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THE PROFESSIONAL RISK MANAGER (PRM™)
C E R T I F I C AT I O N P R O G R A M
PRM Self Study Guide –
Sample Questions
(FIVE OF FIVE)
2011 EDITION
U P D AT E D - J A N U A R Y - 2 0 1 3
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PRMIA
FROM THE CRADLE TO THE PINNACLE OF YOUR CAREER
A Higher Standard for Risk Professionals
A
s a non-profit, member-led association of professionals, the Professional
Risk Managers’ International Association (PRMIA) is dedicated to advancing
the standards of the profession worldwide through the free exchange of ideas.
We are committed to helping our members achieve these standards through the
following resources.
■
CONNECTION TO A LOCAL CHAPTER NETWORK OF 90,000 MEMBERS WORLDWIDE –
PRMIA offers 200 meetings each year are offered through its local chapters, giving members
access to the best practices of the global risk profession and to a local network of colleagues.
■
THE PROFESSIONAL RISK MANAGER (PRM) CERTIFICATION – Endorsed by leading
universities and businesses, the PRM certification is the global standard for financial risk
managers.
■
ASSOCIATE PRM CERTIFICATE – Covers the core concepts of risk management, allowing
non-specialists to interpret risk management information and reports, make critical
assessments, and evaluate the implications and the limitations of such results.
■
PRMIA MEMBERS HAVE ACCESS TO A WEALTH OF ONLINE RESOURCES
cluding a Jobs Board with risk management job openings
cities around the world, links to past presentations and
papers, and much more.
■
PRMIA EDUCATION – Offering classroom instruction
and over 700 online professional development courses,
all customizable to your personal or corporate needs.
Inin
W W W. P R M I A . O R G
J
oin thousands of other risk professionals dedicated to advancing the standards of the risk profession worldwide by becoming a Sustaining member of PRMIA. This exclusive membership
provides the highest level of benefits, discounts, and opportunities available. Visit
http://www.prmia.org/membership or email support@prmia.org to become a member or
to learn more.
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TM
PRM SELF-STUDY GUIDE – SAMPLE QUESTIONS
OVERVIEW
T
TM
he PRM certification tests a candidate’s knowledge and understanding of the foundations of
finance theory, the financial instruments that provide tools for the mitigation or transfer of risk,
and the financial markets in which instruments are traded and capital is raised.
This Self-Study Guide helps in focusing your study on the key Learning Outcome Statements from each
chapter. These Learning Outcome Statements form the basis for the questions asked during the PRM
TM
examination. We recommend that you first read the chapter, then review the Learning Outcome Statements, then re-read the chapter with particular emphasis on these points.
We recommend strongly that you do not simply read the Learning Outcome Statements and then try to
find the information about each in the books as a short-cut way of preparing for the exam. Real-life risk
management requires your ability to assemble information from many simultaneous inputs and you
can expect that some exam questions will draw from multiple Learning Outcome Statements.
TM
Taking the PRM qualification, as well as working as a risk officer, requires a certain amount of mathematical expertise. This is not excessive. Anyone who was passed mathematics studies at advanced high
school level, or who has completed the first year of a university degree in a mathematical-based qualification (physics, economics, engineering, etc) should have no problem with the requirements. For others,
we recommend that they take tuition in the mathematics required and that they focus on this as the
TM
first part of their studies for the PRM .
This section of the Study Guide provides some Sample Exam Questions. You may also wish to
purchase access to further online Sample Exams via the PRMIA website to assess your readiness.
Please note that testing conditions, your state of mind and various factors can make your performance
on the actual exams somewhat less strong than on the Sample Exams. If your Sample Exam scores
are near to the passing mark, you may wish to study the subject materials even
further.
TABLE OF CONTENTS
TM
Please remember that the exams of the PRM certification are very challenging.
Overview
p. 1
After all it’s “a higher standard in risk certification” and you would expect nothing
Sample Exam Questions
p. 4
less. There is no guarantee that using the Self-Study Guide, in combination with
Exam I
p. 4
the reading materials and Sample Exams will give you a passing score. But, they
Exam II
p. 7
should all provide you with assistance in doing your best. We wish you much suc-
Exam III
p. 9
cess in your effort to become certified as a Professional Risk Manager!
Exam IV
p. 12
Answers
p. 14
1
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WORD DEFINITIONS
In this guide, we use Command Words. These are similar to those used by the CFA Institute, with a few
additional words, and indicate levels of ability expected from successful candidates on each Learning
Outcome Statement.
Calculate
To ascertain or determine by mathematical processes.
Characterize
To describe the essential character or quality of.
Compare
To examine the character or qualities of, for the primary purpose of
discovering resemblances.
Construct
To create by organizing ideas or concepts logically and coherently.
Contrast
To compare in respect to differences.
Deconstruct
To disassemble the key elements of ideas or concepts.
Define
To set forth the meaning of; specifically, to formulate a definition of.
Demonstrate To prove or make clear by reasoning or evidence; to illustrate and explain,
especially with examples.
2
Derive
To obtain by reasoning.
Describe
To transmit a mental image, an impression, or an understanding of the nature
and characteristics of.
Differentiate
To mark or show a difference in; to develop different characteristics in.
Discuss
To discourse about through reasoning or argument; to present in detail.
Draw
To express graphically in words; to delineate.
Explain
To give the meaning or significance of; to provide an understanding of;
to give the reason for or cause of.
Identify
To establish the identity of; to show or prove the sameness of.
List
To enumerate.
Show
To set forth in a statement, account, or description; to make evident or clear.
State
To express in words.
PRM
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USAGE OF THE CALCULATOR
At the exam centre you will have access to an on-line Texas Instrument TI308XS calculator. No other materials
may be brought into the exam room with you. It is suggested that candidates purchase the hand-held version
(TI-30XS) to fully familiarize themselves with the calculator. User guide for the calculator can be found by
clicking on the link:
http://education.ti.com/guidebooks/scientific/30xmv/TI30XSMultiViewGuide_en.pdf
TI308XS Calculator Download Instructions
For system requirements please click on system requirements and download instructions
Note: The practice exam is not accessible on Mac computers.
1. Download the Pearson Vue Tutorial & Practice Exam by clicking here – if the link does not work, cut and paste
this in your browser: http://www.pearsonvue.com/athena/PearsonVueTutorialDemo.msi
2. Click "run" if you have that option otherwise click "save file"
3. Open the saved file. (If you clicked "Run" skip this step)
4. Follow the Software Installation prompts
5. Run the installed software
6. Check the box for the Practice Exam
7. Click on the "next" button until you get to the screen with the calculator icon in the upper left hand corner of
the screen.
8. Click on the calculator icon to be able practice with the TI308XS calculator.
O VE RVIEW
3
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SAMPLE EXAM QUESTIONS
T
he following sample questions should give you a flavor for the format and content of the actual
exams. They are only part of the length of the actual exams and therefore do not cover all subjects
contained in the detailed content descriptions provided in this Study Guide. Questions on any of the
subjects listed in the Study Guide documents may appear on the actual exam.
EXAM I – FINANCE THEORY, FINANCIAL INSTRUMENTS AND MARKETS
1.
Assume you live in a CAPM world and the expected return on the market portfolio is 9%, while the risk free
rate is 3%. If the beta of stock A is 1.3, the expected return on A is:
a) 14.7%
b) 12.9%
c) 10.8%
d) 16.8%
2.
In the valuation of derivatives, the expression "change of measure" means:
a) Setting the drift to zero
b) Change of volatility
c) Both (a) and (b)
d) None of the above
3.
Which of the following is true?
a) Non-Markovian interest rate processes are usually represented by recombining trees
b) Markovian interest rate processes are usually represented by recombining trees
c) Non-Markovian interest rate processes are usually represented by trinomial trees
d) None of the above
4.
Which of the following is/are true concerning preferred stocks?
a) They are somehow similar to subordinated debt, but unlike bond holders preferred share holders could
not force a company into bankruptcy if preferred coupons (dividends) were not paid on time
b) Many preferred shares provide for cumulative preferred dividend payments having priority over
ordinary dividends
c) From an issuer’s tax perspective, preferred stocks are a more expensive source of financing than bonds
d) All of the above
4
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5.
A fixed income instrument will pay 12-month Libor on a 1,000 Swiss Francs(CHF) face value two times: one
year from today and two years from today (no principal payment). The rates are set in arrears (payments at
the end of a year reflect the Libor rate at the beginning of the year). What is the price of this instrument if
the (zero-coupon) two-year CHF swap curve is a 3% for all maturities?
a) CHF 57.4
b) CHF 1000
c) CHF 1067
d) CHF 67.6
6.
In a long option straddle strategy, where one buys a put and a call simultaneously at the same strike, the
following is true:
a) Delta will be zero, regardless of the level of the spot price
b) Gamma will be the highest at the money and approaching maturity
c) Delta will be near to 1 at the money and approaching maturity
d) Gamma will be zero at the money and approaching maturity
7.
Herstatt Risk relates to:
a) the market risk of an FX contract
b) the German Mark debacle of 1978
c) the settlement risk of an FX contract
d) none of the above
8.
If a dealer sells a security to a customer and the customer pledges to resell that security to the dealer,
the dealer calls the trade:
a) A reverse repo
b) A forward sale
c) A repo
d) A reverse forward
9.
A gas market maker (MM) has agreed to deliver gas at $3/MMBtu 6 months from now. The spot price for
gas is $2.50/MMBtu, the 6 month forward price is $2.75/MMBtu, the interest rate is 6% and storage cost is
$0.03/month per MMBtu. The MM is confident that the price would be $2.70 six months from now. Given
the MM’s market view, what is the best strategy for the MM to meet its obligation?
a) Buy on the spot market
b) Buy the forward
c) Do nothing
d) MM is indifferent between c) and b)
E XA M I – FINANCE THEORY, F IN A N CIA L IN STRUM EN T S A N D M A RKE T S
5
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10.
Assume the following price curve for crude oil in bbl and ignore the time value of money.
Month
Price
1
$21
2
$22
3
$23
4
$24
5
$25
6
$26
A customer wants a tailored six month swap with constant volumes but request the fixed price for the last
two months to be set at $20/bbl. What must be the fixed price for the first four months?
a) Not determinable
b) 26.0
c) 23.7
d) None of the above
6
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EXAM II – MATHEMATIC FOUNDATIONS OF RISK MEASUREMENT
1.
Find a linear polynomial p(x) that is a tangent-line approximation for the function: ƒ(x) = exp(2x – 4)
at the point x0 = 3.
a) 14.778x – 36.945
b) 7.389x + 2.718
c) 2.718x
d) 14.778x + 0.018
₂
ʃ xex
2
₀
dx
2.
Evaluate the definite integral:
3.
Which of the following statements is false?
4.
a) 5.437
b) 26.799
c) 21.285
d) 7.389
a) Singular matrices have determinant 0.
b) Singular matrices have columns that are not independent vectors.
c) A product of two non-singular matrices can be singular.
d) Singular matrices have 0 as an eigenvalue.
(
)
(
)
Determine the inverse matrix of:
a)
1 2
0 0.5
b)
1 -1
0 0.5
(
1 2
0 2
c)
(
)
0.5 -1
0 1
)
d)
(
)
1 -1
0.5 0
5. What can we say about the sum X + Y of two independent normal random variables X and Y:
a) It is normal only if X and Y have the same mean
b) It is always normal
c) It is chi-squared
d) It is chi-squared if X and Y both have mean 0
6. What is the formula for the skewness of a random variable x that has mean μ and standard deviation σ?
2
a) E ([ x– σ ] )
μ2
4
b) E ([ x–μ ] )
σ4
3
c) E ([ x–μ ] )
σ3
E XA M II – MAT HEMATICA L F OUN DATION S OF RISK M E A SURE M E N T
4
d) E ([ x–μ ] )
E ([ x–σ ]4)
7
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7.
A covariance matrix for a random vector:
a) Is strictly positive definite, if it exists
b) Is nonsingular, if it exists
c) Always exists
d) None of the above
8.
What is the standard deviation of a random variable Q with probability function ØO =
a) .6875
b) .4727
c) .8291
d) .4281
8
PRM
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{
.25 = 0
.25 = 1
.50 = 2
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EXAM III – RISK MANAGEMENT PRACTICES
1.
Under the standard parametric VaR methodology, which of the following assumptions is true?
a) Returns follow a log normal distribution
b) Log returns follow a normal distribution
c) Mean log return is zero for daily VaR
d) All of the above
2.
Under the RiskMetrics cashflow mapping method for interest rates, price volatility is required. The formula
to convert yield volatility (expressed as a percentage of current yield) to price volatility is:
σy
Y
a) Price Vol ( ) = Modified Duration (MD) x interest rate (Y) x Yield Vol (σy)
b) Price Vol (σp ) = MD x
c) Price Vol (σp ) = MD x σ y
d) Price Vol ( σp ) = MD x (1 + Y) x q y
3.
For EWMA (Exponentially Weighted Moving Average), using a decay factor of 0.94 and a tolerance level of
1% (i.e. excluding exponential weights below 1%), the effective number of data points used to estimate the
covariance matrix is:
a) 74
b) 150
c) 100
d) 250
4.
The portfolio has one risky bond from company A. Company A is a subsidiary of XYZ and if XYZ defaults
Company A does so too. The probability of default of XYZ is 0.3 and the probability of company A going into
bankruptcy without XYZ defaulting is 0.5. What is the probability of having a default on the risky bond?
a) Cannot be determined
b) 0.60
c) 0.70
d) None of the above
E XA M III – RISK MANA GEM EN T PRA CTICES
9
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5.
Assuming independence and a recovery rate of 70%, what is the expected loss on the following portfolio?
Face value of the bond
Probability of Default
Bond A
1,000 Euros (EUR)
0.4
Bond B
2,000 EUR
0.3
a) 300 EUR
b) 900 EUR
c) 1,000 EUR
d) None of the above
6.
How is the loss given default incorporated in the CreditMetrics Technical Document?
a) The document does not consider it
b) By a parameterized distribution
c) By a look up table
d) By a constant
7.
What is characteristic of a default mode credit risk model?
a) A model which considers two states of nature
b) A model which incorporates a default definition
c) A model which considers default as a reflecting state
d) None of the above
8.
What is the one-year transition matrix assuming only two categories [i.e. default (d) and non-default (nd)]
from a portfolio with 300 loans and the following payment history?
Number of loans that transited from non default to default in 2000
a)
10
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
0
9
0
0
0
6
0
3
3
0
6
3
0.7
0.3
0
1
b)
0.9
0.1
0
1
c)
0.9
0.1
0.1
0.9
PRM
TM
d)
0.3
0.7
1
0
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9.
The Merton (1974) model implies that a position in a credit-sensitive bond is equivalent to:
a) A long position in the firm’s equity and a short position in a risk-free bond
b) A long put and a long call position on the firm’s assets
c) A long position in a credit-risk-free bond and a short put on the firm’s assets
d) An up-and-in call on a credit-risk-free bond and a short call on the firm’s equity
10.
Given a one-year probability of default of 20%, what would be the cumulative probability of default for the
bond for the three years?
a) 45.4%
b) 48.8%
c) 60.5%
d) None of the above
11.
The Bank for International Settlement’s, Basel Committee on Banking Supervision, has defined Operational
risk as “The risk of loss due to inadequate or failed internal processes, people, and systems, or from
external events.” This definition excludes:
a) Reputational risk
b) Strategic risk
c) Legal risk
d) a) and b)
12.
The Bank for International Settlement’s, Basel Committee on Banking Supervision recommends the
operational risk management process at the corporate and business unit levels to be validated by:
a) Audit
b) A committee of the board of directors
c) A designated member of senior management
d) None of the above
E XA M III – RISK MANA GEM EN T PRA CTICES
11
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EXAM IV – CASE STUDIES, PRMIA STANDARDS OF BEST PRACTICE, CONDUCT AND ETHICS
1.
Which position would have partially hedged Nick Leeson’s primary option position at Barings?
a) Long futures
b) Short Strangle
c) Long Strangle
d) Total Return Swap
2.
Nick Leeson tried to hide his losses using what method?
a) Portaling
b) Switching
c) Re-margining
d) Volatility Smiles
3.
What caused the losses for Metallgesellschaft?
a) At the final maturity date the price in the futures was well below the market price
b) To hold the position, they assumed a constant interest rate to invest the proceeds
c) At the final maturity date the price in the futures was well above the market price
d) To hold the position, they assumed an unbounded pool of resources
4.
In the Metallgesellschaft case, what was the communication problem between the subsidiary and the
parent company?
a) They did not communicate the loss as soon as it started to kick in
b) They did not communicate the intrinsic bet on the price of gas
c) They did not explain the economics of the strategy
d) They did not explain why they had to buy more future contracts
5.
The strategy of getting creditors to lend money and invest equity in LTCM had the effect of:
a) Increasing transparency to the creditors
b) Reducing leverage
c) Giving LTCM partners a put on the value of the fund
d) No relevant effect as equity and debt offset each other
12
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6.
LTCM’s balance sheet as of August 31, 1998 showed the following:
a) $100 billion in assets, $-0.5 billion in equity
b) $125 billion in assets, $2.3 billion in equity
c) $400 billion in assets, $4.0 billion in equity
d) $125 billion in assets, $6.1 billion in equity
7.
According to the G-30, derivative credit exposure should be measured by:
a) Current Exposure
b) Potential Exposure
c) a) plus b)
d) a) plus b) minus Posted Collateral
8.
According to the G-30 report, an ISDA master agreement is:
a) Sufficient to prevent loss from counterparty default
b) Not substantially enhanced by a netting provision as bankruptcy courts widely recognize netting as a
best practice
c) Enhanced when multiple master agreements exist between the same counterparties so that the legal risk
of an oversight in documentation is reduced
d) None of these
9.
Which of the following is not part of PRMIA’s guidance on Best Practices?
a) Only standard methods of assessing risk should be used
b) PRMIA members must possess, be under the supervision of someone who possesses, or inform their
supervisor of the lack of required skills and/or certification to complete their risk assessment work
c) PRMIA members must not intentionally deceive others
d) PRMIA members must value validation of their work by peers
E XA M IV – CASE STUDIES, PRM IA STA N DA RDS OF BE ST PRA CT I CE , CO N DUCT A N D E T HI CS
13
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ANSWERS
Exam I
Exam II
Exam III
Exam IV
1. c
1. a
1. c
1. c
2. d
2. b
2. a
2. b
3. b
3. c
3. a
3. d
4. d
4. b
4. d
4. c
5. a
5. b
5. a
5. c
6. b
6. c
6. b
6. b
7. c
7. d
7. a
7. d
8. c
8. c
8. b
8. d
9. c
9. c
9. a
10. d
10. b
10. a
11. d
12. a
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PRM Self-Study Resources
T
o meet the demand from PRM candidates for
distance learning opportunities, PRMIA has developed a suite of self-study
options to make studying for the PRM exam convenient and effective.
EPRM COACH ONLINE TRAINING
ePRM Coach is a comprehensive self-study guide for the PRMTM Certification Exam. Designed in accordance
with the PRMTM exam structure, the ePRM Coach is equipped with concepts and practices, including:
■ Exhaustive theoretical material supplemented with contemporary case studies
■ Learner friendly courses complete with formulae, definitions, concise summaries,
and interactive simulations
■ State-of-the-art simulated learning environment
■ Solved examples, practice exercises and quizzes
■ Mock exams from a proprietary database
■ Timed tests in exam format
■ Personalized results for self assessment
■ Glossary, FAQs, tips center and pocket reference
■ Valuable reference extracts
■ Online access with 24x7 customer support
EPRM DIAGNOSTIC EXAMS
ePRM Diagnostic Exams are mock exams designed in
accordance with PRMIA’s exam structure and feature:
■ Simulation of the actual PRMTM Exam
■ State-of-the-art learning environment
■ Timed tests in exam format
■ Personalized results for self-assessment
■ 24x7 online access
www.PRMIA.org
To learn more about all of these
PRM self-study resources please visit
www.prmia.org or contact
support@prmia.org.
The Professional Risk Managers’ International Association · www.PRMIA.org · support@PRMIA.org