8008 : Exam III: Risk Management Frameworks Exam

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8008
Exam III: Risk Management Frameworks
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Question: 95
Which of the following are considered properties of a ‘coherent’ risk measure:
I. Monotonicity
II. Homogeneity
III. Translation Invariance
IV. Sub-additivity
A. II and III
B. II and IV
C. I and III
D. All of the above
Answer: B
Explanation:
All of the properties described are the properties of a ‘coherent’ risk measure. Monotonicity means that if a portfolio’s
future value is expected to be greater than that of another portfolio, its risk should be lower than that of the other
portfolio. For example, if the expected return of an asset (or portfolio) is greater than that of another, the first asset
must have a lower risk than the other. Another example: between two options if the first has a strike price lower than
the second, then the first option will always have a lower risk if all other parameters are the same. VaR satisfies this
property.
Homogeneity is easiest explained by an example: if you double the size of a portfolio, the risk doubles. The linear
scaling property of a risk measure is called homogeneity. VaR satisfies this property.
Translation invariance means adding riskless assets to a portfolio reduces total risk. So if cash (which has zero standard
deviation and zero correlation with other assets) is added to a portfolio, the risk goes down. A risk measure should
satisfy this property, and VaR does. Sub-additivity means that the total risk for a portfolio should be less than the sum
of its parts. This is a property that VaR satisfies most of the time, but not always. As an example, VaR may not be
sub-additive for portfolios that have assets with discontinuous payoffs close to the VaR cutoff quantile.
Question: 96
Which of the following credit risk models focuses on default alone and ignores credit migration when assessing credit
risk?
A. CreditPortfolio View
B. The contingent claims approach
C. The CreditMetrics approach
D. The actuarial approach
Answer: D
Explanation:
The correct answer is Choice ‘d’. The following is a brief description of the major approaches available to model
credit risk, and the analysis that underlies them:
Question: 97
For a US based investor, what is the 10-day value-at risk at the 95% confidence level of a long spot position of EUR
15m, where the volatility of the underlying exchange rate is 16% annually. The current spot rate for EUR is 1.5.
(Assume 250 trading days in a year).
A. 526400
B. 2632000
C. 1184400
D. 5922000
Answer: C
Explanation:
The VaR for a spot FX position is merely a function of the standard deviation of the exchange rate. If V be the value
of the position (in this case, EUR 15m x 1.5 = USD 22.5m), z the appropriate z value associated with the level of
confidence desired, and be the standard deviation of the portfolio, the VaR is given by ZV.
In this case, the 10-day standard deviation is given by SQRT(10/250)*16%. Therefore the VaR is
=1.645*15*1.5*(16%*SQRT(10/250)) = USD 1.1844m. Choice ‘c’ is the correct answer.
Question: 98
Which of the following statements are true:
I. Top down approaches help focus management attention on the frequency and severity of loss events, while bottom
up approaches do not.
II. Top down approaches rely upon high level data while bottom up approaches need firm specific risk data to estimate
risk.
III. Scenario analysis can help capture both qualitative and quantitative dimensions of operational risk.
A. III only
B. II and III
C. I only
D. II only
Answer: B
Explanation:
Top down approaches do not consider event frequency and severity, on the other hand they focus on high level
available data such as total capital, income volatility, peer group information on risk capital etc. Bottom up approaches
focus on severity and frequency distributions for events. Statement I is therefore not correct.
Top down approaches do indeed rely upon high level aggregate data and tend to infer operational risk capital
requirements from these. Bottom up approaches look at more detailed firm specific information. Statement II is correct.
Scenario analysis requires estimating losses from risk scenarios, and allows incorporating the judgment and views of
managers in addition to any data that might be available from internal or external loss databases. Statement III is
correct. Therefore Choice ‘b’ is the correct answer.
Question: 99
Which of the following need to be assumed to convert a transition probability matrix for a given time period to the
transition probability matrix for another length of time:
I. Time invariance
II. Markov property
III. Normal distribution
IV. Zero skewness
A. I, II and IV
B. III and IV
C. I and II
D. II and III
Answer: C
Explanation:
Time invariance refers to all time intervals being similar and identical, regardless of the effects of business cycles or
other external events. The Markov property is the assumption that there is no ratings momentum, and that transition
probabilities are dependent only upon where the rating currently is and where it is going to. Where it has come from,
or what the past changes in ratings have been, have no effect on the transition probabilities. Rating agencies generally
provide transition probability matrices for a given period of time, say a year. The risk analyst may need to convert
these into matrices for say 6 months, 2 years or whatever time horizon he or she is interested in. Simplifying
assumptions that allow him to do so using simple matrix multiplication include these two assumptions – time
invariance and the Markov property. Thus Choice ‘c’ is the correct answer. The other choices (normal distribution and
zero skewness) are non-sensical in this context.
Question: 100
The CDS rate on a defaultable bond is approximated by which of the following expressions:
A. Hazard rate / (1 – Recovery rate)
B. Loss given default x Default hazard rate
C. Credit spread x Loss given default
D. Hazard rate x Recovery rate
Answer: B
Explanation:
The CDS rate is approximated by the [Loss given default x Default hazard rate]. Thus Choice ‘b’ is the correct answer.
Note that this is also equal to the credit spread on the reference bond over the risk free rate. Therefore credit spreads
and CDS rates are generally the same. Also, ‘loss given default’ is nothing but (1 – Recovery rate). This can be
substituted in the formula for the credit spread to get an alternative expression that directly refers to the recovery rate.
Therefore all other choices are incorrect.
Question: 101
Which of the following steps are required for computing the aggregate distribution for a UoM for operational risk once
loss frequency and severity curves have been estimated:
I. Simulate number of losses based on the frequency distribution
II. Simulate the dollar value of the losses from the severity distribution
III. Simulate random number from the copula used to model dependence between the UoMs
IV. Compute dependent losses from aggregate distribution curves
A. I and II
B. III and IV
C. None of the above
D. All of the above
Answer: A
Explanation:
A recap would be in order here: calculating operational risk capital is a multi-step process. First, we fit curves to
estimate the parameters to our chosen distribution types for frequency (eg, Poisson), and severity (eg, lognormal). Note
that these curves are fitted at the UoM level – which is the lowest level of granularity at which modeling is carried out.
Since there are many UoMs, there are are many frequency and severity distributions. However what we are interested
in is the loss distribution for the entire bank from which the 99.9th percentile loss can be calculated.
From the multiple frequency and severity distributions we have calculated, this becomes a two step process:
– Step 1: Calculate the aggregate loss distribution for each UoM. Each loss distribution is based upon and underlying
frequency and severity distribution.
– Step 2: Combine the multiple loss distributions after considering the dependence between the different UoMs. The
‘dependence’ recognizes that the various UoMs are not completely independent, ie the loss distributions are not
additive, and that there is a sort of diversification benefit in the sense that not all types of losses can occur at once and
the joint probabilities of the different losses make the sum less than the sum of the parts.
Step 1 requires simulating a number, say n, of the number of losses that occur in a given year from a frequency
distribution. Then n losses are picked from the severity distribution, and the total loss for the year is a summation of
these losses. This becomes one data point. This process of simulating the number of losses and then identifying that
number of losses is carried out a large number of times to get the aggregate loss distribution for a UoM.
Step 2 requires taking the different loss distributions from Step 1 and combining them considering the dependence
between the events. The correlations between the losses are described by a ‘copula’, and combined together
mathematically to get a single loss distribution for the entire bank. This allows the 99.9th percentile loss to be
calculated.
Question: 102
Which of the following are valid techniques used when performing stress testing based on hypothetical test scenarios:
I. Modifying the covariance matrix by changing asset correlations
II. Specifying hypothetical shocks
III. Sensitivity analysis based on changes in selected risk factors
IV. Evaluating systemic liquidity risks
A. I, II, III and IV
B. II, III and IV
C. I, II and III
D. I and II
Answer: D
Explanation:
Each of these represent valid techniques for performing stress testing and building stress scenarios. Therefore d is the
correct answer. In practice, elements of each of these techniques is used depending upon the portfolio and the exact
situation.
Question: 103
For identical mean and variance, which of the following distribution assumptions will provide a higher estimate of
VaR at a high level of confidence?
A. A distribution with kurtosis = 8
B. A distribution with kurtosis = 0
C. A distribution with kurtosis = 2
D. A distribution with kurtosis = 3
Answer: A
Explanation:
A fat tailed distribution has more weight in the tails, and therefore at a high level of confidence the VaR estimate will
be higher for a distribution with heavier tails. At relatively lower levels of confidence however, the situation is
reversed as the heavier tailed distribution will have a VaR estimate lower than a thinner tailed distribution.
A higher level of kurtosis implies a ‘peaked’ distribution with fatter tails. Among the given choices, a distribution with
kurtosis equal to 8 will have the heaviest tails, and therefore a higher VaR estimate. Choice ‘a’ is therefore the correct
answer. Also refer to the tutorial about VaR and fat tails.
Question: 104
Which of the following measures can be used to reduce settlement risks:
A. escrow arrangements using a central clearing house
B. increasing the timing differences between the two legs of the transaction
C. providing for physical delivery instead of netted cash settlements
D. all of the above
Answer: C
Explanation:
increasing the timing differences between the two legs of the transaction will increase settlement risk and not reduce it.
Using escrow arrangements, such as central clearing houses to settle transactions (eg the DTCC in the United States)
reduces settlement risk. Cash settlements based on netting arrangements reduce settlement risk, while physical delivery
combined with gross cash payments increase it. Therefore Choice ‘a’ is the correct answer.
Question: 105
CORRECT TEXT
The standard error of a Monte Carlo simulation is:
A. Zero
B. The same as that for a lognormal distribution
C. Proportional to the inverse of the square root of the sample size
D. None of the above
Answer: C
Explanation:
When we do a Monte Carlo simulation, the statistic we obtain (eg, the expected price) is an estimate of the real
variable. The difference between the real value (which would be what we would get if we had access to the entire
population) and that estimated by the Monte Carlo simulation is measured by the ‘standard error’, which is the
standard deviation of the difference between the ‘real’ value and the simulated value (ie, the ‘error’).
As we increase the number of draws in a Monte Carlo simulation, the closer our estimate will be to the true value of
the variable we are trying to estimate. But increasing the sample size does not reduce the error in a linear way, ie
doubling the sample size does not halve the error, but reduces it by the inverse of the square root of the sample size. So
if we have a sample size of 1000, going up to a sample size of 100,000 will reduce the standard error by a factor of 10
(and not 100), ie, SQRT(1/100) = 1/10. In other words, standard error is proportional to 1/N, where N is the sample
size.
Therefore Choice ‘c’ is correct and the others are incorrect.
Question: 106
If the 1-day VaR of a portfolio is $25m, what is the 10-day VaR for the portfolio?
A. $7.906m $79.06m
B. $250m
C. Cannot be determined without the confidence level being specified
Answer: B
Explanation:
The 10-day VaR is = $25m x SQRT(10) = $79.06m. Choice ‘b’ is the correct answer.
Question: 107
Which of the following are elements of ‘group risk’:
I. Market risk
II. Intra-group exposures
III. Reputational contagion
IV. Complex group structures
A. II, III and IV
B. II and III
C. I and IV
D. I and II
Answer: A
Explanation:
The term ‘group risk’ has been defined in the FSA document 08/24 on stress testing as the risk that a firm may be
adversely affected by an occurrence (financial or non-financial) in another group entity or an occurrence that affects
ther group as a whole.
These risks may occur through:
– reputational contagion,
– financial contagion,
– leveraging,
– double or multiple gearing,
– concentrations and large exposures (particularly intra-group).
Thus, the insurance sector may be considered a group, and a firm may suffer just because another group firm has had
losses or reputational issues.
The FSA statement goes on to identify some elements of group risk as follows:
– intra-group exposures (credit or operational exposures through outsourcing or service arrangements, as well as more
standard business exposures);
– concentration risks (from credit, market or insurance risks which could put a strain on capital resources across
entities simultaneously);
– contagion (reputational damage, operational or financial pressures); and
– complex group structures (with dependencies, complex split of responsibilities and accountabilities).
Therefore Choice ‘a’ is the correct answer and the rest of the choices are incorrect.

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