合格させる8010試験一発合格保証100%カバー率でリアル試験問題 [2022年03月]
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質問 21
Concentration risk in a creditportfolio arises due to:
- A. Issuers of the securities in the portfolio being located in the same country
- B. A high degree of correlation between the default probabilities of the credit securities in the portfolio
- C. Independence of individual default losses for the assets in the portfolio
- D. A low degree of correlation between the default probabilities of the credit securities in the portfolio
正解: A
解説:
Explanation
Concentration risk in a credit portfolio arises due to a high degree of correlation betweenthe default probabilities of the issuers of securities in the portfolio. For example, the fortunes of the issuers in the same industry may be highly correlated, and an investor exposed to multiple such borrowers may face 'concentration risk'.
A low degreeof correlation, or independence of individual defaults in the portfolio actually reduces or even eliminates concentration risk.
The fact that issuers are from the same country may not necessarily give rise to concentration risk - for example, a bank withall US based borrowers in different industries or with different retail exposure types may not face practically any concentration risk. What really matters is the default correlations between the borrowers, for example a lender exposed to cement producersacross the globe may face a high degree of concentration risk.
質問 22
If the cumulative default probabilities of default for years 1 and 2 for a portfolio of credit risky assets is 5% and 15% respectively, what is the marginal probability of default in year 2 alone?
- A. 10.53%
- B. 10.00%
- C. 11.76%
- D. 15.79%
正解: A
解説:
Explanation
One way to think about this question is this: we are provided with two pieces of information: if the portfolio is worth $100 to start with, it will be worth $95 at the end of year 1 and $85 at the end of year 2. What it isasking for is the probability of default in year 2, for the debts that have survived year 1. This probability is $10/$95 =
10.53%. Choice 'b' is the correct answer.
Note that marginal probabilities of default are the probabilities for default for a given period, conditional on survival till the end of the previous period. Cumulative probabilities of default are probabilities of default by a point in time, regardless of when the default occurs. If the marginal probabilities of default for periods 1, 2... n are p1, p2...pn, then cumulative probability of default can be calculated as Cn = 1 - (1 - p1)(1-p2)...(1-pn). For this question, we can calculate the probability of default for year 2 as [1 - (1 - 5%)(1 - 10.53%)] = 15%.
質問 23
A bank's detailed portfolio data on positions held in a particular security across the bank does not agree with the aggregate total position for that security for the bank. What data quality attribute is missing in this situation?
- A. Auditability
- B. Data extensibility
- C. Data completeness
- D. Data integrity
正解: D
解説:
Explanation
The term 'data quality' has multiple elements, ie, data in order to be considered of a high quality must have multiple attributes such ascompleteness, timeliness, auditability etc. Because this is not an exact science, every expert or text book will have a different view of what goes into data quality. For our purposes however, we will stick to what the PRMIA study material specifies, and according to the study material the following are the elements that can be considered attributes that make for quality data:
1. Integration
2. Integrity
3. Completeness
4. Accessibility
5. Flexibility
6. Extensibility
7. Timeliness
8. Auditability
I am notgoing to describe each of these here as that would be repetitive of the study material, but suffice it to say that the break-down of a number into its constituents should tie to the aggregate total. If that is not true, then the data lacks integrity - andtherefore Choice 'b' is the correct answer. The other choices address other aspects of data quality but not this, and therefore are not correct.
質問 24
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. Damage to physical assets
- D. Employment practices and workplace safety
正解: D
解説:
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.
質問 25
The Options Theoretic approach to calculating economic capital considers the value of capital as being equivalent to a call option with a strike price equal to:
- A. The value of the assets
- B. The notional value ofthe debt
- C. The value of the firm
- D. The market value of the debt
正解: B
解説:
Explanation
The Options Theoretic approach to calculating economic capital is a top-down approach that considers the value of capital as being equivalent to a calloption with a strike price equal to the notional value of the debt - ie, the shareholders have a call option on the assets of the firm which they can acquire by paying the debt holders a value equal to their notional claim (ie the face value of the debt).Therefore Choice 'a' is the correct answer and the other choices are incorrect.
質問 26
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. II and III
- B. I and II
- C. III and IV
- D. I, II and IV
正解: B
解説:
Explanation
Time invariance refers to all timeintervals 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.
質問 27
Which of the following formulae describes CVA (Credit Valuation Adjustment)? All acronyms have their usual meanings (LGD=Loss Given Default, ENE=Expected Negative Exposure, EE=Expected Exposure, PD=Probability of Default, EPE=Expected Positive Exposure, PFE=Potential Future Exposure)
- A. LGD * EE * PD
- B. LGD * EPE * PD
- C. LGD * PFE * PD
- D. LGD * ENE * PD
正解: B
解説:
Explanation
The correct definition of CVA is LGD * EPE * PD. All other answers areincorrect.
CVA reflects the adjustment for counterparty default on derivative and other trading book transactions. This reflects the credit charge, that neeeds to be reduced from the expected value of the transaction to determine its true value. It is calculated as a product of the loss given default, the probability of default and the average weighted exposure of future EPEs across the time horizon for the transaction.
The future exposures need to be discounted to the present, and occasionally the equations for CVA will state that explicitly. Similarly, in some more advanced dynamic models the correlation between EPE and PD is also accounted for. The conceptual ideal though remains the same: CVA=LGD*EPE*PD.
質問 28
The probability of default of a security over a 1 year period is 3%. What is the probability that it would not have defaulted at theend of four years from now?
- A. 11.47%
- B. 88.53%
- C. 12.00%
- D. 88.00%
正解: B
解説:
Explanation
The probability that the security would not default in the next 4 years is equal to the probability of survival raised to the power four. In other words, =(1 -3%)^4 = 88.53%. Choice 'b' is the correct answer.
質問 29
The CDS quote for the bonds of Bank X is 200 bps. Assuming a recovery rate of 40%, calculate the default hazard rate priced in the CDS quote.
- A. 5.00%
- B. 2.00%
- C. 3.33%
- D. 0.80%
正解: C
解説:
Explanation
Hazard rate x Loss given default = CDS quote. In other words, Hazard rate x (1 - recovery rate) = CDS quote.
We can therefore calculate the hazard rate for this problem as 200 bps/(1 - 40%) = 3.33%.
質問 30
A corporate bond maturing in 1 year yields 8.5% per year,while a similar treasury bond yields 4%. What is the probability of default for the corporate bond assuming the recovery rate is zero?
- A. 4.15%
- B. 8.50%
- C. Cannot be determined from the given information
- D. 4.50%
正解: A
解説:
Explanation
Theprobability of default would make the future cash flows from both the bonds identical. If p be the probability of default, the cash flows from the risky corporate bond would be
= (cash flows in the event of default x probability of default) + (cash flows without default x (1 - probability of default))
=> p*0 + (1 - p)*(1 + 8.5%) = (1 - p)*1.085.
The cash flows from the treasury bond would be 1.04. These two should be equal, ie,
1.04 = (1- p)*1.085, implying p = 4.15%.
(Note: The above is a simplification intended for the exam. In reality investors would demand a 'credit risk premium' for the corporate bond over and above the expected default loss rate. They are unlikely to be happy with just being compensated with exactly the expected default loss rate plus the risk-fre rate because the expected default loss rate itself is uncertain. They would demand some premium over and above what the default rate alone might mathematically imply above the risk free rate. In this question, this credit risk premium is ignored.)
質問 31
Which of the following is true in relation to the application of Extreme Value Theory when applied to operational risk measurement?
I. EVT focuses on extreme losses that are generally not covered by standard distribution assumptions II. EVT considers the distribution of losses in the tails III. The Peaks-over-thresholds (POT) and the generalized Pareto distributions are used to model extreme value distributions IV. EVT is concerned with average losses beyond a given level of confidence
- A. II and III
- B. I and IV
- C. I, II and IV
- D. I, II and III
正解: D
解説:
Explanation
EVT, when used in the context of operational risk measurement, focuses on tail events and attempts to build a distribution of losses beyond what is covered by VaR. Statements I, II and II are correct. Statement IV describes conditional VaR (CVAR) andnot EVT.
Choice 'c' is the correct answer.
質問 32
Which of the following statements are correct in relation to the financial system just prior to the current financial crisis:
I. The system was robustagainst small random shocks, but not against large scale disturbances to key hubs in the network II. Financial innovation helped reduce the complexity of the financial network III. Knightian uncertainty refers to risk that can be quantified and measured IV. Feedback effects under stress accentuated liquidity problems
- A. I and IV
- B. II and III
- C. III and IV
- D. I, II and IV
正解: A
解説:
Explanation
Statement I is correct. The financial system proved to be stable against small shocks and disturbances, or shocksof a particular type (eg, the dotcom crash, the wars in the Persian Gulf); but rather fragile against other types of shocks, including disturbances to key market participants caused by a worsening of mortgage defaults.Statement II is incorrect. Financialinnovation, in particular the slicing and dicing of 'risk' through securitization, significantly increased interrelationships, dependence on the same risk factors, and the complexity of the system as a whole.Statement III is incorrect. A distinction is sometimes made between risk that is knowable, measureable, and quantifiable through parameters; and uncertainty, where the parameters are not known at all. The latter is called 'Knightian uncertainty' after the name of the scholar who came up with the distinction between the two.Statement IV is correct. Feedback effects had the greatest impact on liquidity which was tended to be hoarded, and on asset prices that tumbled as market participants tried to sell assets to become more liquid.Thus, choice is a the correct answer.
質問 33
If EV be the expected value of a firm's assets in a year, and DP be the 'default point' per the KMV approach to credit risk, and be the standard deviation of future asset returns, then the distance-to-default is given by:
A)
B)
C)
D)
- A. Option B
- B. Option D
- C. Option A
- D. Option C
正解: B
解説:
Explanation
The distance to default is the number of standard deviations that expected asset values are away from the default point. The expression in Choice 'd' represents distance to default. Choice 'd' is the correct answer. The other choices are incorrect.
質問 34
Once the frequency and severity distributions for loss events have been determined, which of the following is an accurate description of the process to determine a full loss distribution for operational risk?
- A. A firm wide operational risk distribution is set to be equal to the product of the frequency and severity distributions
- B. The frequency distribution alone forms the basis for the loss distribution for operational risk
- C. A firm wide operational risk distribution is generated by adding together the frequency and severity distributions
- D. A firm wide operational risk distribution is generated using Monte Carlo simulations
正解: D
解説:
Explanation
Once the frequency distribution has been determined (for example, using the binomial, Poisson or the negative binomial distributions) and the severity distribution has also been determined (for example, using the lognormal, gamma or other functions), the loss distribution can be produced by a Monte Carlo simulation using successive drawings from each of these two distributions. It is assumed that the severity and frequency are independent of each other. The resulting distribution gives a distribution showing the losses for operational risk, from whichthere Op Risk VaR can be determined using the appropriate percentile.Therefore Choice 'b' is the correct answer.
質問 35
Which of the following credit risk models relies upon theanalysis of credit rating migrations to assess credit risk?
- A. KMV's EDF based approach
- B. The contingent claims approach
- C. The CreditMetrics approach
- D. The actuarial approach
正解: C
解説:
Explanation
The correct answer is Choice 'b'. 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).
質問 36
For a given mean, which distribution would you prefer for frequency modeling where operational risk events are considered dependent, or in other words are seen as clustering together (as opposed to being independent)?
- A. Binomial
- B. Gamma
- C. Poisson
- D. Negative binomial
正解: D
解説:
Explanation
An interesting property that distinguishes the three most used distributions for modeling event frequency is that for a given mean, their variances differ. The ratio of variance to mean (the variance-mean ratio, calculated as variance/mean) can then be used to decide the kind of distribution to use. Both the variance and the mean can be estimated from available data points from the internal or external loss databases, or the scenario exercise.
The variance-mean ratio reflects how dispersed a distribution is. (In the PRMIA handbook, the variance to mean ratio has been described as the "Q-Factor".) The Poisson distribution has its mean equal to its variance, and therefore the variance to mean ratio is 1. For the negative binomial distribution, this ratio is always greater than 1, which means there is greater dispersion compared to the mean - or more intervals with low counts as well as more intervals with high counts. For the binomial distribution, the variance to mean ratio is less than one, which means it is less dispersed than the Poisson distribution with values closer to the mean.
In a situation where operational risk events are seen as clustering together, ordependent, the variance will be higher and it would be more appropriate to use the negative binomial distribution.
質問 37
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. Shareholders' equity
- B. Economic capital
- C. Regulatory capital
- D. Book value
正解: B
解説:
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.
質問 38
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. 0.15
- B. 0.12
- C. 0.125
- D. 0.08
正解: A
解説:
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.
質問 39
Which of the following are valid methods for selecting an appropriate model from the model space for severity estimation:
I. Cross-validation method
II. Bootstrap method
III. Complexity penalty method
IV. Maximum likelihood estimation method
- A. II and III
- B. I and IV
- C. I, II and III
- D. All of the above
正解: D
解説:
Explanation
Once we have a number of distributions in themodel space, the task is to select the "best" distribution that is likely to be a good estimate of true severity. We have a number of distributions to pick from, an empirical dataset (from internal or external losses), and we can estimate the parameters for the different distributions.
We then have to decide which distribution to pick, and that generally requires considering both approximation and fitting errors.
There are three methods that are generally used for selecting a model:
1. Thecross-validation method: This method divides the available data into two parts - the training set, and the validation set (the validation set is also called the 'testing set'). Parameter estimation for each distribution is done using the training set, anddifferences are then calculated based on the validation set. Though the temptation may be to use the entire data set to estimate the parameters, that is likely to result in what may appear to be an excellent fit to the data on which it is based, but without any validation. So we estimate the parameters based on one part of the data (the training set), and check the differences we get from the remaining data (the validation set).
2. Complexity penalty method: This is similar to the cross-validation method, but with an additional consideration of the complexity of the model. This is because more complex models are likely to produce a more exact fit than simpler models, this may be a spurious thing - and therefore a 'penalty' is added to the more complex modelsas to favor simplicity over complexity. The 'complexity' of a model may be measured by the number of parameters it has, for example, a log-normal distribution has only two parameters while a body-tail distribution combining two different distributions mayhave many more.
3. The bootstrap method: The bootstrap method estimates fitting error by drawing samples from the empirical loss dataset, or the fit already obtained, and then estimating parameters for each draw which are compared using some statistical technique. If the samples are drawn from the loss dataset, the technique is called a non-parametric bootstrap, and if the sample is drawn from an estimated model distribution, it is called a parametric bootstrap.
4. Using goodness of fit statistics: The candidate fits can be compared using MLE based on the KS distance, for example, and the best one selected. Maximum likelihood estimation is a technique that attempts to maximize the likelihood of the estimate to be as close to the true value of the parameter.It is a general purpose statistical technique that can be used for parameter estimation technique, as well as for deciding which distribution to use from the model space.
All the choices listed are the correct answer.
質問 40
Which of the following are true:
I. The total of the component VaRs for all components of a portfolio equals the portfolio VaR.
II. The total of the incremental VaRs for each position in a portfolio equals the portfolio VaR.
III. Marginal VaR and incremental VaR are identical for a $1 change in the portfolio.
IV. The VaR for individual components of a portfolio is sub-additive, ie the portfolio VaR is less than (or in extreme cases equal to) the sum of the individual VaRs.
V. The component VaR for individual components of a portfolio is sub-additive, ie the portfolio VaR is less than the sum of the individual component VaRs.
- A. II and IV
- B. I and II
- C. II and V
- D. I,III and IV
正解: D
解説:
Explanation
Statement I is true - component VaR for individual assets in the portfolio add up to the total VaR for the portfolio. This property makes component VaR extremely useful for risk disaggregation and allocation.
Stateent II is incorrect, the incremental VaRs for the positions in a portfolio do not add up to the portfolio VaR, in fact their sum would be greater.
Statement III is correct. Marginal VaR for an asset or position in the portfolio is by definition the change in the VaR as a result of a $1 change in that position. Incremental VaR is the change in the VaR for a portfolio from a new position added to the portfolio - and if that position is $1, it would be identical to the marginal VaR.
Statement IV is correct, VaR is sub-additive due to the diversification effect. Adding up the VaRs for all the positions in a portfolio will add up to more than the VaR for the portfolio as a whole (unless all the positions are 100% correlated, which effectively would mean they are all identical securities which means the portfolio has only one asset).
Statement V is in incorrect. As explained for Statement I above, component VaR adds up to the VaR for the portfolio.
質問 41
The generalized Pareto distribution, when used in the context of operational risk, is used to model:
- A. Average losses
- B. Unexpected losses
- C. Expected losses
- D. Tail events
正解: D
解説:
Explanation
Some risk experts have suggested the use of extreme value theory to model tail risk or extreme events for operational risk. The generalized Pareto model or the Peaks-over-Threshold (POT) model are often used to model extreme value distributions, and therefore Choice 'a' is the correct answer.
質問 42
Under the standardized approach to calculating operational risk capital under Basel II, negative regulatory capital charges for any of the business units:
- A. Should be included after ignoring the negative sign
- B. Should be offset againstpositive capital charges from other business units
- C. Should be ignored completely
- D. Should be excluded from capital calculations
正解: B
解説:
Explanation
According to Basel II, in any given year, negative capital charges(resulting from negative gross income) in any business line may offset positive capital charges in other business lines without limit. Therefore Choice 'b' is the correct answer.
質問 43
A bank prices retail credit loans based on median default rates. Over the long run, it can expect:
- A. Underestimation and therefore underpricing of risk in it retail portfolio
- B. A reduction in the rate of defaults
- C. Overestimation of risk and overpricing, leading to lossof market share
- D. Correct pricing of risk in the retail credit portfolio
正解: A
解説:
Explanation
The key to pricing loans is to make sure that the prices cover expected losses. The correct measure of expected losses is the mean, and not the median. To the extent the median is different from the mean, the loans would be over or underpriced.
The loss curve for credit defaults is a distribution skewed to the right. Therefore its mode is less than its median which is less than its mean. Since the median is less than the mean, the bank is pricing in fewer losses than the mean, which means over the long run it is underestimating risk and underpricing its loans. Therefore Choice 'd' is the correct answer.
If on the other hand for some reason the bank were overpricing risk, its loans would be more expensive than its competitors and it would lose market share. In this case however, this does not apply.Loan pricing decisions are driven by the rate of defaults, and not the other way round, therefore any pricing decisions will not reduce the rate of default.
質問 44
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