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NEW QUESTION # 113
Which of the following are considered properties of a 'coherent' risk measure:
I. Monotonicity
II. Homogeneity
III. Translation Invariance
IV. Sub-additivity
- A. I and III
- B. All of theabove
- C. II and IV
- D. II and III
Answer: C
Explanation:
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 thatof 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 thanthe 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 thetime, 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.
NEW QUESTION # 114
Which of the following statements are true:
I. Heavy tailed parametricdistributions are a good choice for severity modeling in operational risk.
II. Heavy tailed body-tail distributions are a good choice for severity modeling in operational risk.
III. Log-likelihood is a means to estimate parameters for a distribution.
IV. Body-tail distributions allow modeling small losses differently from large ones.
- A. All of the above
- B. II, III and IV
- C. I and IV
- D. II and III
Answer: A
Explanation:
Explanation
When modeling for operational risk, we are generally concerned with tail losses - this isbecause the horizon for operational risk is 1 year at the 99.9th percentile. Since the 99.9th percentile is in the tail region, we would like to ensure that the tails are modeled as accurately as possible. Operational risk distributions are modeled usingheavy tailed distributions.
Heavy tailed parametric distributions such as log-normal, pareto and others are therefore a good choice for modeling risk severity, therefore statement I is correct.
Body-tail distributions are combinations of parametric distributions, with different types of distributions being used to model the body and the tail - this provides flexibility because small and medium losses upto a threshold can be modeled using one distribution, and losses beyond the threshold can be modeled usinga different distribution that is a better estimate of the tail. Statement II is therefore correct.
A log-likelihood function simplifies the optimization of a regular likelihood function. We generally maximize (or minimize the risk functional) a likelihoodfunction with a view to estimating the parameters of the underlying distribution. If the likelihood function is complex, it may sometimes make it mathematically easier to optimize the log of the function - as that changes exponents and multiplications toadditions, while behaving in the same way as the underlying function. Therefore statement III is correct, log-likelihood is a means to estimate parameters for a distribution.
Statement IV is correct as body-tail distributions allow modeling different partsof the distribution differently from each other.
NEW QUESTION # 115
Which of the following are valid approaches for extreme value analysis given a dataset:
I. The Block Maxima approach
II. Least squares approach
III. Maximum likelihood approach
IV. Peak-over-thresholds approach
- A. All of the above
- B. I, III and IV
- C. I and IV
- D. II and III
Answer: C
Explanation:
Explanation
For EVT, we use the block maxima or the peaks-over-threshold methods. These provide us the data points that can be fitted to a GEVdistribution.
Least squares and maximum likelihood are methods that are used for curve fitting, and they have a variety of applications across risk management.
NEW QUESTION # 116
Loss from a lawsuit from an employee due to physical harm caused while at work is categorized per Basel II as:
- A. Execution delivery and process management
- B. Unsafe working environment
- C. Employment practices and workplace safety
- D. Damage to physical assets
Answer: C
Explanation:
Explanation
Choice 'a' is the correct answer. Refer to the detailed loss event type classification under Basel II (see Annex 9 of the accord). You should know the exact names of all loss event types, and examples of each.
NEW QUESTION # 117
If X represents a matrix with ratings transition probabilities for one year, the transition probabilities for 3 years are given by the matrix:
- A. P ^ (-3)
- B. P x P x P
- C. 3 [P]
- D. 3 [P ^ (-1)]
Answer: B
Explanation:
Explanation
Assuming timeinvariance and the Markov property, it is easy to calculate the transition matrix for any time period as P^n, where P is the given transition matrix for one period and n the number of time periods that we need to compute the new transition matrix for. ThusChoice 'b' is the correct answer.
NEW QUESTION # 118
The sensitivity (delta) of a portfolio to a single point move in the value of the S&P500 is $100. If the current level of the S&P500 is 2000, and has a one day volatility of 1%, what is the value-at-risk for this portfolio at the 99% confidence and a horizon of 10 days? What is this method of calculating VaR called?
- A. $14,736, parametric VaR
- B. $4,660, Monte Carlo simulation VaR
- C. $14,736, historical simulation VaR
- D. $4,660, parametric VaR
Answer: A
Explanation:
Explanation
If the current level of the S&P 500 is 2000, and a single day volatility is 1%, and the delta (ie change in portfolio value from a one point change) is $100, then the 1 day volatility for the portfolio in dollars is 2000 *
1% * $100 = $2,000.
At the 99% confidence level, the value of the inverse cumulative density function for the normal distribution is
2.33 (=NORMSINV(99%), in Excel). Therefore the 1 day VaR will be 2.33 * $2000 =$4,660. Extending it to
10 days using the square root of time rule, we get the 10 day VaR as equal to SQRT(10)*4660 = $14,736.
Since this method of calculating VaR relies upon a delta approximation of a risk factor (in this case the S&P500), it is the parametric approach to calculating VaR (the other methods being historical simulation, and Monte Carlo simulation).
The
2015 Handbook provides an excellent example of parametric (and other) VaR calculations in Chapter 3 of Volume III of Book 3. The spreadsheet used for the illustration can be downloaded from
http://www.prmia.org/prm-exam/handbook-resources.
NEW QUESTION # 119
The standalone economic capital estimates for the three business units of a bank are $100, $200 and $150 respectively. What is the combined economic capital for the bank, assuming the risks of the three business units are perfectly correlated?
- A. 0
- B. 1
- C. 2
- D. 3
Answer: A
Explanation:
Explanation
Since the business units are perfectly correlated, we can get the combined EC as equal to the sum of the individual EC estimates.Therefore Choice 'a' is the correct answer.
NEW QUESTION # 120
Which of the following event types is hacking damage classified under Basel II operational risk classifications?
- A. Information security
- B. Technology risk
- C. External fraud
- D. Damage to physical assets
Answer: C
Explanation:
Explanation
Choice 'b' is the correct answer. All other answers are incorrect.
Refer to the detailed loss event type classification underBasel II (see Annex 9 of the accord). You should know the exact names of all loss event types, and examples of each.
NEW QUESTION # 121
Which of the following is a measure of the level of capital that an institution needs to hold in order to maintain a desired credit rating?
- A. Regulatory capital
- B. Economic capital
- C. Book value
- D. Shareholders' equity
Answer: B
Explanation:
Explanation
Economic capital is a measure of the level of capital needed to maintain adesired credit rating. Regulatory capital is the amount of capital required to be held by regulation, and this may be quite different from economic capital. Book value is an accounting measure reflecting the assets minus liabilities as measured per accounting rules, this is often expressed per share. Shareholders' equity is a narrow term which is the amount of capital attributable to the shareholders and includes paid up capital and reserves but not long term debt or other non-equity funding.
Therefore Choice 'b' is the correct answer.
NEW QUESTION # 122
Which of the following credit risk models considers debt as including a put option on the firm's assets toassess credit risk?
- A. The CreditMetrics approach
- B. The actuarial approach
- C. CreditPortfolio View
- D. The contingent claims approach
Answer: D
Explanation:
Explanation
The correct answer is Choice 'c'. The following is a brief description of the major approaches available to model credit risk, and the analysis that underlies them:
1. CreditMetrics: based on the credit migration framework. Considers the probability of migration to other credit ratings and the impact of such migrations on portfolio value.
2. CreditPortfolio View: similar to CreditMetrics, but adds the impact of the business cycle to the evaluation.
3. The contingent claims approach: uses option theory by considering a debt as a put option on the assets of the firm.
4. KMV's EDF (expected default frequency) based approach: relies on EDFs and distance to default as a measure of credit risk.
5. CreditRisk+: Also called the 'actuarial approach', considers default as a binary event that either happens or does not happen. This approach does not consider the loss of value from deterioration in credit quality (unless the deterioration implies default).
NEW QUESTION # 123
Which of the following decisions need to be made as part of laying down a system for calculating VaR:
I. The confidence level and horizon
II. Whether portfolio valuation is based upon a delta-gamma approximation or a full revaluation III. Whether the VaR is to be disclosed in the quarterly financial statements IV. Whether a 10 day VaR will be calculated based on 10-day return periods, or for 1-day and scaled to 10 days
- A. II and IV
- B. I and III
- C. All of the above
- D. I, II and IV
Answer: D
Explanation:
Explanation
While conceptually VaR is a fairly straightforward concept, a number of decisions need to be made to select between the different choices available for the exact mechanism to be used for the calculations.
The Basel framework requires banks toestimate VaR at the 99% confidence level over a 10 day horizon. Yet this is a decision that needs to be explicitly made and documented. Therefore 'I' is a correct choice.
At various stages of the calculations, portfolio values need to be determined. The valuation can be done using a 'full valuation', where each position is explicitly valued; or the portfolio(s) can be reduced to a handful of risk factors, and risk sensitivities such as delta, gamma, convexity etc be used to value the portfolio. The decisionbetween the two approaches is generally based on computational efficiency, complexity of the portfolio, and the degree of exactness desired. 'II' therefore is one of the decisions that needs to be made.
The decision as to disclosing the VaR in financial filings comes after the VaR has been calculated, and is unrelated to the VaR calculation system a bank needs to set up. 'III' is therefore not a correct answer.
Though the Basel framework requires a 10-day VaR to be calculated, it also allows the calculation of the 1-day VaR and and scaling it to 10 days using the square root of time rule. The bank needs to decide whether it wishes to scale the VaR based on a 1-day VaR number, or compute VaR for a 10 day period to begin with. 'IV' therefore is a decision tobe made for setting up the VaR system.
NEW QUESTION # 124
When modeling operational risk using separate distributions for loss frequency and loss severity, whichof the following is true?
- A. Loss severity and loss frequency are modeled as conditional probabilities
- B. Loss severity and loss frequency are considered independent
- C. Loss severity and loss frequency are modeled usingthe same units of measurement
- D. Loss severity and loss frequency distributions are considered as a bivariate model with positive correlation
Answer: B
Explanation:
Explanation
When modeling operational loss frequency distribution (which, for example, may be based upon a Poisson distribution) and a loss severity distribution (for example, based upon a lognormal distribution), it is assumed that the frequency of losses and the severity of the losses are completely independent and do not impact each other. Therefore Choice 'a' is correct, and the others are not validassumptions underlying the operational loss modeling.
Once each of these distributions has been built, a random number is drawn from each to determine a loss scenario. The process is repeated many times as part of a Monte Carlo simulation to get a the lossdistribution.
NEW QUESTION # 125
Which of the following best describes the concept of marginalVaR of an asset in a portfolio:
- A. Marginal VaR is the value of the expected losses on occasions where the VaR estimate is exceeded.
- B. Marginal VaR is the change in the VaR estimate for the portfolio as a result of including the asset in the portfolio.
- C. Marginal VaR is the contribution of the asset to portfolio VaR in a way that the sum of such calculations for all the assets in the portfolio adds up to the portfolio VaR.
- D. Marginal VaR describes the change in total VaR resulting from a $1 change in the value of the asset in question.
Answer: D
Explanation:
Explanation
The correct answer is choice 'd'
Marginal VaR is just the change in total VaR from a $1 change in the value of the asset in the portfolio. All other answers are incorrect. Mathematically, it is expressed as follows, where VaRp is the VaR for the portfolio, and Vi is the value of the asset in question.
Other answers describe other VaR related concepts such as incremental VaR, Component VaR and Conditional VaR.
NEW QUESTION # 126
What percentage of average annual gross income is to be held as capital for operational risk under the basic indicator approach specified under Basel II?
- A. 0.125
- B. 0.15
- C. 0.08
- D. 0.12
Answer: B
Explanation:
Explanation
Banks using the basic indicator approach must hold 15% of the average annual gross income for the past three years, excluding any year that had a negative gross income.Therefore Choice 'd' is the correct answer.
NEW QUESTION # 127
For creditrisk calculations, correlation between the asset values of two issuers is often proxied with:
- A. Equity correlations
- B. Default correlations
- C. Credit migration matrices
- D. Transition probabilities
Answer: A
Explanation:
Explanation
Asset returns are relevant for credit risk models where a default is related to the value of the assets of the firm falling below the default threshold. When assessing credit risk for portfolios with multiple credit assets, it becomes necessary to know the asset correlations of the different firms. Since this data is rarely available, it is very common to approximate asset correlations using equity prices. Equity correlations are used as proxies for asset correlation, therefore Choice 'c' is the correct answer.
NEW QUESTION # 128
Which of the following will be a loss not covered by operational risk as defined under Basel II?
- A. Systems failure
- B. Strategic planning
- C. Fat finger losses
- D. Earthquakes
Answer: B
Explanation:
Explanation
Operational risk isdefined as the risk of loss resulting from inadequate or failed internal processes, people and systems or from external events. This definition includes legal risk, but excludes strategic and reputational risk.
Therefore any losses from poor strategic planning will not be a part of operational risk. Choice 'd' is the correct answer.
Note that floods, earthquakes and the like are covered under the definition of operational risk as losses arising from loss or damage to physical assets from natural disaster orother events.
NEW QUESTION # 129
Altman's Z-score does not consider which of the following ratios:
- A. Net income to total assets
- B. Working capital to totalassets
- C. Sales to total assets
- D. Market capitalization to debt
Answer: A
Explanation:
Explanation
A computation of Altman's Z-score considers the following ratios:
- Working capital to total assets
- Retained earnings to total assets
- EBIT to total assets
- Market cap to debt
- Sales to total assets
It does not consider Net Income to total assets, therefore Choice 'c' is the correct answer. This makes sense as net income is after interest and taxes, both of which are not relevant for considering the cash flows for debt servicing.
NEW QUESTION # 130
Which of the following is not a parameter to be determined by the risk manager that affects the level of economic credit capital:
- A. Probability of default
- B. Confidence level
- C. Definition of credit losses
- D. Risk horizon
Answer: A
Explanation:
Explanation
Three parameters define economic credit capital: the risk horizon, ie the time horizon over which the risk is being assessed; the confidence level, ie the quintile of the loss distribution; and the definition of credit losses, ie whether mark-to-market losses are considered in addition to default-only losses. The probability of default is not a parameter within the control of the risk manager, but an input into the capital calculation process that he has to estimate. Therefore Choice 'c' is the correct answer.
NEW QUESTION # 131
If F be the face value of a firm's debt, V the value of its assets and E the market value of equity, then according to the option pricing approach a default on debt occurs when:
- A. V < E
- B. F < V
- C. F > V
- D. F - E < V
Answer: C
Explanation:
Explanation
According to the option pricing approach developed by Merton, the shareholders of a firm have a put on the assets of the firm where the strike price is equal to the face value of the firm's debt. This is just a more complicated way of saying that the debt holders are entitled to all the assets of the firm if these assets are insufficient to pay off the debts, and because of limited liability of the shareholders of a corporation this part payment will fully extinguish thedebt.
A firm will default on its debt if the value of the assets falls below the face value of the debt. Therefore Choice
'a' is the correct answer. All other choices are incorrect.
(There are two ways to consider this sort of optionality, and I have mentioned only one for this question:
1. The equity holders can sell the assets of the firm to the debt holders at a price equal to the face value of the debt, ie a put. (ie they can extinguish their liability to the debt holders in full by handing them the assets of the firm, effectively selling them the assets at the value of the debt)
2. The equity holders have a long position in a call option where they can keep the assets of the firm by paying a price equal to the face value of the debt (ie, they can pay off the debt holders and keep the assets) For this question, perspective 1 applies but you should be aware of the second one too as a question may reference that view point.)
NEW QUESTION # 132
When pricing credit risk for an exposure, which of the following is a better measure than the others:
- A. Potential Future Exposure (PFE)
- B. Expected Exposure (EE)
- C. Notional amount
- D. Mark-to-market
Answer: B
Explanation:
Explanation
Exposure for derivative instruments can vary significantly over the lifetimeof the instrument, depending upon how the market moves. The potential future exposure represents the extremes, not the most likely outcome.
The expected exposure is the most suitable measure for pricing the credit risk. Over time, as multiple transactionsare entered into, the expectation (or the mean) will be realized - though individual transactions may have more or less by way of exposure.
The notional amount may not be relevant, though for loans it may be the most important contributor to the expected exposure. Mark-to-market will represent the exposure at a given point in time, but cannot be predicted nor be used to price the credit risk.
NEW QUESTION # 133
For a bank using the advanced measurement approach to measuring operational risk, which of the following brings the greatest 'model risk' to its estimates:
- A. Insufficient number of simulations when building the loss distribution
- B. Choice of incorrect parameters for loss severity distributions
- C. Choice of an incorrect distribution for loss event frequencies
- D. Aggregation risk, from selecting an incorrect value of estimated correlations between different operational risk estimates
Answer: D
Explanation:
Explanation
The greatest model risk when calculating operational risk capital comes fromincorrect assumptions about correlations between different operational risks for which standalone risk calculations have been made.
Generally, the correlation can be expected to be positive, and would therefore vary between 0 and 1. These two values determine the 'bounds' between which the total operational risk capital would lie, and these bounds are generally quite far apart. Therefore the total value of the operational risk capital is very sensitive to the value chosen for the correlation, and this is the source of the biggest model risk under the AMA.
NEW QUESTION # 134
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