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プロフェッショナル・リスク・マネージャーズ・インターナショナル・アソシエーション（PRMIA）は、リスク管理の専門知識と資格を取得するためのさまざまな認定コースを提供しています。そのうちの1つが、オペレーショナル・リスク・マネジメント（ORM）を専門とするPRMIA 8010試験です。ORMは、組織の運用やプロセスから生じるリスクを識別、評価、監視、管理するプロセスです。
質問 # 27
If E denotes the expected value of a loan portfolio at the end on one year and U the value of the portfolio in the worst case scenario at the 99% confidence level, which of the following expressions correctly describes economic capital requiredin respect of credit risk?
- A. E - U
- B. E
- C. U
- D. U/E
正解：A
解説：
Explanation
Economic capital in respect of credit risk is intended to absorb unexpected losses. Unexpected losses are the losses above and beyond expected losses and up to the level ofconfidence that economic capital is being calculated for. The capital required to cover unexpected losses in this case is E - U, and therefore Choice 'a' is the correct answer.
This question does raise an important point - are expected losses a part of economic capital, or are they not?
Different text books say different things, and sometimes they say both the things. I have tried to take an approach that uses what I read in the PRMIA handbook.
This
writeup - http://www.riskprep.com/all-tutorials/37-exam-3/111-credit-var-an-intuitive-understanding - may help clarify things further.
質問 # 28
The Altman credit risk score considers:
- A. A combination of accounting measures and market values
- B. A historical database of the firms that have survived
- C. A historical database of the firms that have defaulted
- D. A quadratic approximation of the credit risk based on underlying risk factors
正解：A
解説：
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
Nearly all thenumbers above are accounting measures derived straight from the balance sheet or the income statement. Market capitalization is a market driven number. Therefore Choice 'c' is the correct answer as the Altman credit risk score considers both accounting andmarket based measures.
Altman's score, though computationally straightforward and intuitively easy to understand, was introduced in the late sixties and has been very accurate in predicting corporate bankruptcies, which is why it continues to be used extensively.
質問 # 29
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. 0.08
- B. 0.15
- C. 0.125
- D. 0.12
正解：B
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 # 30
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 and II
- B. III and IV
- C. I, II and IV
- D. II and III
正解：A
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 # 31
Under the KMV Moody's approach to credit risk measurement, how is the distance to default converted to expected default frequencies?
- A. Using migration matrices
- B. Using a proprietary database based on historical information
- C. Using a normal distribution
- D. Using Monte Carlo simulations
正解：B
解説：
Explanation
KMV Moody's uses a proprietary database to convert the distance to default to expected default probabilities.
質問 # 32
According to the Basel II framework, subordinated term debt that was originally issued 4 years ago with amaturity of 6 years is considered a part of:
- A. Tier 2 capital
- B. Tier 3 capital
- C. None of the above
- D. Tier 1 capital
正解：A
解説：
Explanation
According to the Basel II framework, Tier 1 capital, also called core capital or basic equity, includes equity capital and disclosed reserves.
Tier 2 capital, also called supplementary capital, includes undisclosed reserves, revaluation reserves, general provisions/general loan-loss reserves, hybrid debt capital instruments and subordinated term debt issued originally for 5 years or longer.
Tier 3 capital, or short term subordinated debt, is intended only to cover market risk but only at the discretion of their national authority. This only includes short term subordinated debt originally issued for 2 or more years.
An interesting thing to note is the difference between 'subordinated term debt' under Tier 2 and the 'short term subordinated debt' under Tier 3. The distinction is based upon the years to maturity at the time the debt was issued. The remaining time to maturity is not relevant. For the subordinated term debt included under Tier 2, the amount that can be counted towards capital is reduced by 20% for every year when the debt is due within 5 years. This takes care of the time to maturity problem for Tier 2subordinated debt. For Tier 3 short term subordinated debt, this is not an issue because debt will only qualify for Tier 3 if it has a lock-in clause stipulating that the debt is not required to be repaid if the effect of such repayment is to take the bank below minimum capital requirements.
質問 # 33
Which of the following is not an event of default covered in the ISDA Master Agreement?
I. failure to pay or deliver
II. credit support default
III. merger without assumption
IV. Bankruptcy
- A. All are considered events of default
- B. I
- C. IV
- D. II and III
正解：B
解説：
Explanation
Note that events of default under the ISDA MA are caused by one of the parties that is considered 'atfault'. In contrast, "termination events" are events for which no one is at fault, for example changes in legislation, illegality etc that still justify termination of the transactions under the contract.
The ISDA MA describes the following 8 types of events of default:
1. failure of pay or deliver
2. breach of agreement
credit support default
4. misrepresentation
5. default under specified transaction
6. cross default
7. bankruptcy
8. merger without assumption
All of the options presented in the question are events of default.
質問 # 34
Which of the formulae below describes incremental VaR where a new position 'm' is added to the portfolio?
(where p is theportfolio, and V_i is the value of the i-th asset in the portfolio. All other notation and symbols have their usual meaning.) A)
B)
C)
D)
- A. Option D
- B. Option C
- C. Option A
- D. Option B
正解：C
解説：
Explanation
Incremental VaR is the change in portfolio VaR resulting from a change in a single position. This is accurately described by VaR_(p+a) - VaR_p. The other answers are incorrect, and describe other concepts.
It is important to know and understand the ideas behind MVaR (marginal VaR), CVaR (component VaR) and iVaR (incremental VaR), and the differences between them.
質問 # 35
Which of the following credit risk models relies upon theanalysis of credit rating migrations to assess credit risk?
- A. The contingent claims approach
- B. The actuarial approach
- C. The CreditMetrics approach
- D. KMV's EDF based 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
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. 15.79%
- B. 11.76%
- C. 10.00%
- D. 10.53%
正解：D
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 # 37
Which of the following is closest to the description of a 'risk functional'?
- A. A risk functional is a model distribution that is an approximation of the true loss distribution of a risk
- B. A risk functional is the distribution thatmodels the severity of a risk
- C. A risk functional assigns a penalty value for the difference between a model distribution and a risk's severity distribution
- D. Risk functional refers to the Kolmogorov-Smirnov distance
正解：C
解説：
Explanation
For operational risk modeling, both frequency and severity distributions need to be modeled. Modeling severity involves finding an analyticaldistribution, such as log-normal or other that approximates the distribution best represented by known data - whether from the internal loss database, the external loss database or scenario data. A 'risk functional' is a measure of the deviation of the model distribution from the risk's actual severity distribution. It assigns a penalty value for the deviation, using a statistical measure, such as the KS distance (Kolmogorov-Smirnov distance).
The problem of finding the right distribution then becomes the problem of optimizing the risk functional. For example, if F is the model distribution, and G is the actual, or empirical severity distribution, and we are using the KS test, then the Risk Functional R is defined as follows:
Note that supx stands for 'supremum', which is a more technical way of saying 'maximum'. In other words, we are calculating the maximum absolute KS distance between the two distributions. (Note that the KS distance is the max of the distance between identical percentiles of the two distributions using the CDFs of the two.) Once the risk functional is identified, we can minimize it to determine the best fitting distribution for severity.
質問 # 38
If the odds of default are 1:5, what is the probability of default?
- A. 20.00%
- B. 50.00%
- C. 12.00%
- D. 16.67%
正解：D
解説：
Explanation
Odds are the ratio between the probability of the occurence of an event to the probability that the event does not occur.
If odds are H, then p = H/(1 + H) and H = p/(1-p). In this case the odds are 1:5, or 1/5, therefore the correct answer is Choice 'a', equal to (1/5)/(1 + 1/5) = 1/6 = 16.67%. All other choices are incorrect.
質問 # 39
Which of the following is the most accurate description of EPE (Expected Positive Exposure):
- A. The price that would be received to sell an asset or paid to transfer a liability in an orderly transaction between market participants at the measurement date
- B. The average of the distribution of positive exposures at a specified future date
- C. Weighted average of thefuture positive expected exposure across a time horizon.
- D. The maximum average credit exposure over a period of time
正解：C
解説：
Explanation
When a derivative transaction is entered into, its value generally is close to zero. Over time, as the value of the underlying changes, the transaction acquires a positive or negative value. It is not possible to predict the future value of the transaction in advance, however distributional assumptions can be made and potential exposure can be measured in multiple ways. Of all the possible future exposures, it is generally positive exposures that are relevant to credit risk because that is the only situation where the bank may lose money from a default of the counterparty.
The maximum (generally aquantile eg, the 97.5th quantile) exposure possible over the time of the transaction is the 'Potential Future Exposure', or PFE.
The average of the distribution of positive exposures at a specified date before the longest trade in the portfolio is called'Expected Exposure', or EE.
The expected positive exposure calculated as the weighted average of the future positive Expected Exposure across a time horize is called the EPE, or the 'Expected Positive Exposure'.
The price that would be received to sell anasset or paid to transfer a liability in an orderly transaction between market participants at the measurement date - is the 'fair value', as defined under FAS 157.
Therefore the corect answer is that EPE is the weighted average of the future positive expected exposure across a time horizon.
質問 # 40
Which of the following statements are true:
I. Capital adequacy implies the ability of a firm to remain a going concern II. Regulatory capital and economic capital are identical as they target the same objectives III. The role of economic capital is to provide a buffer against expected losses IV. Conservative estimates of economic capital are based upon a confidence level of 100%
- A. I
- B. I, III and IV
- C. III
- D. I and III
正解：A
解説：
Explanation
Statement I is true - capital adequacy indeed is a reference to the ability of the firm to stay a 'going concern'.
(Going concern is an accounting term that means the ability of the firm to continue in business without the stress of liquidation.) Statement II is not true because even though the stated objective of regulatory capital requirements is similar to the purposes for which economic capital is calculated, regulatory capital calculations are based upon a large number of ad-hoc estimates and parameters that are 'hard-coded' into regulation, while economic capital is generally calculated for internal purposes and uses an institution's own estimates and models. They are rarely identical.
Statement II is not true as the purpose of economic capital is to provide a buffer against unexpected losses.
Expected losses are covered by the P&L (or credit reserves), and not capital.
Statement IV is incorrect as even though economic capital may be calculated at very high confidence levels, that is never 100% which would require running a 'risk-free' business, which would mean there are no profits either. The level of confidence is set at a level which is an acceptable balance between the interests of the equity providers and the debt holders.
質問 # 41
Which loss event type is the loss of personally identifiableclient information classified as under the Basel II framework?
- A. Technology risk
- B. Information security
- C. Clients, products and business practices
- D. External fraud
正解：C
解説：
Explanation
Choice 'b' is the correct answer. All other answers areincorrect.
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 # 42
When compared to a low severity high frequency risk, the operational risk capital requirement for a medium severity medium frequency risk is likely to be:
- A. Higher
- B. Lower
- C. Zero
- D. Unaffected by differences in frequency or severity
正解：A
解説：
Explanation
High frequency and low severity risks, for example the risks of fraud losses for a credit card issuer, may have high expected losses, but low unexpected losses. In other words, we can generally expect these losses tostay within a small expected and known range. The capital requirement will be the worst case losses at a given confidence level less expected losses, and in such cases this can be expected to be low.
On the other hand, medium severity medium frequency risks, such as the risks of unexpected legal claims,
'fat-finger' trading errors, will have low expected losses but a high level of unexpected losses. Thus the capital requirement for such risks will be high.
It is also worthwhile mentioning high severity andlow frequency risks - for example a rogue trader circumventing all controls and bringing the bank down, or a terrorist strike or natural disaster creating other losses - will probably have zero expected losses & high unexpected losses but only at very highlevels of confidence. In other words, operational risk capital is unlikely to provide for such events and these would lie in the part of the tail that is not covered by most levels of confidence when calculating operational risk capital.
Note that risk capital is required for only unexpected losses as expected losses are to be borne by P&L reserves. Therefore the operational risk capital requirements for a low severity high frequency risk is likely to be low when compared to other risks that are lower frequency but higher severity.
Thus Choice 'c' is the correct answer.
質問 # 43
The definition of operational risk per Basel II includes which of the following:
I. Riskof loss resulting from inadequate or failed internal processes, people and systems or from external events II. Legal risk III. Strategic risk IV. Reputational risk
- A. I and II
- B. I, II, III and IV
- C. I and III
- D. II and III
正解：A
解説：
Explanation
Operational risk as defined in Basel II specifically excludes strategic and reputational risk. Therefore Choice
'd' is the correct answer.
Note that Basel II defines operational risk as follows:
Operational risk is defined as the risk of lossresulting from inadequate or failed internal processes, people and systems or from external events. This definition includes legal risk, but excludes strategic and reputational risk.
質問 # 44
Economic capital under the Earnings Volatility approach is calculated as:
- A. [Expected earningsless Earnings under the worst case scenario at a given confidence level]/Required rate of return for the firm
- B. Expected earnings/Required rate of return for the firm
- C. Earnings under the worst case scenario at a given confidence level/Required rate of return for the firm
- D. Expected earnings/Specific risk premium for the firm
正解：A
解説：
Explanation
The Earnings Volatility approach to calculating economic capital is a top down approach that considers economic capital as being the capital required to make for the worst case fall in earnings, and calculates EC as equal to the worst case decrease in earnings capitalized at the rate of return expected of the firm. The worst case decrease in earnings, or the earnings-at-risk can only be stated at a given confidence level, and is equal to the Expected Earnings less Earnings under the worst case scenario.
質問 # 45
If the marginal probabilities of default for a corporate bond for years 1, 2 and 3 are 2%, 3% and 4% respectively, what is the cumulative probability of default at the end of year 3?
- A. 9.58%
- B. 91.26%
- C. 9.00%
- D. 8.74%
正解：D
解説：
Explanation
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 3 as =1 - (1-2%)*(1-3%)*(1-4%) = 8.74%
質問 # 46
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