portfolio is closest to:
A) 10.64.
B) 12.06.
C) 13.28.
D) 13.57.
Explanation
The duration of a portfolio of bonds is the weighted average (using market value
weights) of the durations of the bonds in the portfolio. First, let's find the weights.
Bond
Price as Percentage of
Par
Face Value
$
Market Value $
1 95.5000 2,000,000 1,910,000
2 88.6275 3,000,000 2,658,825
3 114.8750 5,000,000 5,743,750
Total 10,312,575
The weights based on market values are:
Weight of bond 1 = 1,910,000 / 10,312,575 = 0.1852
Weight of bond 2 = 2,658,825 / 10,312,575 = 0.2578
Weight of bond 3 = 5,743,750 / 10,312,575 = 0.5570
Bond Weights Duration
Weighted
Duration
1 0.1852 6.95 1.2871
2 0.2578 9.77 2.5187
3 0.5570 14.81 8.2492
Total 12.0550
(Book 4, Module 56.2, LO 56.g)
Question #12 of 100 Question ID: 1261691
Vega is the sensitivity of an option's price to changes in volatility. Increases in an
underlying instrument's volatility will usually increase the value of options since
increases in volatility produce a greater probability that an option will find its way into
the money. Of the four options listed below, which investment has the potential to
produce a negative vega measure?
A) Exchange options.
B) Call options.
C) Put options.
D) Barrier options.
Explanation
Increased volatility on down-and-out and up-and-out barrier options does not
increase value because the closer the underlying instrument gets to the barrier
price, the greater the chance the option will expire. Therefore, vega may be negative
for a barrier option.
(Book 3, Module 39.2, LO 39.e)
Question #13 of 100 Question ID: 1261679
Nevin Woodcomb is a portfolio manager for the Matrix Tactical Growth Fund, a
mutual fund with total assets of $225 million. The mandate of the mutual fund is to
make active tactical shifts in long and short exposure based on current views of stock
market action. Recently, Woodcomb has been cautious on stocks and has positioned
the fund with a beta of −0.30; however, the most recent jobless claims were more
positive than Woodcomb expected, and he expects the stock market to rally strongly
when the monthly non-farm payroll data is released. Woodcomb would like to take
advantage of this market rally using S&P 500 index futures and increase the fund's
beta to 1.25. Currently, S&P 500 futures are trading at 2,398 and the multiplier is 250.
How can Woodcomb achieve his objective for his fund?
A) Sell 135 contracts.
B) Buy 155 contracts.
C) Buy 388 contracts.
D) Buy 582 contracts.
Explanation
Woodcomb wants to increase exposure to systematic risk so he will want to buy S&P
index futures. Buying futures will increase the current beta to his target of 1.25.
number of contracts = (target beta − current beta) × (portfolio value /
futures value)
number of contracts = [1.25 − (−0.30)] × [$225 million / (2,398 × 250)]
number of contracts = (1.55) × (375.31)
number of contracts = 582
(Book 3, Module 32.2, LO 32.f)
Question #14 of 100 Question ID: 1261702
A hedge fund is considering using one of the following non-parametric methods for
estimating value at risk (VaR): traditional historical simulation or multivariate density
estimation. Which of the following statements is an advantage of these methods
compared to parametric methods for estimating VaR?
A)
B)
C)
D)
Deviations from normality may be a concern for non-parametric methods. 
Data is used more e�ciently with non-parametric methods than with parametric 
methods.
The multivariate density estimation is very �exible in introducing dependence on 
economic state variables.
Parametric methods require a large amount of data that is directly related to the 
number of conditioning variables used in the model.
Explanation
Non-parametric methods do not require assumptions regarding the entire
distribution of returns to estimate VaR. The multivariate density estimation is very
flexible in introducing dependence on economic state variables. Deviations from
normality are not as big of a concern for non-parametric compared to parametric
methods. Data is used more efficiently with parametric methods. Multivariate
density estimation requires a large amount of data that is directly related to the
number of conditioning variables used in the model.
(Book 4, Module 47.2, LO 47.f)
Question #15 of 100 Question ID: 1261643
A supervisor at Country Bank is examining the Basel Committee's principles for
effective risk data aggregation and reporting. Which of the following statements
would be incorrect regarding the role that supervisors should play in monitoring and
implementing these principles? Supervisors should:
A)
B)
C)
D)
have a variety of tools available to address risk data aggregation and reporting 
de�ciencies.
test a bank’s risk data aggregation and reporting capabilities for both normal and 
stress scenarios.
use internal and external auditors and have access to all documentation produced 
from internal validations and audit reports.
limit sharing roadblocks and constraints when evaluating the quality of risk data 
aggregation and reporting capabilities with supervisors in other jurisdictions.
Explanation
Principle 14 covering "cooperation" suggests that supervisors should share
experiences with evaluating the quality of risk data aggregation and reporting
capabilities with supervisors in other jurisdictions.
(Book 1, Module 7.2, LO 7.g)
Question #16 of 100 Question ID: 1261655
An analyst is concerned with the symmetry and tails of a distribution of returns over a
period of time for a company she is examining. She does some calculations and finds
that the median return is 4.2%, the mean return is 4.8%, and the modal return is 3.7%.
She also finds that the measure of excess kurtosis is 2. Based on this information, the
correct characterization of the distribution of returns over time is:
Skewness
A) Positive
B) Positive
C) Negative
D) Negative
Kurtosis
Leptokurtic 
Platykurtic 
Platykurtic 
Leptokurtic
Explanation
The fact that mean > median > mode is consistent with a distribution that is
positively skewed. For all normal distributions, kurtosis = 3. Excess kurtosis =
kurtosis− 3, which is 0 for a normal distribution. In this case, excess kurtosis = 2,
which means kurtosis = 5. This means that the distribution being examined has
fatter tails than the normal distribution and is said to be leptokurtic.
(Book 2, Module 16.2, LO 16.h)
Question #17 of 100 Question ID: 1261718
Fixed income portfolio managers must always be concerned with the impact of
interest rate and reinvestment risk on client portfolios. Which of the following
statements regarding interest rate and reinvestment risk is incorrect?
I. The lower the coupon rate, the lower the interest rate risk.
II. The longer the term of the bond, the greater the reinvestment risk.
A) I only.
B) II only.
C) Both I and II.
D) Neither I nor II.
Explanation
The lower the coupon rate, the higher the interest rate risk.
(Book 4, Module 55.1, LO 55.a)
Question #18 of 100 Question ID: 1156193
A portfolio manager of an endowment wants to calculate a daily VaR for the portfolio.
The €5,000,000 portfolio is restricted from using derivative securities. The manager
uses a 5% level of significance to estimate the VaR. The manager ranked the 100 daily
returns from last year, and reports the lowest eight returns to be: −0.0159, −0.0132,
−0.0211, −0.0106, −0.0254, −0.0099, −0.0368, and −0.0584. Which of the following
amounts is closest to the daily VaR using the historical simulation method?
A) −€66,000.
B) −€79,500.
C) −€105,500.
D) −€127,000.
Explanation
The historical simulation VaR for 5% is the fifth lowest return, which is −1.59%;
therefore, the correct VaR is: −79,500 = (−0.0159) × (5,000,000)
(Book 1, Module 1.1, LO 1.c)
Question #19 of 100 Question ID: 1261684
The spot rate for a commodity is $19. The annual lease rate for the commodity is 5%.
The appropriate annually compounded annual risk-free rate is 6.5%. Which of the
following amounts is closest to the 3-month commodity forward price?
A) $18.46.
B) $18.93.
C) $19.07.
D) $19.55.
Explanation
The 3-month forward rate is calculated as follows:
F0,T = S0 × [(1 + r) / (1 + δ)]T = 19 × [(1.065) / 1.05)]0.25 = 19.07
(Book 3, Module 35.2, LO 35.f)
Question #20 of 100 Question ID: 1261677
A buffalo farmer is concerned that the price he can get for his buffalo herd will be less
than he has forecasted. To protect himself from price declines in the herd, the farmer
has decided to hedge with live cattle futures. Specifically, he has entered into the
appropriate number of cattle future positions for September delivery that he believes
will help offset any buffalo price declines during the winter slaughter season. The
appropriate position and the likely sources of basis risk in the hedge are, respectively:
A) short; choice of futures delivery date.
B) short; choice of futures asset.
C) short; choice of futures delivery date and asset.
D) long; choice of futures delivery date and asset.
Explanation
The farmer needs to be short the futures contracts. The two sources of basis risk
confronting the farmer will result from the fact that he is using a cattle contract to
offset the price movement of his buffalo herd. Cattle prices and buffalo prices may
not be perfectly positively correlated. As a result, the correlation between buffalo
and cattle prices will have an impact on the basis of the cattle futures contract and
spot buffalo meat. The delivery date is a problem in this situation, because the
farmer's hedge horizon is winter, which probably will not commence until December
or January. In order to maintain a hedge during this period, the farmer will have to
enter into another futures contract, which will introduce an additional source of
basis risk.
(Book 3, Module 32.1, LO 32.c)
Question #21 of 100 Question ID: 1261668
An investment manager at Java Investments collects five years of historical returns in
order to calculate Spearman's rank correlation coefficient for the stock returns of
stocks A and B. The stock returns for A and B from 2011 to 2015 are as follows:
Year A B
2011 −3% 6%
2012 12% −3%
2013 −8% 4%
2014 −11% 8%
2015 3% 3%
What is Spearman's rank correlation coefficient for the stock returns of A and B?
A) −0.9.
B) −0.7.
C) −0.3.
D) +0.2.
Explanation
The following table illustrates the calculations used to determine the sum of
squared ranking deviations:
Year X Y X Rank Y Rank di
2014 −11% 8% 1 5 −4 16
2013 –8% 4% 2 3 −1 1
2011 –3% 6% 3 4 −1 1
2015 3% 3% 4 2 2 4
2012 12% −3% 5 1 4 16
Sum = 38
Thus, the Spearman rank correlation coefficient is −0.9:
(Book 2, Module 23.3, LO 23.f)
Question #22 of 100 Question ID: 1261689
d2i
= 1 − = 1 − = −0.9ρS
6∑
i=1
n
d2i
n( −1)n2
6×38
5(25−1)
Kyle Hickey believes that the price of SCU's stock will have little volatility over the next
three months and wants to construct a butterfly spread option strategy to take
advantage of the opportunity he believes to exist. Looking at his computer screen,
Hickey sees the following 3-month options are available on SCU's stock:
Put option with a strike price of $35 and a price of $1.25.
Put option with a strike price of $40 and a price of $3.50.
Put option with a strike price of $45 and a price of $5.50.
Call option with a strike price of $40 and a price of $5.90.
Hickey can use any number of contracts of the above options to construct his
strategy. Assuming the price of the underlying stock at expiration is $41, what is the
total profit (loss) on a properly constructed butterfly spread?
A) −$1.15.
B) +$1.15.
C) +$4.25.
D) +$6.90.
Explanation
Given the options available to him, Hickey should construct a butterfly spread with
puts, which is accomplished by buying one put with a low exercise price, buying a
second put with a high exercise price, and selling two puts with an intermediate
exercise price. The call option will not be used. Net proceeds received from
constructing butterfly spread = (2 × $3.50) − ($1.25 + $5.50) = $7 − $6.75 = $0.25.
With the stock expiring at $41, only the long put with the high exercise price will be
in- the-money, resulting in a profit of $4.00 + $0.25 = $4.25.
(Book 3, Module 38.2, LO 38.c)
Question #23 of 100 Question ID: 1261671
A hedge fund with a 2-plus-20% fee structure has equal probabilities of a 10% loss or
a 30% gain in its first year. The expected return to an investor in the fund for the first
year is closest to:
A) –2.0%.
B) 5.2%.
C) 8.8%.
D) 17.6%.
Explanation
With a 30% gain, the fund would earn fees of 2% + 0.20(30% – 2%) = 7.6%. With a
10% loss, the fund would only earn its management fee of 2%. To the investor, the
expected return is 0.5(–10% – 2%) + 0.5(30% – 7.6%) = 5.2%. (Book 3, Module 27.2,
LO 27.e)
Question #24 of 100 Question ID: 1261644
There are many benefits of an enterprise-risk-management (ERM) approach to
managing risks. Which of the following statements is least accurate regarding these
benefits? ERM:
A)
B)
C)
D)
identi es threats to the entire operation that arise from individual business lines. 
helps managers understand crossover risks and correlations between speci c risk 
types.
helps managers de ne the risk appetite of the entire enterprise and helps rms 
adhere to the constraints put on risk.
allows managers to focus on day-to-day threats to speci c units and business lines 
rather than the largest threats to the firm.
Explanation
ERM allows managers to focus on the largest threats to the firm—threats to the
firm's survival—rather than day-to-day threats to specific units and business lines.
(Book 1, Module 8.1, LO 8.b)
Question #25 of 100 Question ID: 1261664
Analyst Joseph Lockwood examines a single-factor regression for a hedge fund and
makes the following two statements:
Statement
1:
Heteroskedasticity exists if the regression residuals are
correlated with their lagged values.
Statement
2:
Heteroskedasticity causes the t-statistics of the regression to
be incorrectly calculated using ordinary least squares
methods.
Which of Lockwood's claims are correct?
A) Statement 1 is correct andStatement 2 is correct.
B) Statement 1 is correct and Statement 2 is incorrect.
C) Statement 1 is incorrect and Statement 2 is correct.
D) Statement 1 is incorrect and Statement 2 is incorrect.
Explanation
Heteroskedasticity exists if the variance of the residuals is not constant. In a
heteroskedastic regression, the t-statistics will be incorrectly calculated using
ordinary least squares methods.
(Book 2, Module 20.1, LO 20.a)
Question #26 of 100 Question ID: 1261725
A stock currently trades at $10. At the end of three months, the stock will either be
$11 or $9. The continuously compounded risk-free rate of interest is 3.5% per year.
Using a binomial tree, the value of a 3-month European call option with a strike price
of $10 is closest to:
A) $0.11.
B) $0.54.
C) $0.65.
D) $1.01.
Explanation
In this case, U = 1.1, D = 0.9, r = 0.035, and the value of the option is $1 if the stock
increases and $0 if the stock decreases. The probability of an up movement, πU, can
be calculated as (e(0.035 × 3/12) − 0.9) / (1.1 − 0.9) = 0.5439. The value of the call
option is therefore (0.5439 × $1) / e(0.035 × 3/12) = $0.54.
(Book 4, Module 58.1, LO 58.a)
Question #27 of 100 Question ID: 1261648
An investment advisor has a client base composed of high net worth individuals. In
her personal portfolio, the advisor has an investment in Torex, a company that has
developed software to speed up internet browsing. She has thoroughly researched
Torex and believes the company is financially strong yet currently significantly
undervalued. According to the GARP Code of Conduct, the investment advisor may:
A)
B)
C)
D)
not recommend Torex as long as she has a personal investment in the stock.
not recommend Torex to a client unless her employer gives written consent to do 
so.
recommend Torex to a client, but she must disclose her investment in Torex to the 
client.
recommend Torex to a client without disclosure as long as it is a suitable investment 
for the client.
Explanation
Standards 2.1 and 2.2—Conflicts of Interest. Members and candidates must act
fairly in all situations and must fully disclose any actual or potential conflict to all
affected parties. Sell-side members and candidates should disclose to their clients
any ownership in a security that they are recommending.
(Book 1, Module 11.1, LO 11.a)
Question #28 of 100 Question ID: 1261638
Donaldson Capital Management, a regional money management firm, manages nearly
$400 million allocated among three investment managers. All portfolios have the
same objective, which is to produce superior risk-adjusted returns (by beating the
market) for their clients. You have been hired as a consultant to measure the
performance of the portfolio managers. You have collected the following information
based on the last 10 years of returns.
Portfolio
Manager
Mean Annualized
Rate of Return
Beta
Standard
Deviation of
Return
A 0.18 1.35 0.24
B 0.21 1.95 0.25
C 0.24 2.10 0.22
During the same time period the average annual rate of return on the market
portfolio was 13% with a standard deviation of 19%. In order to assess the portfolio
performance of the above managers, you should use:
A) the Treynor measure of performance.
B) the Sharpe measure of performance.
C) the Jensen measure of performance.
D) the Sortino measure of performance.
Explanation
The Treynor measure is most appropriate for comparing well-diversified portfolios.
That is, the Treynor measure is the best to compare the excess returns per unit of
systematic risk earned by portfolio managers, provided all portfolios are well-
diversified.
All three portfolios managed by Donaldson Capital Management are clearly less
diversified than the market portfolio. Standard deviation of returns for each of the
three portfolios is higher than the standard deviation of the market portfolio,
reflecting a low level of diversification.
Jensen's alpha is the most appropriate measure for comparing portfolios that have
the same beta. The Sharpe measure can be applied to all portfolios because it uses
total risk and it is more widely used than the other two measures. Also, the Sharpe
ratio evaluates the portfolio performance based on realized returns and
diversification. A less-diversified portfolio will have higher total risk and vice versa.
(Book 1, Module 5.3, LO 5.g)
Question #29 of 100 Question ID: 1261660
Mark Johnson is an analyst who is studying the relationship between Stock XYZ and
the S&P 500 Index. The stock return's annual standard deviation is 15% and the S&P
500's standard deviation is 16%. He performs a regression on the stock's returns
against the market's returns and discovers the following simple linear regression
model:
Stock XYZ return = 0.01 + 0.82 × S&P 500 return
What is the correlation coefficient between Stock XYZ and the S&P 500 Index?
A) 0.02.
B) 0.34.
C) 0.74.
D) 0.88.
Explanation
CovS,M = Beta × VarM = 0.82 × 0.162 = 0.02099
CorrS,M = CovS,M / (SDS × SDM) = 0.02099 / (0.15 × 0.16) = 0.875
(Book 2, Module 18.2, LO 18.b)
Question #30 of 100 Question ID: 1261708
Bank regulators are examining the loan portfolio of a large, diversified lender. The
regulators' main concern is that the bank remains solvent during turbulent economic
times. Which of the following statements is most likely the area on which the
regulators will want to focus?
A)
Expected loss, since each asset can expect, on average, to decline in value from a
positive probability of default.
B)
C)
D)
Expected loss, given the decrease in underwriting standards of new loans. 
Unexpected loss, since the bank will need to set aside additional capital for the 
unlikely event that recovery rates are smaller than expected.
Unexpected loss, since the bank will need to set aside additional capital for the 
unlikely event that loss rates are smaller than expected.
Explanation
Unexpected loss is a measure of the variation in expected loss. As a precaution, the
bank needs to set aside sufficient capital in the event that actual losses exceed
expected losses with a reasonable likelihood. For example, smaller recovery rates
would be indicative of larger actual losses.
(Book 4, Module 50.1, LO 50.d)
Question #31 of 100 Question ID: 1261650
An analyst develops the following probability distribution about the state of the
economy and the market.
Initial Probability
P(A)
Conditional Probability
P(B|A)
Good economy 60%
Bull market 50%
Normal market 30%
Bear market 20%
Poor economy 40%
Bull market 20%
Normal market 30%
Bear market 50%
Which of the following statements about this probability distribution is least likely
accurate?
A) The probability of a normal market is 0.30.
B)
C)
D)
The probability of having a good economy and a bear market is 0.12.
Given that the economy is good, the chance of a poor economy and a bull market is
0.15.
Given that the economy is poor, the combined probability of a normal or a bull
market is 0.50.
Explanation
Given that the economy is good, the probability of a poor economy and a bull
market is zero. The other statements are true. The P(normal market) = (0.60 × 0.30)
+ (0.40 × 0.30) = 0.30. P(good economy and bear market) = 0.60 × 0.20 = 0.12. Given
that the economy is poor, the probability of a normal or bull market = 0.30 + 0.20 =
0.50.
(Book 2, Module 12.2, LO 12.e)
Question #32 of 100 Question ID: 1261670
A bank manager is preparing a white paper on the topic of risk for the CEO of the
bank. The focus of the paper is on the three primary types of risk exposure and how
they should be managed going forward. Each of the following descriptions contained
in the paper is accurate except:
A)
B)
C)
D)
a bank’s credit risk relates to its ability to secure a strong credit rating.
concerns over losses on trading activities from declines in investments ties to 
market risk.
market risk is evaluated on a shorter time horizon than both credit risk and 
operational risk.
operational risk includes both losses dueto events outside of the bank and internal 
control failures.
Explanation
Credit risk relates to borrowers or counterparties to contracts defaulting on their
obligations. Market risk relates to losses (investment declines) from the bank's
trading activities, and is evaluated on a shorter time horizon than credit risk and
operational risk. Operational risk relates to the possibility of losses from external
events or internal control failures. (Book 3, Module 25.1, LO 25.a)
Question #33 of 100 Question ID: 1261729
To create a delta-neutral portfolio, an investor who has written 15,000 call options
(that are currently exactly at-the-money) will have to:
A) long 7,500 shares in the underlying instrument.
B) short 7,500 shares in the underlying instrument.
C) long 15,000 shares in the underlying instrument.
D) short 15,000 shares in the underlying instrument.
Explanation
If the investor has written 15,000 call options, he must go long delta times the short
option position to create a delta-neutral position, or buy $15,000 × 0.50 = 7,500
shares. Note that the delta of a call option, which is exactly at-the-money, is 0.5.
(Book 4, Module 60.2, LO 60.e)
Question #34 of 100 Question ID: 1261635
James Tulsma is analyzing a publicly traded firm and is using the company's beta, the
risk-free rate of return, and the expected return on the market to estimate the
company's required rate of return. He is somewhat concerned that the underlying
assumptions of this technique are not realistic. Which of the following statements is
an assumption of the capital asset pricing model (CAPM)?
A) Taxes and transaction costs exist.
B) Fractional investments are not possible.
C) Investors make their decisions solely based on expected returns and variances.
D) Market participants can only borrow and lend limited amounts at the risk-free rate.
Explanation
The capital asset pricing model (CAPM) assumes the following:
There are no taxes and commissions or transaction costs.
Fractional investments are possible.
Investors make their decisions solely based on expected returns and
variances.
Market participants can borrow and lend unlimited amounts at the risk-free
rate.
(Book 1, Module 5.2, LO 5.c)
Question #35 of 100 Question ID: 1261681
A 9-month futures contract on the S&P 500 is currently priced at 2,175. The underlying
stocks within the index are valued at 2,150 and pay dividends at an annual rate of
2.20%. The risk-free rate is currently 3.10%. Assuming a trader wants to attempt to
profit through a potential arbitrage opportunity, which of the following statements is
correct?
A)
The trader should buy the futures and sell the stocks in the index for an arbitrage
pro�t of $25.
B)
The trader should buy the stocks in the index and sell the futures contract for an
arbitrage pro�t of $25.
C)
D)
The trader should buy the futures and sell the stocks in the index for an arbitrage 
pro�t of $39.
The trader should buy the stocks in the index and sell the futures contract for an 
arbitrage pro�t of $39.
Explanation
First, calculate the value of the futures as:
F = 2,150 × [(1.022) / (1.031)]0.75 = 2,135.91
The actual futures price is 2,175, so selling the futures and buying the underlying
index nets a profit of 2,175 − 2,135.91 = $39.09.
(Book 3, Module 34.1, LO 34.f)
Question #36 of 100 Question ID: 1261662
An analyst is concerned that the trading strategy she recently identified has generated
a statistically insignificant result and has asked for guidance in assessing the strategy.
A result is statistically significant if it is:
A)
B)
C)
D)
unlikely to have occurred merely by chance, and the p-value is less than the 
signi�cance level.
likely to have occurred merely by chance, and the p-value is less than the 
signi�cance level.
unlikely to have occurred merely by chance, and the p-value is greater than the 
signi�cance level.
likely to have occurred merely by chance, and the p-value is greater than the 
signi�cance level.
Explanation
A result is statistically significant if it is unlikely to have happened by chance. The
decision rule is to reject the null hypothesis if the p-value is less than the
significance level. If the p-value is less than the significance level, then we conclude
that the sample estimate is statistically different than the hypothesized value.
(Book 2, Module 18.3, LO 18.g)
Question #37 of 100 Question ID: 1261676
To equitize the cash portion of assets under management, a portfolio manager enters
into a long futures position on a stock index with a multiplier of 250. The cash position
is $5,000,000, which at the current futures value of 1,000 requires the manager to be
long 20 contracts. If the current initial margin is $12,500 per contract, and the current
maintenance margin is $10,000 per contract, the variation margin the portfolio
manager needs to advance if the futures contract value falls to 985 at the end of the
first day of the position is closest to:
A) $25,000.
B) $30,000.
C) $50,000.
D) $75,000.
Explanation
The futures contract ended at 985 on the first day. This represents a decrease in
value in the position of (1,000 − 985) × $250 × 20 = $75,000. The initial margin placed
by the manager was $12,500 × 20 = $250,000. The maintenance margin for this
position requires $10,000 × 20 = $200,000. Since the value of the position declined
$75,000 on the first day, the margin account is now worth $175,000 (below the
$200,000 maintenance margin) and will require a variation margin of $75,000 to
bring the position back to the initial margin. It is not sufficient just to bring the
position back to the maintenance margin.
(Book 3, Module 31.1, LO 31.c)
Question #38 of 100 Question ID: 1261654
Let A and B be two random variables that represent the annual returns of two
different portfolios. If the expected value of A is equal to 2, the expected value of B is
equal to 3, and the expected value of A and B is 10, what is the covariance between A
and B?
A) 4.
B) 5.
C) 12.
D) 13.
Explanation
Cov(A,B) = E{[A − E(A)][B − E(B)]}. This equation can be rewritten as: E(AB) − E(A) ×
E(B). Plugging in the values gives us: Cov(A,B) = 10 − (2 × 3) = 4. (Book 2, Module 15.2,
LO 15.d)
Question #39 of 100 Question ID: 1261649
WEB, an investment-banking firm, is the principal underwriter for MTEX's upcoming
debenture issue. Lynn Black, FRM, is an analyst with WEB, and she learned from an
employee in MTEX's programming department that a serious problem was recently
discovered in the software program of its major new product line. In fact, the problem
is so bad that many customers have canceled their orders with MTEX. Black checked
the debenture's prospectus and found no mention of this development. The red
herring prospectus has already been distributed. According to the GARP Code of
Conduct, Black's best course of action is to:
A) inform her immediate supervisor at WEB of her discovery.
B) keep quiet because this is material nonpublic inside information.
C) notify potential investors of the omission on a fair and equitable basis.
D)
report her discovery to the Division of Corporation Finance of the Securities and
Exchange Commission.
Explanation
Standards 3.1 and 3.2 relate to the preservation of confidentiality. The simplest,
most conservative, and most effective way to comply with these Standards is to
avoid disclosing any information received from a client, except to authorized fellow
employees who are also working for the client. If the information concerns illegal
activities by MTEX, Black may be obligated to report activities to authorities.
(Book 1, Module 11.1, LO 11.a)
Question #40 of 100 Question ID: 1261673
Todd Walter believes the British Pound will weaken against the U.S. Dollar over the
next six months and would like to speculate on his view with a value of £375,000. He
could sell pounds in the spot market at 1.52$/£ or sell six futures contracts at 1.48$/£
with an initial margin of $15,000. What isthe profit (loss) from the futures position if
the spot rate in six months is 1.45$/£?
A) −$15,000.
B) −$3,750.
C) $11,250.
D) $26,250.
Explanation
Since the investor expects the pound to weaken and the investor is short the futures
contracts the investor must subtract the spot price (what the investor effectively
pays) from the futures price (what the investor effectively receives). Profit =
£375,000 × (1.48$/£ − 1.45$/£) = $11,250.
(Book 3, Module 28.2, LO 28.g)
Question #41 of 100 Question ID: 1261726
The binomial option pricing model can be altered to value a stock that pays a
continuous dividend yield. Assuming the size of the up-move factor in a binomial
model is 1.25, the risk-free rate is 4%, and the dividend yield is equal to 2%, what is
the probability of the up move for the first period of the binomial tree?
A) 45%.
B) 49%.
C) 51%.
D) 55%.
Explanation
Because the size of the up-move factor is 1.25, the size of the down-move factor is
equal to: 1 / 1.25 = 0.8.
The probability of the up move, given a dividend yield, q, is computed as:
(Book 4, Module 58.2, LO 58.e)
Overview for Questions #42-43 of
100 Question ID: 1261714
Use the following information to answer Questions 42 and 43.
Maturity
(Years)
STRIP Price Spot Rate Forward Rate
0.5 99.2556 1.50% 1.50%
1.0 98.2240 1.80% 2.10%
1.5 96.7713 2.20% ?
2.0 95.1524 ? 3.40%
Question #42 of 100 Question ID: 1261715
The price of a $1,000 par value Treasury bond (T-bond) with a 3% coupon that
matures in 1.5 years is closest to:
= = = = 0.488 = 4.9%πu
−De(r−q)t
U−D
−0.8e(0.04−0.02)1
1.25−0.8
0.22
0.45
A) $1,010.02.
B) $1,011.85.
C) $1,013.68.
D) $1,015.51.
Explanation
The price is calculated as $15(0.992556) + $15(0.982240) + $1,015(0.967713) =
$1,011.85.
(Book 4, Module 54.2, LO 54.b)
Question #43 of 100 Question ID: 1261716
The 6-month forward rate on an investment that matures in 1.5 years is closest to:
A) 2.50%.
B) 2.75%.
C) 3.00%.
D) 3.25%.
Explanation
The forward rate can be calculated as [(98.2240 / 96.7713) − 1] × 2 = 3%.
(Book 4, Module 54.2, LO 54.c)
Question #44 of 100 Question ID: 1261699
Many different types of swaps exist including interest rate swaps, currency swaps,
commodity swaps, equity swaps, and volatility swaps. A swaption is an option that
gives the holder the right to enter into a swap. Which of the following statements
about swaps and swaptions is most likely correct?
A)
B)
C)
D)
Equity swap payments may be �oating on both sides.
Unlike options, premiums for swaptions are not dependent on the strike rate 
speci�ed in the swaption.
The most common reason for entering into commodity swap agreements is to 
speculate on commodities prices.
For the �xed-rate payer in an S&P 500 Index swap, a negative index return does not 
require a payment from the �xed-rate payer.
Explanation
Unique among swaps, equity swap payments may be floating on both sides (and the
payments not known until the end of the settlement period). Similar to options,
premiums for swaptions are dependent on the strike rate specified in the swaption.
The most common reason for entering into commodity swap agreements is to
control the costs of purchasing resources, such as oil and electricity. A negative
index return requires the fixed-rate payer to pay the percentage decline in the
index.
(Book 3, Module 44.3, LO 44.m)
Question #45 of 100 Question ID: 1261703
An option trader is attempting to judge whether an option's premium is cheap or
expensive. To do so, he employs a GARCH(1,1) model to forecast volatility. The
particular model he estimates has an intercept term equal to 0.000005, a parameter
estimate on the latest estimate of variance of 0.85, and a parameter estimate on the
latest innovation of 0.13. If the latest volatility estimate from the model were 2.2% per
day and the option's underlying asset changed 3%, the trader's estimate of the next
period's standard deviation is closest to:
A) 0.07%.
B) 2.31%.
C) 5.20%.
D) 2.62%.
Explanation
The GARCH(1,1) estimate of volatility will be: 0.000005 + (0.13)(0.03)2 + (0.85)(0.022)2
= 0.000533
(Book 4, Module 47.3, LO 47.i)
Question #46 of 100 Question ID: 1261727
The current price of a stock is $25. A put option with a $20 strike price that expires in
six months is available. N(d1) = 0.9737 and N(d2) = 0.9651. If the underlying stock
exhibits an annual standard deviation of 25%, and the current continuously
compounded risk-free rate is 4.25%, the Black-Scholes-Merton value of the put is
closest to:
A) $0.01.
B) $0.03.
volatility = = 0.0231 = 2.31%0.000533
− −−−−−−
√
C) $0.33.
D) $0.36.
Explanation
P = ($20 × e−0.0425×0.5 × 0.0349) − ($25 × 0.0263) = $0.02582 ≈ $0.03
(Book 4, Module 59.2, LO 59.d)
Question #47 of 100 Question ID: 1261705
John Bone is a junior bond analyst for XYZ investments. He is examining both
investment grade bonds and speculative grade bonds. In particular, he is looking for
bonds located below the separation between these two bond classifications. Which of
the following bonds would be classified as a speculative grade bond?
A) FHLMC discount note.
B) ACC rail bond rated Baa.
C) OMC Corp. MTN rated BB.
D) Traveler’s �oating-rate note rated Aa.
Explanation
Any security with a rating below BBB by S&P or Baa by Moody's is a speculative or
non-investment grade instrument.
(Book 4, Module 48.1, LO 48.a)
Question #48 of 100 Question ID: 1261653
An analyst is testing the hypothesis that the variance of monthly returns for Index A
equals the variance of monthly returns for Index B based on samples of 50 monthly
observations. The sample variance of Index A returns is 0.085, whereas the sample
variance of Index B returns is 0.084. Assuming the samples are independent and the
returns are normally distributed, which of the following represents the most
appropriate test statistic?
A)
B)
C)
sample variance of Index A
sample variance of Index B
sample variance of Index A−sample variance of Index B
standard error of sample statistic
sample variance of Index B
sample variance of Index A
D)
Explanation
The appropriate test is an F-test, where the larger sample variance (Index A) is
placed in the numerator.
(Book 2, Module 14.1, LO 14.a)
Question #49 of 100 Question ID: 1261639
For a given portfolio, the expected return is 10% with a standard deviation of 15%.
The beta of the portfolio is 0.75. The expected return of the market is 11% with a
standard deviation of 18%. The risk-free rate is 4%. The portfolio's Treynor measure is
closest to:
A) 0.0075.
B) 0.0120.
C) 0.0400.
D) 0.0800.
Explanation
The formula for the Treynor measure is:
Thus, the value for the Treynor measure in this case is (0.10 − 0.04) / 0.75 = 0.08.
(Book 1, Module 5.3, LO 5.g)
Question #50 of 100 Question ID: 1261669
Rick Powell is conducting a Monte Carlo simulation by generating random values from
a standard normal probability distribution. He is interested in reducing Monte Carlo
sampling error and knows that increasing the number of scenarios will improve the
accuracy of this simulation. However, he is also aware that increasing the number of
scenarios can become costly for complex simulations. As a result, Powell is
researching variance reduction techniques as an alternative way to reduce sampling
error. Which of the following statements best explains the implementation of the
antithetic variate technique? Monte Carlo sampling error is reduced by:
sample variance of Index B−sample variance of Index A
standard error of sample statistic
[ ]
E( )−RP RF
βP
A)
B)
C)
D)
replacing a simulated variable that has unknown properties with a similar variable 
that has known properties.
reusing the same set of standard normal random variables for each simulation run 
while testing with di�erent Dickey–Fuller (DF) parameters.
splitting a longer time series into shorter time frames, such that a six- month time 
series of data can be subdivided into three sets of two-monthexperiments.
rerunning the simulation using a complement set of random numbers, such that 
the complement set of values may be a negative value of the original random 
number drawn.
Explanation
The antithetic variate technique reduces Monte Carlo sampling error by rerunning
the simulation using a complement set of the original set of random variables. If the
original set of random draws is denoted ut for each replication, then the simulation
is rerun with the complement set of random numbers denoted −ut.
(Book 2, Module 24.1, LO 24.c)
Question #51 of 100 Question ID: 1261710
Canadian Bank, Inc., (CBI) has the following annual gross income amounts in its
business lines over its most recent three years:
2018 2017 2016
Retail banking $380 million $344 million $326 million
Commercial
banking
$712 million $645 million $599 million
Corporate finance $846 million $777 million $687 million
Using the standardized approach, which of the following amounts represents CBI's
operational risk capital requirement for 2019? (Assume that the beta factors for retail
banking, commercial banking, and corporate finance are 12%, 15%, and 18%,
respectively.)
A) $253.2 million.
B) $265.8 million.
C) $274.9 million.
D) $278.4 million.
Explanation
For the standardized approach, CBI must apply different beta factors to specific
business lines. The amounts are multiplied by the average annual gross income over
the past 3-year period.
Average annual gross revenues for retail banking:
(380 + 344 + 326) / 3 = 350 million
Average annual gross revenues for commercial banking:
(712 + 645 + 599) / 3 = 652 million
Average annual gross revenues for corporate finance:
(846 + 777 + 687) / 3 = 770 million
Operational risk capital requirement:
0.12(350) + 0.15(652) + 0.18(770) = 278.4 million
(Book 4, Module 51.1, LO 51.b)
Question #52 of 100 Question ID: 1261682
The 3-month futures contract of a certain asset is priced at $1,020. Its underlying is
valued at $1,010 and pays an annual dividend rate of 1%. If the current risk-free rate
is 2.75%, the arbitrage profit opportunity is closest to:
A) $0.49.
B) $5.65.
C) $7.83.
D) $9.96.
Explanation
According to the cash-and-carry formula, the futures price should be:
1,010 × (1.0275 / 1.01)0.25 = $1,014.35
Hence, the futures is overvalued, indicating it should be sold and the asset be
purchased for a risk-free profit of $1,020 − $1,014.35 = $5.65.
(Book 3, Module 34.1, LO 34.f)
Question #53 of 100 Question ID: 1261636
An analyst derives expected returns for stocks A and B. Both are efficiently priced. If
the beta for Stock A is 0.72 and the beta for Stock B is 1.18, the slope of the security
market line (SML) for Stock A relative to the slope of the SML for Stock B will be:
A) lower.
B) higher.
C) the same.
D) �at.
Explanation
Since both stocks are efficiently priced, it means that their returns are both
represented by the SML. The slope of the SML is the difference between the
expected return on the market and the risk-free rate, and this differential is the
same along the entire SML. (Book 1, Module 5.2, LO 5.b)
Question #54 of 100 Question ID: 1261696
An investor with a short position and is preparing to deliver a bond for this position.
The bond to purchase for delivery is based on a settlement price of $98.03 (also
known as the quoted futures price). Which of the following four bonds is cheapest to
deliver?
Bond
Quoted Bond
Price
Conversion Factor
A 103 1.03
B 116 1.12
C 105 1.07
D 124 1.23
A) Bond A.
B) Bond B.
C) Bond C.
D) Bond D.
Explanation
Bond C is the cheapest-to-deliver bond, at $0.11.
Bond Cost of Delivery
A 103 − (98.03 × 1.03) = $2.03
B 116 − (98.03 × 1.12) = $6.21
C 105 − (98.03 × 1.07) = $0.11
D 124 − (98.03 × 1.23) = $3.42
(Book 3, Module 43.2, LO 43.e)
Question #55 of 100 Question ID: 1261652
An analyst estimates a stock has a 40% chance of earning 10%, a 40% chance of
earning 12.5%, and a 20% chance of earning 30%. Which of the following amounts is
closest to the stock's standard deviation of expected returns?
A) 2.44%.
B) 3.87%.
C) 6.00%.
D) 7.58%.
Explanation
Expected value = (0.4)(10%) + (0.4)(12.5%) + (0.2)(30%) = 15%
Variance = (0.4)(10 − 15)2 + (0.4)(12.5 − 15)2 + (0.2)(30 − 15)2 = 57.5
(Book 2, Module 13.2, LO 13.c)
Question #56 of 100 Question ID: 1261678
A hedger calculates the covariance between the spot and the futures prices to be
0.05, the spot standard deviation to be 0.3, and the futures standard deviation to be
0.2. Which of the following amounts is closest to the optimal hedge ratio for this
position?
A) 0.556.
B) 0.800.
C) 0.833.
D) 1.250.
Explanation
(Book 3, Module 32.1, LO 32.d)
Question #57 of 100 Question ID: 1261724
Standard deviation = = 7.58%57.5
− −−−√
HR = = = = 1.25BetaS,F
CovS,F
σ
2
F
0.05
0.22
For an option-free bond, which of the following are the effects of the convexity
adjustment on the magnitude (absolute value) of the approximate bond price change
in response to an increase in yield and in response to a decrease in yield,
respectively?
Decrease in yield Increase in yield
A) Increase in magnitude Decrease in magnitude
B) Increase in magnitude Increase in magnitude
C) Decrease in magnitude Decrease in magnitude
D) Decrease in magnitude Increase in magnitude
Explanation
Option-free bonds have positive convexity and the effect of (positive) convexity is to
increase the magnitude of the price increase when yields fall and to decrease the
magnitude of the price decrease when yields rise.
(Book 4, Module 56.2, LO 56.f)
Question #58 of 100 Question ID: 1261634
Which of the following is least correct in relation to the compensation committee? The
compensation committee should:
A) set remuneration that encourages management to take appropriate risks.
B) consider limiting bonuses.
C) consider introducing clawback provisions.
D) be able to understand and communicate risk exposures.
Explanation
Being able to understand and communicate risk exposures is a responsibility of the
risk management committee. (Book 1, Module 3.2, LO 3.c)
Question #59 of 100 Question ID: 1261663
A quantitative analyst runs a regression of monthly value stock returns on six
independent variables over 30 months. The total sum of squares for the regression is
350 and the sum of squared residuals is 130. Given this regression information, what
are the coefficient of determination (R2) and adjusted R2 measures, respectively?
A) 37.1%; 53.4%.
B) 37.1%; 79.0%.
C) 46.6%; 37.1%.
D) 63.0%; 53.4%.
Explanation
R2 = (350 − 130) / 350 = 0.63 = 63%
adjusted R2 = 1 − [(30 − 1) / (30 − 6 − 1) × (1 − 0.63)] = 0.534 = 53.4%
The R2 of 63% suggests that the six independent variables together explain 63% of
the variation in monthly value stock returns.
(Book 2, Module 19.2, LO 19.c)
Question #60 of 100 Question ID: 1261680
Suppose the spot rate is 1.1562 CHF/EUR. The two-year risk-free rate in Switzerland is
4.50% compounded annually, while the two-year risk-free rate in Germany is 3.50%
compounded annually. What is the two-year forward price of the CHF in terms of EUR
so that no arbitrage opportunity exists?
A) 1.1333.
B) 1.1447.
C) 1.1672.
D) 1.1787.
Explanation
Forward = spot × [(1 + quote currency rate) / (1 + base currency rate)]T =
1.1562 × (1.045 / 1.035)2 = 1.1787
(Book 3, Module 33.2, LO 33.k)
Question #61 of 100 Question ID: 1261646
Which of the following statements regarding the factors leading to the downfall of
Long-Term Capital Management (LTCM) is correct?
A)
Their trading strategies for �xed income instruments were based on the notion that
the credit spreads would ultimately increase.
B)
Their trading strategies for equity options were based on the notion that market
volatility would ultimately increase.
C)
D)
Their balance sheet leverage was far above the levels of other large investment 
banks.
Their models assumed that low-frequency/high-severity events were uncorrelated 
over time.
Explanation
LTCMbelieved that, although yield differences between risky and riskless fixed-
income instruments varied over time, the risk premium (or credit spread) tended to
revert (decrease) to average historical levels. This was similar to their equity
volatility strategy. Also, their balance sheet leverage was actually in line with other
large investments banks (but their true leverage, economic leverage, was not
considered).
(Book 1, Module 9.2, LO 9.a)
Question #62 of 100 Question ID: 1261640
For the past four years, the returns on a portfolio were 6%, 9%, 4%, and 12%. The
corresponding returns of the benchmark were 7%, 10%, 4%, and 14%. The risk-free
rate of return is 7%, and downside deviation is 1.58%. The portfolio's Sortino ratio is
closest to:
A) 0.3000.
B) 0.4747.
C) 0.7000.
D) 1.1068.
Explanation
The benchmark returns are not important here. The average of the portfolio returns
is (6 + 9 + 4 + 12) / 4 = 31 / 4 = 7.75.
Note: If the minimum acceptable return is not provided, it is reasonable to use the
risk-free rate instead.
(Book 1, Module 5.3, LO 5.g)
Question #63 of 100 Question ID: 1261692
Sortino ratio = = = 0.4743
E( )−RP Rmin
MSDmin
− −−−−−−√
7.75−7
2.5−−−√
Trader A purchased a three-month floating lookback call option on ABA stock three
months ago. Trader B purchased a three-month fixed lookback call option on the
same stock during the same time period as Trader A. ABA stock finished at $50 at the
end of the three-month option term, and the initial strike price was equal to $40. The
minimum stock price over the investment horizon was $35, and the maximum stock
price over the investment horizon was $53. The payoff difference between the floating
lookback call and the fixed lookback call is closest to:
A) $2.
B) $3.
C) $8.
D) $10.
Explanation
A floating lookback call pays the difference between the expiration price and the
minimum price of the stock over the horizon of the option. Therefore, its payoff is
equal to: $50 − $35 = $15. A fixed lookback call has a payoff function equal to the
difference between the maximum price during the option's life and the strike price.
Therefore, its payoff is equal to $53 − $40 = $13. The payoff difference between the
two exotic options is equal to $2.
(Book 3, Module 39.2, LO 39.e)
Question #64 of 100 Question ID: 1261706
Given the following 1-year transition matrix, which of the following amounts is closest
to the probability that an Aaa-rated firm will default over a 2-year period?
Rating From
Rating To
Aaa Baa Caa Default
Aaa 90% 10% 0% 0%
Baa 10% 80% 5% 5%
Caa 1% 4% 80% 15%
A) 0.00%.
B) 0.23%.
C) 0.50%.
D) 0.65%.
Explanation
At the end of year 1 there is a 0% chance of default and a 90% chance that the firm
will maintain an Aaa rating. In year 2, there is a 0% chance of default if the firm was
rated Aaa after 1 year (90% × 0% = 0%). There is a 5% chance of default if the firm
was rated Baa after 1 year (10% × 5% = 0.5%). Also, there is a 15% chance of default
if the firm was rated Caa after 1 year (0% × 15% = 0%). The probability of default is
0% from year 1 plus 0.5% chance of default from year 2 for a total probability of
default over a 2-year period of 0.5%.
(Book 4, Module 48.2, LO 48.h)
Question #65 of 100 Question ID: 1261711
The standardized approach for calculating operational risk capital requirements uses
beta factors for a given business line and annual gross income for business lines over
a 3-year period. Which of the following business units has the highest beta factor?
A) Trading and sales.
B) Retail banking.
C) Agency services.
D) Asset management.
Explanation
The beta factors used in the standardized approach for operational risk are as
follows: trading and sales: 18%; retail banking: 12%; agency services: 15%; asset
management: 12%.
(Book 4, Module 51.1, LO 51.b)
Question #66 of 100 Question ID: 1261686
An investor is following the real-time changes in the price of options on a particular
asset. She notices that both a European call and a European put on the same
underlying asset each have an exercise price of $45. The two options have six months
to expiration and are both selling for $4. She also observes that the underlying asset
is selling for $43 and that the rate of return on a 1-year Treasury bill is 6%. According
to put-call parity, which series of transactions would be necessary to take advantage
of any mispricing in this case?
A)
B)
Sell the call, sell a T-bill equal to the present value of $45, buy the put, and buy the 
underlying asset.
Buy the call, buy a T-bill equal to the present value of $45, sell the put, and sell the 
underlying asset.
C)
Buy the call, sell a T-bill equal to the present value of $45, sell the put, and buy the
underlying asset.
D)
Sell the call, buy a T-bill equal to the present value of $45, buy the put, and sell the
underlying asset.
Explanation
According to put-call parity:
c0 + PV(X) = p0 + S0
The left-hand side = $4 + $45 / (1.06)0.5 = $47.71
The right-hand side = $4 + $43 = $47
Since the value of the fiduciary call is not equal to the value of the protective put,
put-call parity is violated and there is an arbitrage opportunity.
Sell overpriced and buy underpriced. That is, sell the fiduciary call and buy the
protective put.
Therefore, sell the call for $4, sell the Treasury bill for $43.71 (i.e., borrow at the risk-
free rate), buy the put for $4 and buy the underlying asset for $43. The arbitrage
profit is $0.71.
(Book 3, Module 37.2, LO 37.c)
Question #67 of 100 Question ID: 1261667
Suppose we have the following regression equation using dummy variables for
explaining quarterly expenses in terms of the quarter of their occurrence:
EXPENSESt = β0 + β1D1,t + β2D2,t + β3D3,t + εt
where:
EXPENSESt = a quarterly observation of expenses
D1,t = 1 if period t is the first quarter, D1,t = 0 otherwise
D2,t = 1 if period t is the second quarter, D2,t = 0 otherwise
D3,t = 1 if period t is the third quarter, D3,t = 0 otherwise
The intercept term β0 represents the average value of EXPENSES for:
A) the rst quarter.
B) quarters one through four.
C) quarters one through three.
D) the fourth quarter.
Explanation
The intercept term represents the average value of EXPENSES for the fourth quarter.
The slope coefficient on each dummy variable estimates the difference in EXPENSES
(on average) between the respective quarter (i.e., quarter 1, 2, or 3) and the omitted
quarter (the fourth quarter, in this case). (Book 2, Module 22.2, LO 22.b)
Question #68 of 100 Question ID: 1261672
Suppose a firm with stock currently trading at $22 a share offers three shares of its
stock for one share of a target firm. The target firm's share price increases from $45
to $53 immediately following the announcement. To execute a traditional merger
arbitrage strategy, which of the following sets of positions should be taken?
A)
B)
C)
D)
Purchase three shares of the acquiring rm’s stock and short sell one share of the 
target rm’s stock.
Purchase one share of the acquiring rm’s stock and short sell three shares of the 
target rm’s stock.
Purchase three shares of the target rm’s stock and short sell one share of the 
acquiring rm’s stock.
Purchase one share of the target rm’s stock and short sell three shares of the 
acquiring rm’s stock.
Explanation
To execute a traditional merger arbitrage strategy, one would buy one share of
target firm stock with proceeds from every three shares of the acquiring firm's stock
sold short.
(Book 3, Module 27.2, LO 27.f)
Question #69 of 100 Question ID: 1261637
Which of the following statements concerning the capital asset pricing model (CAPM)
and the security market line (SML) is correct?
A)
Beta identifies the appropriate level of risk for which an investor should 
be compensated.
B) Unsystematic risk is not diversi�able, so there is no reward for taking on such risk.
C) Assets with equivalent betas will always earn di�erent returns.
D)
The market risk premiumis calculated by multiplying beta by the di�erence
between the expected return on the market and the risk-free rate of return.
Explanation
Beta identifies the appropriate level of risk for which an investor should be
compensated. Unsystematic risk is asset-specific and, therefore, a diversifiable risk.
The market risk premium is calculated as the excess of the expected return on the
market over the risk-free rate of return. Assets with equivalent betas should earn
the same return because arbitrage will prevent assets with the same risk from
earning different returns.
(Book 1, Module 5.2, LO 5.b)
Question #70 of 100 Question ID: 1261656
An analyst obtains sample statistics on return information for Vay Industries and
Ranch Meatpacking as follows:
Based on this information, which of the following amounts are the covariance
between the two sets of returns and the correlation coefficient, respectively?
Covariance Correlation coefficient
0.32
0.42
0.32
A) 5.98
B) 5.98
C) 6.52
D) 6.52 0.42
Explanation
[ − E ( )] × [ − E ( )] = 71.75∑
i=j=1
12
Ri Ri Rj Rj
= 379.90∑
i=1
12
[ − E ( )]Ri Ri
2
= 135.06∑
j=1
12
[ − E ( )]Rj Rj
2
(Book 2, Module 16.2, LO 16.k)
Question #71 of 100 Question ID: 1156192
A firm has determined that the value at risk (VaR) of its investment portfolio is $18
million for one day at a 95% confidence level. Which of the following statements
regarding this VaR measure is correct?
A)
B)
There is a 95% probability that the portfolio will lose $18 million on a given day. 
There is a 95% probability that the portfolio will lose no more than $18 million on a 
given day.
C) There is a 5% probability that the portfolio will lose $18 million on a given day.
D)
There is a 5% probability that the portfolio will lose no more than $18 million on a
given day.
Explanation
The VaR of this investment can be interpreted as either (1) there is a 95% probability
that the portfolio will lose no more than $18 million on a given day or (2) there is a
5% probability that the portfolio will lose more than $18 million on a given day.
(Book 1, Module 1.1, LO 1.c)
Question #72 of 100 Question ID: 1261709
= = = 6.52Covij
[ −E( )]×[ −E( )]∑
i=j=1
12
Ri Ri Rj Rj
n−1
71.75
11
= = = 5.88σi
∑
i=1
12
[ −E( )]Ri Ri
2
11
− −−−−−−−−−−−−−−
⎷
 379.90
11
− −−−−−−
√
= = = 3.5σj
∑
j=1
12
[ −E( )]Rj Rj
2
11
− −−−−−−−−−−−−−−−
⎷
 135.06
11
− −−−−−−
√
= = = 0.32rij
Covij
×σi σj
6.52
(5.88)(3.5)
Big City Bank has contractually agreed to a $20,000,000 credit facility with Upstart
Corp. Upstart will immediately access 40% of the total commitment (i.e., 60% remains
outstanding). Big City Bank estimates a 1-year probability of default between 1% and
2% and assigns a 20% recovery rate. Which of the following amounts represents the
difference between the minimum and maximum expected loss for Big City Bank?
A) Less than $100,000.
B) Between $100,000 and $200,000.
C) Between $200,000 and $300,000.
D) Greater than $300,000.
Explanation
We can calculate the expected loss as follows.
EL = EA × PD × LR
Maximum loss
EL = ($12,000,000) × (0.02) × (0.80) = $192,000
Minimum loss
EL = ($12,000,000) × (0.01) × (0.80) = $96,000
Therefore, the difference between maximum and minimum loss is $192,000 −
$96,000 = $96,000.
(Book 4, Module 50.1, LO 50.c)
Question #73 of 100 Question ID: 1261731
An existing option short position is delta-neutral, but has a −5,000 gamma exposure.
An option is available that has a gamma of 2 and a delta of 0.7. What actions should
be taken to create a gamma-neutral position that will remain delta-neutral?
A) Go long 2,500 options and sell 1,750 shares of the underlying stock.
B) Go long 2,500 options and buy 1,750 shares of the underlying stock.
C) Go long 10,000 options and sell 7,000 shares of the underlying stock.
D) Go long 10,000 options and buy 7,000 shares of the underlying stock.
Explanation
Since the current position is short gamma, the action that must be taken is to go
long the option in the ratio of the current gamma exposure to the gamma of the
instrument to be used to create the gamma-neutral position (5,000 / 2 = 2,500).
However, this will change the delta of the portfolio from zero to (2,500 × 0.7) =
1,750. This means that 1,750 of the underlying stock position will need to be sold to
maintain both gamma and delta neutrality.
(Book 4, Module 60.3, LO 60.h)
Question #74 of 100 Question ID: 1261690
Suppose that you buy a call option with an exercise price of $25 for $3 and sell a call
option with an exercise price of $35 for $1. If the stock price is $34 at expiration, your
net profit per share is closest to:
A) $6.
B) $7.
C) $8.
D) $9.
Explanation
You have purchased a bull spread. You will exercise the call that you purchased for a
net profit of (34 − 25) − 3 = $6 per share. The call that you sold will not be exercised,
so your net profit is the cost of $1 per share. Your total net profit is 6 + 1 = $7 per
share.
(Book 3, Module 38.2, LO 38.c)
Question #75 of 100 Question ID: 1261704
A portfolio manager is using a moving average model in which she assumes weights
decline exponentially back through time. The original volatility was calculated at 1.5%.
However, she believes a decay factor of 0.96 for an exponentially weighted moving
average (EWMA) model is appropriate for modeling a more realistic variance measure.
If the stock market return is 1% today, what is the new estimate of volatility using the
EWMA model?
A) 0.97%.
B) 1.31%.
C) 1.48%.
D) 1.58%.
Explanation
(Book 4, Module 47.3, LO 47.i)
σ2n = + (1 − λ) = 0.96 ( ) + (1 − 0.96) ( )λσ2n−1 u2n−1 0.015
2 0.012
= 0.000216 + 0.000004 = 0.00022
σ = = 0.01483 or 1.48%0.00022− −−−−−√
Question #76 of 100 Question ID: 1261642
Suppose an analyst uses a 2-factor model to analyze expected returns for the Silicon
Valley Internet Company (SVIC). The analyst identifies GDP and 3-month U.S. Treasury
bill rate as two factors for the factor model. Initial expected return for SVIC is 10%.
The following data is available:
GDP growth consensus forecast = 2%
T-bill rate consensus forecast = 0.75%
GDP factor beta for SVIC = +2.00
T-bill rate factor beta for SVIC = –4.00
Suppose that GDP ends up growing by 5% and the 3-month U.S. Treasury bill rate
ends up equaling 1.25%. Also suppose that during the period, SVIC unexpectedly
experiences extreme success with one of their new products, leading to revenues that
are higher than originally expected. Because of this, the firm-specific return is +1%
during the period. Using a 2-factor model with the revised data, the expected return
for SVIC is closest to:
A) 0%.
B) 5%.
C) 14%.
D) 15%.
Explanation
RSVIC = E(RSVIC) + βSVIC,GDPFGDP + βSVIC,IRFIR + eSVIC
RSVIC = 0.10 + 2.00(+0.03) – 4.00(0.005) + 0.01 = 0.15 = 15%. (Book 1, Module
6.2, LO 6.c)
Question #77 of 100 Question ID: 1261700
There are two arbitrary parameters used to calculate value at risk (VaR): the holding
period and the confidence level. Assume that the given return distribution has a mean
greater than zero. Which of the following pairs correctly describes the impact on VaR
for increases in the holding period and increases in the confidence level, respectively?
Holding period increases Confidence interval increases
A) VaR increases at a higher rate
VaR increases at an increasing
rate
B) VaR increases at a lower rate
C) VaR increases at a higher rate
D) VaR increases at a lower rate
VaR increases at an increasing 
rate
VaR increases at a decreasing 
rate
VaR increases at a decreasing 
rate
Explanation
With regard to an increase in holding period, if the return distribution has a mean
greater than zero, then VaR rises at a lower rate (and will eventually decrease). With
regards to an increase in confidence interval, VaR increases when the confidence
level increases. In addition, VaR will increase at an increasing rate as the confidence
level increases.
(Book 4, Module 45.1, LO 45.d)
Question #78of 100 Question ID: 1261712
You simulate the distribution of operational losses for your bank. You find that the
loss that corresponds to the 99th percentile of potential losses is $500,000 and the
mean of the distribution is $50,000. Your estimate of operational risk economic
capital is closest to:
A) $50,000.
B) $450,000.
C) $495,000.
D) $500,000.
Explanation
Operational risk economic capital is the difference between the loss at a given
confidence level and the expected loss. In this case, $500,000 − $50,000 = $450,000.
(Book 4, Module 51.1, LO 51.b)
Question #79 of 100 Question ID: 1261633
The treasurer for the Oakton Company is concerned about foreign currency risk due
to its foreign investment positions and having a significant amount of sales to
customers in foreign countries. To hedge against this risk, the treasurer would likely
take all of the following actions except:
A) entering into a forward contract to lock in an exchange rate.
B)
C)
D)
initiating a derivatives position, assuming the costs exceed the value of the hedge. 
purchasing currency put options to hedge against foreign currencies depreciating in 
the future.
incorporating foreign currency debt to help o�set the value of a decline in foreign 
investments.
Explanation
Due to inevitable exchange rate fluctuations, foreign currency risk is always a
concern for companies with monetary assets denominated in foreign currencies and
with sales to customers paying with foreign currencies. There are several ways to
hedge against this risk, but for each potential method, the costs of implementation
should be balanced against the expected benefit of the hedge. If the costs
associated with the hedge exceed the benefit, the best strategy would be to leave
the exposure unhedged. Assuming they are not cost prohibitive, using a forward
contract to lock in an exchange rate, buying put options to hedge against the
depreciation of foreign currencies, and incorporating foreign currency debt to offset
asset declines are all viable hedging strategies. (Book 1, Module 2.2, LO 2.d)
Question #80 of 100 Question ID: 1261661
A regression of a stock's return (in percent) on an industry index's return (in percent)
provides the following results:
Coefficient Standard Error
Intercept 2.1 2.01
Industry index 1.9 0.31
Degrees of
Freedom
SS
Explained 1 92.648
Residual 3 24.512
Total 4 117.160
Which of the following statements regarding the regression is incorrect?
A) The correlation coe�cient between the X and Y variables is 0.889.
B) The industry index coe�cient is signi cant at the 99% con dence interval.
C) If the return on the industry index is 4%, the stock’s expected return is 9.7%.
D) The variability of industry returns explains 21% of the variation of company returns.
Explanation
The R2 of the regression is calculated as ESS / TSS = (92.648 / 117.160) = 0.79, which
means that the variation in industry returns explains 79% of the variation in the
stock return. By taking the square root of R2, we can calculate that the correlation
coefficient (r) = 0.889. The t-statistic for the industry return coefficient is 1.9 / 0.31 =
6.13, which is sufficiently large enough for the coefficient to be significant at the
99% confidence interval. Since we have the regression coefficient and intercept, we
know that the regression equation is Rstock = 1.9X + 2.1. Plugging in a value of 4% for
the industry return, we get a stock return of 1.9 (4%) + 2.1 = 9.7%.
(Book 2, Module 18.2, LO 18.b)
Question #81 of 100 Question ID: 1261698
A bank entered into a 5-year $150 million annual-pay LIBOR-based interest rate swap
three years ago as the fixed rate payer at 5.5%. The relevant discount rates (annually
compounded) for 1-year and 2-year obligations are currently 5.75% and 6.25%,
respectively. A payment was just made. The value of the swap is closest to:
A) −$2,020,000.
B) $2,020,000.
C) $6,450,000.
D) −$6,450,000.
Explanation
Fixed-rate coupon = 150,000,000 × 0.055 = $8,250,000
Bfixed = 8.25 / 1.05751 + 158.25/ 1.06252 = 7.8014 + 140.1799 =
$147,981,331
Bfloating = $150,000,000
Vswap = $150,000,000 − $147,981,331 = $2,018,669
(Book 3, Module 44.2, LO 44.g)
Question #82 of 100 Question ID: 1261665
A hedge fund manager is analyzing a time series process of copper returns in order to
identify historical patterns that may be useful in forecasting future copper price
movements. Her analysis of the time series indicates that it exhibits serial
independence, is serially uncorrelated, and is normally distributed. Which white noise
process is most likely associated with this time series?
A) Independent white noise.
B) Zero-mean white noise.
C) Gaussian white noise.
D) Strong white noise.
Explanation
A time series process that exhibits serial independence, is serially uncorrelated, and
is normally distributed is referred to as normal (Gaussian) white noise. A time series
process that exhibits both a lack of serial correlation and serial independence is
referred to as independent white noise (or strong white noise). A time series
process with no mean, constant variance, and no serial correlation is referred to as
white noise (or zero-mean white noise).
(Book 2, Module 21.1, LO 21.c)
Question #83 of 100 Question ID: 1261719
Suppose a particular fixed-income instrument offers annual payments in the amount
of $10 per year for 20 years (without any additional payment at maturity). The current
price for this instrument is $150. The yield to maturity (YTM) on this security is closest
to:
A) 0.6%.
B) 1.4%.
C) 2.9%.
D) 8.4%.
Explanation
The YTM is the value of y that solves the following equation: $150 = $10 / (1 + y)1 +
$10 / (1 + y)2 + $10 / (1 + y)3 + … + $10 / (1 + y)20
We can solve for YTM using a financial calculator: N = 20; PMT = 10; PV = –150; CPT
→ I/Y = 2.91%. (Book 4, Module 55.2, LO 55.d)
Question #84 of 100 Question ID: 1261647
In the case of Barings Bank, Nick Leeson incurred huge trading losses. Which of the
following statements correctly describes one of the factors that led to the bankruptcy
of Barings?
A) Barings had insu�cient liquidity to cover marked to market losses.
B) Leeson had a supervisor control the back-o�ce functions on his trades.
C)
Leeson held speculative double short positions in the market for Nikkei 225 futures
contracts.
D)
There was ambiguity concerning who was responsible for performing speci c 
oversight functions.
Explanation
The basic problem at Barings was operation risk control. Nick Leeson was in charge
of trading and settlement. This dual responsibility allowed him to hide losses by
crossing trades at fabricated prices. He then booked the profitable side of the trade
in accounts that were reported and the unprofitable side in an unreported account.
The lack of supervision also permitted him to shift from hedged trading strategies to
speculative strategies in an effort to hide previously incurred losses. Clearly his
reporting to multiple managers in a convoluted organizational structure led to
ambiguity concerning who was responsible for performing specific oversight
functions.
(Book 1, Module 9.2, LO 9.a)
Question #85 of 100 Question ID: 1261713
A portfolio manager has a portfolio of investment securities for a commercial bank.
The portfolio has a current market value equal to $5,334,500 with a daily variance of
0.0002. Over the years, the portfolio has increased its proportionate holdings of
equity securities, and the manager is concerned that the portfolio may be riskier than
the bank's internal regulations allow. The annual VaR (5%) assuming there are 250
trading days in a year is closest to:
A) 0.52%.
B) 2.33%.
C) 36.89%.
D) 43.82%.
Explanation
First convert the daily variance into a daily standard deviation .
daily VaR(5%)percentage basis = z5% × σ = 1.65(0.01414) = 0.02333 = 2.333%
(Book 4, Module 54.1, LO 54.c)
Question #86 of 100 Question ID: 1261651
= 0.014140.0002− −−−−√
annual VaR(5%)percentage basis = daily VaR× = 0.02333 ×(5%)percentage basis 250
−−−√ 250−−−√
= 0.3689 = 36.89%
An economist estimates a 60% probability that the economy will expand next year.
The technology sector has a 70% probability of outperforming the market if the
economy expands and a 10% probability of outperforming the market if the economy
does not expand. Given the new information that the technology sector will not
outperform the market, the probability that the economy will not expand is closest to:
A) 67%.
B) 54%.
C) 33%.
D) 48%.
Explanation
Using the new information we can use Bayes' formula to update the probability.
P(economy does not expand | tech does not outperform) = P(economy does not
expand and tech does not outperform) / P(tech does not outperform)
P(economy does not expand) = 1.00 − P(economy does expand) = 1.00 − 0.60 = 0.40
P(tech does not outperform | economy does not expand) = 1.00 − P(tech does
outperform | economy does not expand) = 1.00 − 0.10 = 0.90
P(economy does not expand and tech does not outperform) = P(tech does not
outperform | economy does not expand) × P(economy does not expand) = 0.90 ×
0.40 = 0.36
P(economy does expand and tech does not outperform) = P(tech does not
outperform | economy does expand) × P(economy does expand) = 0.30 × 0.60 =
0.18
P(tech does not outperform) = P(tech does not outperform and economy does not
expand) + P(tech does not outperform and economy does expand) = 0.36 + 0.18 =
0.54
P(economy does not expand | tech does not outperform) = P(economy does not
expand and tech does not outperform) / P(tech does not outperform) = 0.36 / 0.54 =
0.67
(Book 2, Module 12.2, LO 12.g)
Question #87 of 100 Question ID: 1261694
Two bond analysts are discussing the level of event risk in their bond portfolio. 
Analyst A says that since their portfolio consists of investment grade bonds, event risk 
should not be a concern. Analyst B says that since they have a small number of 
different issues in their portfolio, and event risk is idiosyncratic, the event risk in their 
portfolio is negligible. Which, if either, of these statements is based on correct 
assumptions?
A) Neither statement by the analysts are correct.
B) The statement made by Analyst A is correct, but not the one made by Analyst B.
C) The statement made by Analyst B is correct, but not the one made by Analyst A.
D) Both statements made by the analysts are correct.
Explanation
Even investment grade bonds are exposed to the risk of the issuer being taken over
or merging with another company. Event risk can increase on a market level if there
is a trend toward increasing mergers in the economy.
(Book 3, Module 41.2, LO 41.e)
Question #88 of 100 Question ID: 1261659
An investment analyst takes a random sample of 100 aggressive equity funds and
calculates the average beta as 1.7. The sample betas have a standard deviation of 0.4.
Using a 95% confidence interval and a z-statistic, which of the following statements
about the confidence interval and its interpretation is most likely accurate? The
analyst can be confident at the 95% level that the interval:
A) 0.916 to 2.484 includes the mean of the sample betas.
B) 1.622 to 1.778 includes the mean of the sample betas.
C) 0.916 to 2.484 includes the mean of the population beta.
D) 1.622 to 1.778 includes the mean of the population beta.
Explanation
Given that the population variance is unknown and the sample size is large, the 95%
confidence interval for the population mean is:
The confidence interval is:
(Book 2, Module 17.2, LO 17.f)
Overview for Questions #89-90 of
100 Question ID: 1261720
Use the following information to answer Questions 89 and 90.
±x̄ zα/2
s
n−−√
1.7 ± 1.96( ) = 1.7 ± 1.96 (0.04) = 1.7 ± 0.0784 = 1.622 to 1.7780.4
100− −−√
An investor has a short position in a 20-year, 5% coupon, U.S. Treasury bond (T-bond)
with a yield to maturity (YTM) of 6% and par value of $100. Assume discounting occurs
on a semiannual basis.
Question #89 of 100 Question ID: 1261721
Which of the following amounts is closest to the dollar value of a basis point (DV01)?
A) 0.1053.
B) 0.1061.
C) 0.1351.
D) 0.1360.
Explanation
For the 6% bond, N = 20 × 2 = 40; I/Y = 6 / 2 = 3; PMT = 5 / 2 = 2.5; FV = 100; CPT →
PV = 88.4426. For the 6.01% bond, N = 20 × 2 = 40; I/Y = 6.01 / 2 = 3.005; PMT = 5 / 2
= 2.5; FV = 100; CPT → PV = 88.3365. P0 − P1 = 88.4426 − 88.3365 = 0.1061. Note:
This explanation used an increase in yield. The DV01 for a decrease in yield is
0.1063.
(Book 4, Module 56.1, LO 56.b)
Question #90 of 100 Question ID: 1261722
Using a 30-year, 5% coupon, U.S. T-bond yielding 5% with a DV01 of 0.1544 to hedge
the interest rate risk in the 20-year bond, which of the following actions should the
investor take?
A) Buy $68.20 of the hedging instrument.
B) Buy $68.72 of the hedging instrument.
C) Buy $87.50 of the hedging instrument.
D) Buy $88.08 of the hedging instrument.
Explanation
The hedge ratio is (0.1061 / 0.1544) = 0.6872. Since the investor has a short position
in his bond portfolio, the investor needs to buy $0.6872 of par value of the hedging
instrument for every $1 of par value for the 20-year bond.
(Book 4, Module 56.1, LO 56.c)
Question #91 of 100 Question ID: 1156194
Match the following events to the corresponding risk type.
1. A rogue trader within an institution.
2. Stock XYZ decreases in price due to a market crisis.
3. Using a put option to hedge an equity exposure.
4. Counterparty sues bank to avoid meeting its obligations.
A) 1: legal risk; 2: credit risk; 3: strategic risk; 4: credit risk.
B) 1: business risk; 2: market risk; 3: market risk; 4: settlement risk.
C) 1: operational risk; 2: equity price risk; 3: basis risk; 4: legal risk.
D) 1: reputation risk; 2: basis risk; 3: credit risk; 4: legal risk.
Explanation
"A rogue trader within an institution" is an example of operational risk. "Stock XYZ
decreases in price due to a market crisis" is an example of equity price risk. "Using a
put option to hedge an equity exposure" is an example of basis risk. "Counterparty
sues bank to avoid meeting its obligations" is an example of legal risk.
(Book 1, Module 1.2, LO 1.f)
Question #92 of 100 Question ID: 1261674
A Canadian-based tire company is due a $2,500,000 SGD payment from its Singapore-
based distributor in two months. The Canadian firm hedges the exchange rate risk
using a forward contract priced at $0.80 CAD/SGD. If the Singapore dollar depreciates
over the next two months to a spot rate of $0.73 CAD/SGD, how much more or less
will the Canadian-based tire firm receive in Canadian dollars by hedging, versus an
unhedged position?
A) $175,000 CAD more.
B) $175,000 CAD less.
C) $70,000 CAD more.
D) $29,167 SGD less.
Explanation
Hedged
position:
$0.80 CAD/SGD
$250,000 SGD × $0.80 CAD/SGD = $2,000,000 CAD
Unhedged
position:
$2,500,000 × $0.73 CAD/SGD = $1,825,000 CAD
(Book 3, Module 28.2, LO 28.f)
Question #93 of 100 Question ID: 1261693
Use the following information and the bootstrapping methodology.
Price as a
Percentage of Par
Annual
Coupon
Annual
Period
Maturity
(Years)
102.6364 4.25% 1 1
105.3651 4.75% 2 2
What is the 2-year spot rate?
A) 0.50%.
B) 1.98%.
C) 2.22%.
D) 3.95%.
Explanation
First, solve for the 1-year spot rate:
$102.6364 = ($100 + 4.25) × e−z1
Solving for z1 = −ln[$102.6364 / ($100 + 4.25)] = 1.56%
Next, use this rate to solve for the 2-year spot rate:
$105.3651 = (4.75 × e−0.0156) + (100 + 4.75) × e−z2 × 2
$100.6886 = (100 + 4.75) × e−z2 × 2
Solving for z2 = −ln[$100.6886 / ($100 + 4.75)] / 2 = 0.0198, or 1.98%.
(Book 3, Module 40.2, LO 40.d)
Question #94 of 100 Question ID: 1261728
Which of the following statements is not correct regarding the use of implied volatility
to predict future volatility?
A)
The implied volatility model assumes that asset prices follow a continuous time
lognormal di�usion process.
B) Options with the same underlying assets may trade at di�erent “vol” terms.
C) Implied volatility is lessthan actual volatility on average.
D) Implied volatility data is limited to a few assets and markets.
Explanation
Empirical results suggest implied volatility is greater than realized volatility on
average, causing an upward bias in predictions.
(Book 4, Module 59.3, LO 59.e)
Question #95 of 100 Question ID: 1261666
Consider the following estimated time series model: xt = −6.0 + 1.1xt−1 + 0.3xt−2 + εt.
This model is estimated over 50 periods. The value of the time series for the 49th
observation is 20 and the value of the time series for the 50th observation is 22. What
is the out-of-sample forecast for the 52nd observation?
A) 24.20.
B) 27.22.
C) 28.72.
D) 42.00.
Explanation
First, forecast the 51st observation by plugging the known values into the model.
Next, use the previous two values to forecast the 52nd observation.
Forecasted x51 = −6.0 + 1.1(22) + 0.3(20) = 24.2
Forecasted x52 = −6.0 + 1.1(24.2) + 0.3(22) = 27.22
(Book 2, Module 21.2, LO 21.d)
Question #96 of 100 Question ID: 1261658
A financial analyst wants to determine whether there is a significant difference, at the
5% significance level, between the mean monthly return on Stock GHI and the mean
monthly return on Stock JKL. He assumes the variances of the two stocks' returns are
equal. Using the last 12 months of returns on each stock, Fisher calculates a t-statistic
of 2.0 for a test of equality of means. Based on this result, his test:
A) accepts the null hypothesis.
B) rejects the null hypothesis, and Fisher can conclude that the means are equal.
C) rejects the null hypothesis, and Fisher can conclude that the means are not equal.
D) fails to reject the null hypothesis.
Explanation
The null hypothesis for a test of equality of means is H0: μ1 – μ2 = 0. Assuming the
variances are equal, degrees of freedom for this test are (n1 + n2 – 2) = 12 + 12 – 2 =
22. From the table of critical values for Student's t-distribution, the critical value for
a two-tailed test at the 5% significance level for df = 22 is 2.074. Because the
calculated t-statistic of 2.0 is less than the critical value, this test fails to reject the
null hypothesis that the means are equal. (Book 2, Module 17.1, LO 17.a)
Question #97 of 100 Question ID: 1261707
Political risk is a broad risk, encompassing items such as whether a country is a
democracy or a dictatorship and the smoothness with which a country transfers
political power. Which of the following statements regarding how political risk affects
investing is most likely incorrect?
A)
B)
C)
D)
It is not clear if authoritarian or democratic governmental regimes produce higher 
economic growth.
Some investors prefer the stability of investing in companies from countries where 
one leader controls decision-making.
Countries with democratic governmental policies have discontinuous risk because 
policies change frequently.
Countries with high government corruption impose an implicit tax on investors 
because they directly reduce company pro ts and returns.
Explanation
Risks in democratic governments are continuous, but generally low. Countries with
autocratic leadership have discontinuous risk because policy changes are often
severe and difficult to protect against. (Book 4, Module 49.1, LO 49.b)
Question #98 of 100 Question ID: 1261683
An investor wishes to compute the exchange rate of a 7-month futures contract on
the Swiss franc. Each contract controls 125,000 Swiss francs and is quoted in terms of
dollar/franc. Suppose the current exchange rate is 1.02 dollar/franc. What is the 7-
month futures exchange rate assuming an annually compounded risk-free rate in
Switzerland of 2% and an annually compounded risk-free rate in the U.S. of 1%?
A) 0.987 dollar/franc.
B) 1.002 dollar/franc.
C) 1.014 dollar/franc.
D) 1.225 dollar/franc.
Explanation
Using the interest rate parity formula, the futures exchange rate is computed as
follows:
F0 = 1.02 × (1.01 / 1.02)7/12 = $1.014 / CHF
(Book 3, Module 34.1, LO 34.h)
Question #99 of 100 Question ID: 1261717
You have derived the following spot rate curve and forward rates from the prices of
Treasury STRIPS:
Maturity
(Years)
Spot Rate Forward Rate
0.5 1.50% 1.50%
1.0 2.15% 2.80%
1.5 2.53% 3.29%
2.0 2.94% ?
Using the information in the table, the 6-month forward rate on an investment that
matures in 2.0 years is closest to:
A) 3.40%.
B) 3.70%.
C) 3.78%.
D) 4.18%.
Explanation
The forward rate can be calculated from 
.
Solving for f gives 0.0418, or 4.18%.
(Book 4, Module 54.2, LO 54.c)
Question #100 of 100 Question ID: 1261687
An options portfolio manager is going on vacation and does not plan to return until
the day the options are set to expire. The portfolio manager gives his assistant
instructions on four of the long option positions in his portfolio (all options have the
same expiration date). Which of the following pairs of options and instructions is
correct?
= ×(1 + )0.0294
2
4
(1 + )0.0253
2
3
(1 + )f
2
1
A)
B)
C)
D)
At-the-money American call option with a strike of $50 on a stock that does not pay 
a dividend; exercise if the stock price doubles.
American put option with a strike of $25 on a stock currently selling for $50 that 
does not pay a dividend; exercise the option if the stock price falls by more than 
80%.
Deep-in-the-money European call option with a strike price of $30 and a current 
stock price of $50; exercise immediately.
Deep-in-the-money American call option with a strike price of $100 where the stock 
has a dividend that exceeds the risk-free rate by 4%; exercise on the ex-dividend 
date.
Explanation
American put options on non-dividend-paying stocks may be optimally exercised
early. American call options on non-dividend-paying stocks should never be
exercised before expiration, and European options cannot be exercised prior to
expiration. American call options on dividend-paying stocks may be exercised early
if the dividend received exceeds the amount of forgone interest. If this is the case,
exercise should take place immediately before (not on) the ex-dividend date.
(Book 3, Module 37.2, LO 37.d)