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Part I
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
₀
2. Evaluate the definite integral: ʃ xex2 dx
₂
a) 5.437
b) 26.799
c) 21.285
d) 7.389
3. Which of the following statements is false?
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.
4. Determine the inverse matrix of: (1 2
0 2)
a) (1 2
0 0.5) b) (1 1
0 0.5) 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?
a) E ([x–σ ]2)
b) E ([x–μ ]4)
c) E ([x–μ ]3)
d) E ([x–μ ]4)
μ2
σ4
σ3
E ([x–σ ]4)
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 = { .25 = 0
=1
=2 a) .6875
b) .4727
c) .8291
d) .4281 .25
.50 Part II
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:
a) Price Vol ( ) = Modified Duration (MD) x interest rate (Y) x Yield Vol (σy)
b) Price Vol (σp ) =MDx σy
Y
c) Price Vol (σp ) =MDx σy
d) Price Vol (σp ) =MDx (1 + Y) x qy
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
5. Assuming independence and a recovery rate of 70%, what is the expected loss on the following
portfolio?
Face Value of 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 Jan
0 Feb
9 a)
0.
7
0
c) 0.
3
1 0.
9
0.
1 0.
1
0.
9 Mar
0
b) Apr
0 May
0 Jun
6 Jul
0 Aug
3 Sept
3 Oct
0 Nov
6 Dec
3 0.9 0.1
0
1 d)
0.3 0.7
1
0 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 Part III
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
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
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