Which of the following statements are correct?
I. A reliance upon conditional probabilities and a-priori views of probabilities is called the ‘frequentist’ view
II. Knightian uncertainty refers to things that might happen but for which probabilities cannot be evaluated
III. Risk mitigation and risk elimination are approaches to reacting to identified risks
IV. Confidence accounting is a reference to the accounting frauds that were seen in the past decadeas a reflection of failed governance processes
- A . II, III and IV
- B . II and III
- C . I and IV
- D . All of the above
B
Explanation:
In statistics, which is relevant to risk management, a distinction is often drawn between ‘frequentists’ and ‘Bayesians’. Frequentists rely upon data to draw conclusions as to probabilities. Bayesians consider conditional probabilities, ie, take into account what things are already known, and inject sometimes subjective a-priori probabilities into the calculations. StatementI describes Bayesians, and not frequentists. In reality however, the difference is merely academic. Risk managers use whichever technique best applies to the given situation without making it about ideology.
The difference between ‘Knightian uncertainty ‘and ‘Risk’ is similarly academic. Knightian uncertainty refers to risk that cannot be measured or calculated. ‘Risk’ on the other hand refers to things for which past data exists and calculations of exposure can be made. To give an example in the contextof the financial world, the risk from a pandemic creating systemic failures from a failure of payment and settlement systems and the like is ‘Knightian uncertainty’, but the market risk from equity price movements can be modeled (albeit with limitations) and is calculable. Statement II is therefore correct.
Once a risk is identified, it can be mitigated, accepted, avoided or eliminated, or transferred by way of insurance. Therefore statement III is correct.
Confidence accounting is a conceptual idea that suggests that accounting statements make reference to ranges as opposed to point estimates in financial statements. For example, instead of saying that the pension obligation is $xx million, the company should say the pension obligation is in a range of $xxm – $yy m with a certain confidence level. Statement IV is therefore inaccurate.
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 ignored completely
- B . Should be offset against positive capital charges from other business units
- C . Should be included after ignoring the negative sign
- D . Should be excluded from capital calculations
B
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.
Credit exposure for derivatives is measured using
- A . Current replacement value
- B . Notional value of the derivative
- C . Forward looking exposure profile of the derivative
- D . Standard normal distribution
C
Explanation:
Current replacement values are a very poor measure of the credit exposure from a derivative contract, because the future value of these instruments is unpredictable, ie is stochastic, and the range of values it can take increases the further ahead in the future we look. Therefore it is common for credit exposures for derivatives to be measured using forward looking exposure profiles, which are distributions of the expected value of the derivative at the time horizon for which credit risk is being measured. To be conservative, a high enough quintile of this distribution is taken as the ‘loan equivalent value’ of the derivative as the exposure. Choice ‘c’ is the correct answer.
The notional value of derivative contracts generally tends to be quite high and unrelated to their economic value or the counterparty exposure. Therefore notional value is irrelevant.
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 . II and III
- B . I, III and IV
- C . I and IV
- D . All of the above
C
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.
Which of the following formulae describes Marginal VaR for a portfolio p, where 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)
All of the above
- A . Option A
- B . Option B
- C . Option C
- D . Option D
D
Explanation:
Marginal VaR of a component of a portfolio is the change in the portfolio VaR from a $1 change in the value of the component. It helps a risk analyst who may be trying to identify the best way to influence VaR by changingthe components of the portfolio. Marginal VaR is also important for calculating component VaR (for VaR disaggregation), as component VaR is equal to the marginal VaR multiplied by the value of the component in the portfolio. Marginal VaR is by definitionthe derivative of the portfolio value with respect to the component i. This is reflected in Choice ‘a’ above. Using the definitions and relationships between correlation, covariance, beta and volatility of the portfolio and/or the component, we can show that the other two choices are also equivalent to Choice ‘a’. Therefore all the choices present are correct.
Which of the following should be included when calculating the Gross Income indicator used to calculate operational risk capital under the basic indicator and standardized approaches under Basel II?
- A . Insurance income
- B . Operating expenses
- C . Fees paid to outsourcing service proviers
- D . Net non-interest income
D
Explanation:
Gross income is defined by Basel II (see para 650 of the Basel standard) as net interest income plus netnon-interest income. It is intended that this measure should: (i) be gross of any provisions (e.g. for unpaid interest); (ii) be gross of operating expenses, including fees paid to outsourcing service providers; (iii) exclude realised profits/losses from the sale of securities in the banking book; and (iv) exclude extraordinary or irregular items as well as income derived from insurance.
What this means is that gross income is calculated without deducting any provisions or operating expenses from net interest plus non-interest income; and does not include any realised profits or losses from the sale of securities in the banking book, and also does not include any extraordinary or irregular item or insurance income.
Therefore operating expenses are to be notto be deducted for the purposes of calculating gross income, and neither are any provisions. Profits and losses from the sale of banking book securities are not considered part of gross income, and so isn’t any income from insurance or extraordinary items.
Of the listed choices, only net non-interest income needs to be included for gross income calculations, and the others are to be excluded. Therefore Choice ‘d’ is the correct answer. Try to remember the components of gross income from the definition above because in the exam the question may be phrased differently.
A loan portfolio’s full notional value is $100, and its value in a worst case scenario at the 99% level of confidence is $65. Expected losses on the portfolio are estimated at 10% .
What is the level of economic capital required to cushion unexpected losses?
- A . 25
- B . 65
- C . 10
- D . 35
A
Explanation:
Expected value = $90 ($100 – 10%)
Value at 99% confidence level = $65
Therefore economic capital required at this level of confidence = $90 – $65 = $25.
Choice ‘a’ is the correct answer, the other choices are not.
(We can also look at it this way as explained in section III.B.6.2.2 of the handbook: Economic capital is designed to absorb unexpected losses, which areequal to total losses at a given confidence level minus expected losses. (Expected losses are to be covered by credit reserves). Total losses are $100-$65=$35, and expected losses are 10%*$100=$10, therefore economic capital should be $35-$10=$25.)
Which of the following can be used to reduce credit exposures to a counterparty:
I. Netting arrangements
II. Collateral requirements
III. Offsetting trades with other counterparties
IV. Credit default swaps
- A . I and II
- B . I, II, III and IV
- C . I, II and IV
- D . III and IV
C
Explanation:
Offsetting trades with other counterparties will not reduce credit exposure to a given counterparty. All other choices represent means of reducing credit risk. Therefore Choice ‘c’ is the correct answer.
Which of the following is NOT an approach used to allocate economic capital to underlying business units:
- A . Stand alone economic capital contributions
- B . Marginal economic capital contributions
- C . Fixed ratio economic capital contributions
- D . Incremental economic capital contributions
C
Explanation:
Other than Choice ‘c’, all others represent valid approaches to allocate economic capital to underlying business units. There is no such thing as ‘fixed ratioeconomic capital contribution’
For a given notional amount, which of the following carries the greatest counterparty exposure (assuming the same counterparty credit rating for each):
- A . A futures contract on an equity index
- B . A one year certificate of deposit
- C . A one year forward foreign exchange contract
- D . A one year interest rate swap
B
Explanation:
The exposure at default is the greatest for the certificate of deposit as the entire notional amount is exposed to the risk of default. The other choices represent derivatives for which the current replacement value, which would be far less than notional, would be the credit exposure.
Said another way – if the counterparty were to default, the entire money in the CD would be at risk, whereas for the derivative contracts it would only be the replacement value that would be at risk.
Identify the correct sequence of events as it unfolded in the credit crisis beginning 2007:
I. Mortgage defaults increased
II. Collapse in prices of unrelated assets as banks tried to create liquidity
III. Banks refused to lend or transact with each other
IV. Asset prices for CDOs collapsed
- A . III, IV, I and II
- B . I, III, IV and II
- C . I, IV, III and II
- D . IV, I, II and III
C
Explanation:
According to a paper by the BCBS, here is an excellent summary of what happened. Based on this, Choice ‘c’ is the correct answer.
"At the outset of the crisis, mortgage default shocks played a part in the deterioration of marketprices of collateralised debt obligations (CDOs). Simultaneously, these shocks revealed deficiencies in the models used to manage and price these products. The complexity and resulting lack of transparency led to uncertainty about the value of the underlying investment. Market participants then drastically scaled down their activity in the origination and distribution markets and liquidity disappeared. The standstill in the securitisation markets forced banks to warehouse loans that were intended to be soldin the secondary markets. Given a lack of transparency of the ultimate ownership of troubled investments, funding liquidity concerns were triggered within the banking sector as banks refused to provide sufficient funds to each other. This in turn led to the hoarding of liquidity, exacerbating further the funding pressures within the banking sector. The initial difficulties in subprime mortgages also fed through to a broader range of market instruments since the drying up of market and funding liquidity forced market participants to liquidate those positions which they could trade in order to scale back risk. An increase in risk aversion also led to a general flight to quality, an example of which was the high withdrawals by households from money market funds."
Which of the following belong in a credit risk report?
- A . Exposures by country
- B . Exposures by industry
- C . Largest exposures by counterparty
- D . All of the above
D
Explanation:
All the listed variables are relevant to management monitoring the credit risk profile of an institution, therefore Choice ‘d’ is the correct answer.
Which of the following statements are true:
I. A transition matrix is the probability of a security migrating from one rating class to another during its lifetime.
II. Marginal default probabilities refer to probabilities of default in a particular period, given survival atthe beginning of that period.
III. Marginal default probabilities will always be greater than the corresponding cumulative default probability.
IV. Loss given default is generally greater when recovery rates are low.
- A . I and III
- B . I, III and IV
- C . II and IV
- D . I and IV
C
Explanation:
Statement I is incorrect. A transition matrix expresses the probabilities of moving to a given set of ratings at the end of a period (usually one year) conditional upon a given rating at the beginning of the period. It does not make a reference to an individual security and certainly not to the probability of migrating to other ratings during its entire lifetime.
Statement II is correct. Marginal default probabilities are the probability of default in a given year, conditional upon survival at the beginning of that year.
Statement III is incorrect. Cumulative probabilities of default will always be greater than the marginal probabilities of default – except in year 1 when they will be equal.
Statement IV is correct. LGD= 1 – Recovery Rate, therefore a low recovery rate implies higher LGD.
The VaR of a portfolio at the 99% confidence level is $250,000 when mean return is assumed to be zero. If the assumption of zero returns is changed to an assumption of returns of $10,000, what is the revised VaR?
- A . 260000
- B . 240000
- C . 273260
- D . 226740
B
Explanation:
The exact formula for VaR is = -(Z + ), where Z is the z-multiple for the desired confidence level, and is the mean return. Now Z is always a negative number, or at least will certainly be provided the desired confidence level is greater than 50%, and is often assumed to be zero because generally for the short time periods for which market risk VaR is calculated, its value is very close to zero.
Therefore in practice the formula for VaR just becomes -Z, andsince Z is always negative, we normally just multiply the Z factor without the negative sign with the standard deviation to get the VaR.
For this question, there are two ways to get the answer. If we use the formula, we know that -Z= 250,000 (as =0), and therefore -Z – = 250,000 – 10,000 = $240,000.
The other, easier way to think about this is that if the mean changes, then the distribution’s shape stays exactly the same, and the entire distribution shifts to the right by $10,000 as the mean moves upby $10,000. Therefore the VaR cutoff, which was previously at – 250,000 on the graph also moves up by 10k to -240,000, and therefore $240,000 is the correct answer.
The other choices are intended to confuse by multiplying the z-factor for the 99% confidence level with 10,000 etc.
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
C
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.
Which of the following contributed to the systemic failure during the credit crisis that began in 2007?
- A . Stress tests that did not stress enough
- B . Moral hazard from the strategy of ‘originate and distribute’
- C . Inadequate attentionpaid to liquidity risk
- D . All of the above
D
Explanation:
All the factors listed above contributed to systemic failure. Liquidity risk was not on the radar of regulators, and was a second priority for risk managers, and most of the focus was oncapital adequacy as liquidity was thought to be an unlikely problem. Liquidity, regardless of capital adequacy, was the primary cause of failure of a number of institutions during the crisis.
Similarly, stress tests proved to be much milder than the shocks that were actually experienced, and the strategy of ‘originate and distribute’ implied that the mortgage and other debt originators had no interest in any due diligence as they intended to package and sell the debt to other investors.
Therefore Choice ‘d’ is the correct answer.
If the full notional value of a debt portfolio is $100m, its expected value in a year is $85m, and the worst value of the portfolio in one year’s time at 99% confidence level is $60m, then what is the credit VaR?
- A . $40m
- B . $25m
- C . $60m
- D . $15m
B
Explanation:
Credit VaR is the difference between the expected value of the portfolio and the value of the portfolio at the given confidence level. Therefore the credit VaR is $85m – $ 60m = $25m. Choice ‘b’ is the correct answer.
Note that economic capital and credit VaR are identical at a risk horizon of one year. Therefore if the question asks for economic capital, the answer would be the same. [Again, an alternative way to look at this is to consider the explanation given in III.B.6.2.2:Credit Var = Q(L) – EL where Q(L) is the total loss at a given confidence interval, and EL is the expected loss. In this case Q(L) – $100-$60 = $40, and EL = $100-$85=$15. Therefore Credit VaR = $40-$15=$25.]
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 1 capital
- C . Tier 3 capital
- D . None of the above
A
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.
According to the implied capital model, operational risk capital is estimated as:
- A . Operational risk capital held by similar firms, appropriately scaled
- B . Total capital less market risk capital less credit risk capital
- C . Capitalimplied from known risk premiums and the firm’s earnings
- D . Total capital based on the capital asset pricing model
B
Explanation:
Operational risk capital estimated using the implied capital model is merely the capital that is not attributable to market or credit risk. Therefore Choice ‘b’ is the correct answer. All other responses are incorrect.
Which of the following are a CRO’s responsibilities:
I. Statutory financial reporting
II. Reporting to the audit committee
III. Compliance with risk regulatory standards
IV. Operational risk
- A . I and II
- B . II and IV
- C . III and IV
- D . All of the above
C
Explanation:
Statutory financial reporting is the responsibility of the Chief Financial Officer, not the Chief Risk Officer. The head of internal audit reports to theaudit committee of the board, not the CRO. Therefore statements I and II are incorect.
The CRO is generally expected to drive risk and compliance with related regulatory standards. Market risk, credit risk and operational risk groups report into the CRO, so statements III and IV are correct.
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
B
Explanation:
Top down approaches do not consider event frequency and severity, on the otherhand 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.
When compared to a medium severity medium frequency risk, the operational risk capital requirement for a high severity very low frequency risk is likely to be:
- A . Higher
- B . Lower
- C . Zero
- D . Unaffected by differences in frequency or severity
C
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 to stay 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 below.
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 suchrisks will be high.
It is also worthwhile mentioning high severity and low 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 high levels 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.
The sum of the stand alone economic capital of all the business units of a bank is:
- A . less than the economic capital for the firm as a whole
- B . more than the economic capital for the firm as a whole
- C . equalto the economic capital for the firm as a whole
- D . unrelated to the economic capital for the firm as a whole
B
Explanation:
Economic capital is sub-additive, ie, because of the correlation being less than perfect between the risks of the different business units, the total economic capital for the firm will be less than the sum of the EC for the individual business units. Therefore Choice ‘b’ is the correct answer.
In practice, correlations are difficult to estimate reliably, and banks often use estimates and corroborate their capital calculations with reference to a number of data points.
Which of the following is not a permitted approach under Basel II for calculating operational riskcapital
- A . the internal measurement approach
- B . the basic indicator approach
- C . the standardized approach
- D . the advanced measurement approach
A
Explanation:
The Basel II framework allows the use of the basic indicator approach, the standardized approach and the advanced measurement approaches for operational risk. There is no approach called the ‘internal measurement approach’ permitted for operational risk. Choice ‘a’ is therefore the correct answer.
Which of the following statements are true?
I. Risk governance structures distribute rights and responsibilities among stakeholders in the corporation
II. Cybernetics is the multidisciplinary study of cyber risk and control systems underlying information systems in an organization
III. Corporate governance is a subset of the larger subject of risk governance
IV. The Cadbury report was issued in the early 90s and was one of the early frameworks for corporate governance
- A . I, II and IV
- B . I and IV
- C . II and III
- D . All of the above
B
Explanation:
Governance structures specify the policies, principles and procedures for making decisions about corporate direction. They distribute rights and responsibiliies among stakeholders that typically include executive management, employees, the board etc. Statement I is therefore correct.
"Cybernetics is a transdisciplinary approach for exploring regulatory systems, their structures, constraints, and possibilities. In the 21st century, the term is often used in a rather loose way to imply "controlof any system using technology" (Wikipedia). Governance literature has been affected by cybernetics, which is not the same thing as information security or cyber security. Statement II is incorrect.
Corporate governance includes risk governance, and not the other way round. Therefore statement III is incorrect.
The Cadbury Report, titled Financial Aspects of Corporate Governance, was a report issued in the UK in December 1992 by "The Committee on the Financial Aspects of Corporate Governance". The report is eponymous with the chair of the committee, and set out recommendations on the arrangement of company boards and accounting systems to mitigate corporate governance risks and failures. Statement IV is therefore correct.
The generalized Pareto distribution, when used in the context of operational risk, is used to model:
- A . Tail events
- B . Average losses
- C . Unexpected losses
- D . Expected losses
A
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.
A bank expects the error rate in transaction data entry for a particular business process to be 0.005% .
What is the range of expected errors in a day within +/- 2 standard deviations if there are 2,000,000 such transactions each day?
- A . 80 to 120 errors in a day
- B . 60 to 80 errors in a day
- C . 0 to 200 errors in a day
- D . 90 to 110 errors in a day
A
Explanation:
Error rates are generally modeled using thePoisson distribution. Recall that the Poisson distribution has only one parameter – – which is its mean and also its variance. In the given case, the mean number of errors is 2,000,000 x 0.005% = 100. Since this is the variance as well, the standard deviation is 100 = 10. Therefore the range of outcomes within 2 standard deviations of the mean is 100 +/- (2*10) = 80 to 120 errors in a day.
Which loss event type is the failure to timely deliver collateral classified as under the Basel II framework?
- A . Clients, products and business practices
- B . External fraud
- C . Information security
- D . Execution, Delivery & Process Management
D
Explanation:
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.
An error by a third party service provider results in a loss to a client that the bank has to make up. Such as loss would be categorized per Basel IIoperational risk categories as:
- A . Execution delivery and process management
- B . Outsourcing loss
- C . Business disruption and process failure
- D . Abnormal loss
A
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.
Which of the following is not one of the ‘three pillars’ specified in the Basel accord:
- A . Market discipline
- B . Supervisory review
- C . National regulation
- D . Minimum capital requirements
C
Explanation:
The three pillars are minimum capital requirements, supervisory review and market discipline. National regulation is not a pillar described under the accord. Choice ‘c’ is the correct answer.
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 . F > V
- B . V < E
- C . F < V
- D . F – E < V
A
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 the debt.
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:
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 . F > V
- B . V < E
- C . F < V
- D . F – E < V
A
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 the debt.
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:
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 . F > V
- B . V < E
- C . F < V
- D . F – E < V
A
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 the debt.
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:
Which of the following is the best description of the spread premium puzzle:
- A . The spread premium puzzle refers to observed default rates being much less than implied default rates, leading to lower credit bonds being relatively cheap when compared to their actual default probabilities
- B . The spread premium puzzle refers to dollar denominated non-US sovereign bonds being priced a at significant discount to other similar USD denominated assets
- C . The spread premium puzzle refers to AAA corporate bonds being priced at almost the same prices as equivalent treasury bonds without offering the same liquidity or guarantee as treasury bonds
- D . The spread premium puzzle refers to the moral hazard implicit in the monoline insurance market
A
Explanation:
Choice ‘a’ is the correct answer. The other choices represent non-sensical statements.
Which of the following situations are not suitable for applying parametric VaR:
I. Where the portfolio’s valuation is linearly dependent upon risk factors
II. Where the portfolio consists of non-linear products such as options and large moves are involved
III. Where the returns of risk factors are known to be not normally distributed
- A . I and II
- B . II and III
- C . I and III
- D . All of the above
B
Explanation:
Parametric VaR relies upon reducing a portfolio’s positions to risk factors, and estimating the first order changes in portfolio values from each of the risk factors. This is called the delta approximation approach. Riskfactors include stock index values, or the PV01 for interest rate products, or volatility for options. This approach can be quite accurate and computationally efficient if the portfolio comprises products whose value behaves linearly to changes in risk factors. This includes long and short positions in equities, commodities and the like.
However, where non-linear products such as options are involved and large moves in the risk factors are anticipated, a delta approximation based valuation may not give accurate results, and the VaR may be misstated. Therefore in such situations parametric VaR is not advised (unless it is extended to include second and third level sensitivities which can bring its own share of problems).
Parametric VaR also assumes that the returns of risk factors are normally distributed – an assumption that is violated in times of market stress. So if it is known that the risk factor returns are not normally distributed, it is not advisable to use parametric VaR.
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 . 4.50%
- C . 8.50%
- D . Cannot be determined from the given information
A
Explanation:
The probability 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.)
As the persistence parameter under EWMA is lowered, which of the following would be true:
- A . The model will react slower to market shocks
- B . The model will react faster to market shocks
- C . High variance from the recent past will persist for longer
- D . The model will give lower weight to recent returns
B
Explanation:
The persistence parameter, , is the coefficient of the prior day’s variance in EWMA calculations. A higher value of the persistence parameter tends to ‘persist’ the prior value of variance for longer. Consider an extreme example – if the persistence parameter is equal to 1, the variance under EWMA will never change in response to returns.
1 – is the coefficient of recent market returns. As is lowered, 1 – increases,giving a greater weight to recent market returns or shocks. Therefore, as is lowered, the model will react faster to market shocks and give higher weights to recent returns, and at the same time reduce the weight on prior variance which will tend to persist for a shorter period.
What is the risk horizon period used for credit risk as generally used for economic capital calculations and as required by regulation?
- A . 1-day
- B . 1 year
- C . 10 years
- D . 10 days
B
Explanation:
The credit risk horizon for credit VaR is generally one year. Therefore Choice ‘b’ is the correct answer.
A key problem with return on equity as a measure of comparative performance is:
- A . that return on equity is not adjusted for risk
- B . that return on equity are not adjusted for cash flows being different from accounting earnings
- C . that return on equity measures do not account for interest and taxes
- D . that return on equity ignores the effect of leverage on returns to shareholders
A
Explanation:
The major problem with using return onequity as a measure of performance is that return on equity is not adjusted for risk. Therefore, a riskier investment will always come out ahead when compared to a less risky investment when using return on equity as a performance metric.
Return on equitydoes not ignore the effect of leverage (though return on assets does) because it considers the income attributable to equity, including income from leveraged investments.
Return on equity is generally measured after interest and taxes at the company wide level, though at business unit level it may use earnings before interest and taxes. However this does not create a problem so long as all performance being covered is calculated in the same way.
Cash flows being different from accounting earnings can createliquidity issues, but this does not affect the effectiveness of ROE as a measure of performance.
CORRECT TEXT
Which of the following statements are true in relation to Historical Simulation VaR?
I. Historical Simulation VaR assumes returns are normally distributed but have fat tails
II. It uses full revaluation, as opposed to delta or delta-gamma approximations
III. Acorrelation matrix is constructed using historical scenarios
IV. It particularly suits new products that may not have a long time series of historical data available
- A . II
- B . II and III
- C . I and IV
- D . All of the above
A
Explanation:
Historical Simulation VaR is conceptually very straightforward: actual prices as seen during the observation period (1 year, 2 years, or other) become the ‘scenarios’ forming the basis of the valuation of the portfolio. For each scenario, full revaluationis performed, and a P&L data set becomes available from which the desired loss quantile can be extracted.
Historical simulation is based upon actually seen prices over a selected historical period, therefore no distributional assumptions are required. Thedata is what the data is, and is the distribution. Statement I is therefore not correct.
It uses full revaluation for each historical scenario, therefore statement II is correct. Since the prices are taken from actual historical observations, a correlationmatrix is not required at all. Statement III is therefore incorrect (it would be true for Monte Carlo and parametric Var).
Historical simulation VaR suffers from the limitation that if enough representative data points are no available during the historical observation period from which the scenarios are drawn, the results would be inaccurate. This is likely to be the case for new products. Therefore Statement IV is incorrect.
Which of the following statements are true:
I. Pre-settlement risk is the risk that one of the parties to a contract might default prior to the maturity date or expiry of the contract.
II. Pre-settlement risk can be partly mitigated by providing for early settlement in the agreements between the counterparties.
III. The current exposure from an OTC derivatives contract is equivalent to its current replacement value.
IV. Loan equivalent exposures are calculated even for exposures that are not loans as a practical matter for calculating credit risk exposure.
- A . II and IV
- B . III and IV
- C . I, II, III and IV
- D . II and III
C
Explanation:
Pre-settlement risk is the risk that one of the counterparties defaults prior to the date for the maturity of the transaction in question. This may be an unrelated default, in fact there may have been no default on that particular contract, but the party may have defaulted on its other obligations, or filed for bankruptcy. To deal with such cases and to protect the interests of both the parties, it is common toprovide for immediate termination of positions and settlement based on the current replacement value of the contracts. Therefore statements I and II are correct.
Statement III is correct as well – the exposure from an OTC derivative contract derives fromits current replacement value, and not the notional. If the current replacement value is negative, then the credit exposure is considered equal to zero.
Statement IV is correct as it is quite common to restate all exposures – those from credit lines, OTC derivatives etc – in loan equivalent terms prior to estimating credit risk.
Which loss event type is the loss of personally identifiableclient information classified as under the Basel II framework?
- A . Technology risk
- B . Clients, products and business practices
- C . Information security
- D . External fraud
B
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.
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 notional value ofthe debt
- B . The market value of the debt
- C . The value of the firm
- D . The value of the assets
A
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.
A bank prices retail credit loans based on median default rates. Over the long run, it can expect:
- A . Overestimation of risk and overpricing, leading to lossof market share
- B . A reduction in the rate of defaults
- C . Correct pricing of risk in the retail credit portfolio
- D . Underestimation and therefore underpricing of risk in it retail portfolio
D
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.
In estimating credit exposure for a line of credit, it is usual to consider:
- A . a fixed fraction of the line of credit to be the exposure at default even though the currently drawn amount is quite different from such a fraction.
- B . the full value of the credit line to be the exposure at default as the borrower has an informational advantage that will lead them to borrow fully against the credit line at the time of default.
- C . only the value of credit exposure currently existing against the credit line as the exposure at default.
- D . the present value of the line of credit at the agreed rate of lending.
A
Explanation:
Choice’a’ is the correct answer. Exposures such as those to a line of credit of which only a part (or none) may be drawn at the time of assessment present a difficulty when attempting to quantify credit risk. It is not correct to take the entire amount of the line as the exposure at default, and likewise the current exposure is likely to be too aggressively low a number to consider.
While the borrower has an information advantage in that he would be aware of the deterioration in credit standing before the bank and would probably draw cash prior to default, it is unlikely that the entire amount of the line of credit would be drawn in all cases. In some cases, none may be drawn. In other cases, the bank would become aware of the situation and curtail or cancel access to the credit line in a timely fashion.
Therefore a fixed proportion of existing credit lines is considered a reasonable approximation of the exposure at default against credit lines.
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 . Zero
- B . Lower
- C . Higher
- D . Unaffected by differences in frequency or severity
C
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 and low 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 high levels 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.
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 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.
- C . Marginal VaR is the change in the VaR estimate for the portfolio as a result of including the asset in the portfolio.
- D . Marginal VaR describes the change in total VaR resulting from a $1 change in the value of the asset in question.
D
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.
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 . 8.74%
- B . 9.58%
- C . 9.00%
- D . 91.26%
A
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%
A risk management function is best organized as:
- A . integrated with the risk taking functions as risk management should be a pervasive activity carried out at all levels of the organization.
- B . report independently of the risk taking functions
- C . reporting directly to the traders, as to be closest to the point at which risks are being taken
- D . a part of the trading desks and other risk taking teams
B
Explanation:
The point that this question is trying to emphasize is the independence of the risk management function. The risk function should be segregated from the risk taking functions as to maintain independence and objectivity.
Choice ‘d’, Choice ‘c’ and Choice ‘a’ run contrary to this requirement of independence, and are therefore not correct. The risk function should report directly to senior levels, for example directly to the audit committee, and not be a part of the risk taking functions.
Under the ISDA MA, which of the following terms best describes the netting applied upon the bankruptcy of a party?
- A . Closeout netting
- B . Chapter 11
- C . Payment netting
- D . Multilateral netting
A
Explanation:
Netting is the ability to set just the net balances when amounts are both owed and due. Netting can takemany forms. Payment netting is netting between counterparties that owe moneys to each other in the same currency under the same transaction (or master agreement). Closeout netting is when parties settle a net amount for the value of all outstanding transactions upon the occurrence of an event of default such as bankruptcy. Multiateral netting involves a third party that sets off exposures across counterparties that owe moneys to each other.
Closeout netting under the ISDA master agreement enables a party toterminate transactions early if an Event of Default or Termination Event occurs in respect of the other party. It involves the calculation and netting of the termination values of all transactions to produce a single amount payable between the parties. Closeout netting is therefore the correct answer.
CreditRisk+, the actuarial model for calculating portfolio credit risk, is based upon:
- A . the exponential distribution
- B . the normal distribution
- C . the Poisson distribution
- D . the log-normal distribution
C
Explanation:
CreditRisk+ treats default as a binary event, ignoring downgrade risk, capital structures of individual firms in the portfolio or the causes of default. It uses a single parameter, or the mean default rate, and derives credit risk based upon the Poisson distribution. Therefore Choice ‘c’ is the correct answer.
Which of the following belong to the family of generalized extreme value distributions:
I. Frechet
II. Gumbel
III. Weibull
IV. Exponential
- A . IV
- B . I, II and III
- C . II and III
- D . All of the above
B
Explanation:
Extreme value theory focuses on the extreme and rare events, and in the case of VaR calculations, it is focused on the right tail of the lossdistribution.
In very simple and non-technical terms, EVT says the following:
Which of the following belong to the family of generalized extreme value distributions:
I. Frechet
II. Gumbel
III. Weibull
IV. Exponential
- A . IV
- B . I, II and III
- C . II and III
- D . All of the above
B
Explanation:
Extreme value theory focuses on the extreme and rare events, and in the case of VaR calculations, it is focused on the right tail of the lossdistribution.
In very simple and non-technical terms, EVT says the following:
Which of the following belong to the family of generalized extreme value distributions:
I. Frechet
II. Gumbel
III. Weibull
IV. Exponential
- A . IV
- B . I, II and III
- C . II and III
- D . All of the above
B
Explanation:
Extreme value theory focuses on the extreme and rare events, and in the case of VaR calculations, it is focused on the right tail of the lossdistribution.
In very simple and non-technical terms, EVT says the following:
Which of the following belong to the family of generalized extreme value distributions:
I. Frechet
II. Gumbel
III. Weibull
IV. Exponential
- A . IV
- B . I, II and III
- C . II and III
- D . All of the above
B
Explanation:
Extreme value theory focuses on the extreme and rare events, and in the case of VaR calculations, it is focused on the right tail of the lossdistribution.
In very simple and non-technical terms, EVT says the following:
If a borrower has a default probability of 12% over one year, what is the probability of default over a month?
- A . 12.00%
- B . 1.00%
- C . 2.00%
- D . 1.06%
D
Explanation:
Let theprobability of default over a month be p. Therefore the probability of survival at the end of 12 months would be (1 – p)^12. Since the one year probability of default is 12%, we know that the probability of survival is 88%. Putting (1 – p)^12 = 88% and solving for p, we get p = 1.06%. Therefore Choice ‘d’ is the correct answer.
The frequency distribution for operational risk loss events can be modeled by which of the following distributions:
I. The binomial distribution
II. The Poisson distribution
III. The negative binomial distribution
IV. The omega distribution
- A . I, II and III
- B . I and III
- C . I, III and IV
- D . I, II, III and IV
A
Explanation:
The binomial, Poisson and the negative binomial distributions can all be used to model the loss event frequency distribution. The omega distribution is not used for this purpose, therefore Choice ‘a’ is the correct answer.
Also note that the negative binomial distribution provides the best model fit because it has more parameters than the binomial or the Poisson. However, in practice the Poisson distribution is most often used due to reasons of practicality and the fact that the key model risk in such situations does not arise from the choice of an incorrect underlying distribution.
For a 10 year interest rate swap, what would be the worst time for a counterparty to default (in terms of the maximum likely credit exposure)
- A . 10 years
- B . Right after inception
- C . 2 years
- D . 7 years
D
Explanation:
Right after inception’ is incorrect as the interest rate swap (IRS) would be valued at close to zero right after inception and the credit risk would be minimum. Choice ‘a’ (ie 10 years, at maturity) is incorrect as at maturity there would be no more cash flows to exchange, and the replacement value of the contract would again be close to zero.
Therefore the worst time for the counterparty to default is somewhere between inception and maturity – in fact the range of possible outcomes for the contract increases with the passage of time, and we should find the worst time to default to be a later date. However, towards maturity, the value of the contract starts to go towards zero again, and the maximum value is reached around 7 years. 2 years is too early for the maximum to be reached for the10 year IRS, and therefore choice a is the correct answer.
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 . Data completeness
- B . Data integrity
- C . Auditability
- D . Data extensibility
B
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:
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 . Data completeness
- B . Data integrity
- C . Auditability
- D . Data extensibility
B
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:
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 . Data completeness
- B . Data integrity
- C . Auditability
- D . Data extensibility
B
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:
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 . Data completeness
- B . Data integrity
- C . Auditability
- D . Data extensibility
B
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:
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 . Data completeness
- B . Data integrity
- C . Auditability
- D . Data extensibility
B
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:
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 . Data completeness
- B . Data integrity
- C . Auditability
- D . Data extensibility
B
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:
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 . Data completeness
- B . Data integrity
- C . Auditability
- D . Data extensibility
B
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:
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 . Data completeness
- B . Data integrity
- C . Auditability
- D . Data extensibility
B
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:
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 . Data completeness
- B . Data integrity
- C . Auditability
- D . Data extensibility
B
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:
Loss provisioning is intended to cover:
- A . Unexpected losses
- B . Losses in excessof unexpected losses
- C . Both expected and unexpected losses
- D . Expected losses
D
Explanation:
Loss provisioning is intended to cover expected losses. Economic capital is expected to cover unexpected losses. No capital or provisions are set aside for losses in excess of unexpected losses, which will ultimately be borne by equity. Choice ‘d’ is the correct answer.
For a hypotherical UoM, the number of losses in two non-overlapping datasets is 24 and 32 respectively. The Pareto tail parameters for the two datasets calculated using the maximum likelihood estimation method are 2 and 3 .
What is an estimate of the tail parameter of the combined dataset?
- A . 2.57
- B . 2.23
- C . 3
- D . Cannot be determined
A
Explanation:
For a number of processes, including many in finance, while a distribution such as the normal distribution is a good approximation of the distribution near the modal value of the variable, the same normal distribution may not be a good estimate of the tails. For this reason, the Pareto distribution is one of the distributions that is often used to model the tails of another distribution. Generally, if you have a set of observations, and you discard all observations below a threshold, you are left with what are called ‘exceedances’. The threshold needs to be reasonably far out in the tail. If from each value of the exceedances you subtract the threshold value, the resulting dataset is estimated by the generalized Pareto distribution.
The Pareto distribution has a ‘shape parameter’. The average of two Pareto distributions with tail parameters 1 and 2 (is a Greek character, pronounced as ‘sai’ (saa-eee)), is the weighted average of 1 and 2 with weights proportional to the number of observations in the datasets underlying the distributions.
There are two bonds in a portfolio, each with a market value of $50m. The probability of default of the two bonds are 0.03 and 0.08 respectively, over a one year horizon.
If the probability of the two bonds defaulting simultaneously is 1.4%, what is the default correlation between the two?
- A . 0%
- B . 100%
- C . 40%
- D . 25%
D
Explanation:
Probability of the joint default of both A and B =
We know all the numbers except default correlation, and we can solve for it. DefaultCorrelation*SQRT(0.03*(1 – 0.03)*0.08*(1 – 0.08)) + 0.03*0.08 = 0.014. Solving, we get default correlation = 25%
For creditrisk calculations, correlation between the asset values of two issuers is often proxied with:
- A . Credit migration matrices
- B . Transition probabilities
- C . Equity correlations
- D . Default correlations
C
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.
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 . I and III
- B . II and IV
- C . I, II and IV
- D . All of the above
C
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.
The standalone economic capital estimates for the three uncorrelated business units of a bank are $100, $200 and $150 respectively .
What is the combined economic capital for the bank?
- A . 269
- B . 72500
- C . 21
- D . 450
A
Explanation:
Since the business units are uncorrelated, we can get the combined EC as equal to the square root of the sum of the squares of the individual EC estimates. Therefore Choice ‘a’ is the correct answer. [=SQRT(100^2+200^2+150^2)]
Which of the following risks and reasons justify the use of scenario analysis in operational risk modeling:
I. Risks for which no internal loss data is available
II. Risks that are foreseeable but have no precedent, internally or externally
III. Risks for which objective assessments can be made by experts
IV. Risks that are known to exist, but for which no reliable external or internal losses can be analyzed
V. Reducing the complexity of having to fit statistical models to internal and external loss data
VI. Managing the capital estimation process as to produce estimates in line with management’s desired capital buffers.
- A . I, II and III
- B . I, II, III and IV
- C . V
- D . All of the above
B
Explanation:
All the reasons and risks presented above are valid reasons for using scenario analysis, except V and VI – ie, the need to reduce the complexity of calculations is not a valid reason for using scenario analysis. Similarly, making operational risk capital estimates match management’s desired capital allocation targets is also not a valid reason. Capital calculations are intended to provide adequate capital for managing the risk from operations, regardless of what management may desire them to be.
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 A
- B . Option B
- C . Option C
- D . Option D
D
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.
Which of the following is not a credit event under ISDA definitions?
- A . Restructuring
- B . Obligation accelerations
- C . Rating downgrade
- D . Failure to pay
C
Explanation:
According to ISDA, a credit event is an event linked to the deteriorating credit worthiness of an underlying reference entity in a credit derivative. The occurrence of a credit event usually triggers full or partial termination of the transaction and a payment from protection seller to protection buyer. Credit events include
– bankruptcy,
– failure to pay,
– restructuring,
– obligation acceleration,
– obligation default and
-repudiation/moratorium.
A rating downgrade is not a credit event.
The risk that a counterparty fails to deliver its obligation upon settlement while having received the leg owed to it is called:
- A . Pre-settlement risk
- B . Credit risk
- C . Replacement risk
- D . Settlement risk
D
Explanation:
Choice ‘d’ is the correct answer. Settlement risk, as the name suggests, arises upon settlement when one of the parties delivers its obligation under the transaction and the other does not. Consider a EUR/USD FX forward contract maturing in a month. At maturity, one of the parties will deliver EURs and the other USDs. If one party fails to deliver, then it constitutes a very large risk to the other party. This risk is much larger than pre-settlement risk, because the amount at risk is the entire notional and not just the replacement value. Of course, settlement risk exists for a very short period of time, no more than a number or hours or a day.
There is no such thing as ‘replacement risk’, and credit risk is a larger category of which settlement risks is one component. Settlement risk is the most appropriate answer.
Which of the following is NOT true in respect of bilateral close out netting:
- A . The net amount due is immediately receivable or payable
- B . All transactions are immediately closed out upon the occurrence of a credit event for either of the counterparties
- C . All transactions are netted against each other
- D . Transactions are separated by transaction type and immediately settled separately at each’s replacement value
D
Explanation:
Choice ‘b’, Choice ‘c’ and Choice ‘a’ correctly describe a bilateral close out netting as recommended by the ISDA. However Choice ‘d’ is not correct as it suggests individual settlement of transactions without netting which is the whole pointof bilateral close out netting.
Which of the following techniques is used to generate multivariate normal random numbers that are correlated?
- A . Simulation
- B . Markov process
- C . Cholesky decomposition of the correlation matrix
- D . Pseudo random number generator
C
Explanation:
A PRNG (pseudorandom number generators of the kind included in statistical packages and Excel) is used to generate random numbers that are not correlated with each other, ie they are random. A Markov process is a stochastic model that depends only upon its current state. Simulation underlies many financial calculations. None of these directly relate to generating correlated multivariate normal random numbers. That job is done utilizing a Cholesky decomposition of the correlation matrix.
Specifically, a Cholesky decomposition involves the factorization of the correlation matrix into a lower triangular matrix (a square matrix all of whose entries above the diagonal are zero) and its transpose. This can then be combined with random numbers to generate a set of correlated normal random numbers. This technique is used for calculating Monte Carlo VaR.
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 required in respect of credit risk?
- A . E – U
- B . U/E
- C . U
- D . E
A
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 of confidence 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.
If the default hazard rate for a company is 10%, and the spread on its bondsover the risk free rate is 800 bps, what is the expected recovery rate?
- A . 40.00%
- B . 20.00%
- C . 8.00%
- D . 0.00%
B
Explanation:
The recovery rate, the default hazard rate (also called the average default intensity) and the spread on debt arelinked by the equation Hazard Rate = Spread/(1 – Recovery Rate). Therefore, the recovery rate implicit in the given data is = 1 – 8%/10% = 20%.
What would be the correct order of steps to addressing data quality problems in an organization?
- A . Assess the current state, design the future state, determine gaps and the actions required to be implemented to eliminate the gaps
- B . Articulate goals, do a ‘strategy-fit’ analysis and plan for action
- C . Design the future state, perform a gap analysis, analyze the current state and implement the future state
- D . Call in external consultants
A
Explanation:
The correct answer is choice ‘a’
The correct order of steps to addressing data quality problems in an organization would include:
What would be the correct order of steps to addressing data quality problems in an organization?
- A . Assess the current state, design the future state, determine gaps and the actions required to be implemented to eliminate the gaps
- B . Articulate goals, do a ‘strategy-fit’ analysis and plan for action
- C . Design the future state, perform a gap analysis, analyze the current state and implement the future state
- D . Call in external consultants
A
Explanation:
The correct answer is choice ‘a’
The correct order of steps to addressing data quality problems in an organization would include:
What would be the correct order of steps to addressing data quality problems in an organization?
- A . Assess the current state, design the future state, determine gaps and the actions required to be implemented to eliminate the gaps
- B . Articulate goals, do a ‘strategy-fit’ analysis and plan for action
- C . Design the future state, perform a gap analysis, analyze the current state and implement the future state
- D . Call in external consultants
A
Explanation:
The correct answer is choice ‘a’
The correct order of steps to addressing data quality problems in an organization would include:
What would be the correct order of steps to addressing data quality problems in an organization?
- A . Assess the current state, design the future state, determine gaps and the actions required to be implemented to eliminate the gaps
- B . Articulate goals, do a ‘strategy-fit’ analysis and plan for action
- C . Design the future state, perform a gap analysis, analyze the current state and implement the future state
- D . Call in external consultants
A
Explanation:
The correct answer is choice ‘a’
The correct order of steps to addressing data quality problems in an organization would include:
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 CreditMetrics approach
- C . The actuarial approach
- D . The contingent claims approach
B
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:
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 CreditMetrics approach
- C . The actuarial approach
- D . The contingent claims approach
B
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:
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 CreditMetrics approach
- C . The actuarial approach
- D . The contingent claims approach
B
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:
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 CreditMetrics approach
- C . The actuarial approach
- D . The contingent claims approach
B
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:
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 CreditMetrics approach
- C . The actuarial approach
- D . The contingent claims approach
B
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:
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 CreditMetrics approach
- C . The actuarial approach
- D . The contingent claims approach
B
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:
Which of the following is closest to the description of a ‘risk functional’?
- A . A risk functional is the distribution thatmodels the severity of a risk
- B . A risk functional is a model distribution that is an approximation of the true loss distribution of a risk
- C . Risk functional refers to the Kolmogorov-Smirnov distance
- D . A risk functional assigns a penalty value for the difference between a model distribution and a risk’s severity distribution
D
Explanation:
For operational risk modeling, both frequency and severity distributions need to be modeled. Modeling severity involves finding an analytical distribution, 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.
A bullet bond and an amortizing loan are issued at the same time with the same maturity and with the same principal .
Which of these would have a greater credit exposure halfway through their life?
- A . Indeterminate with the given information
- B . They would have identical exposure half way through their lives
- C . The amortizing loan
- D . The bullet bond
D
Explanation:
A bullet bond is a bond that pays coupons covering interest during the life of the bond and the principal at maturity. An amortizing loan pays the interest as well as a part of the principal with every payment. Therefore, the exposure of the amortizing loan continually reduces, and approaches zero towards the end of its life. The bullet bond will always have a higher exposure at any time during its life when compared to an equivalent amortizing loan. Hence Choice ‘d’ is the correct answer.
Which of the following are ordered correctly in the order of debt seniority in a bankruptcy situation?
I. Equity, Subordinate debt, Senior debt
II. Senior debt, Preferred stock, Equity
III. Secured debt, Accounts payable, Preferred stock
IV. Secured debt, DIP financing, Equity
- A . II and III
- B . I and IV
- C . I
- D . II, III and IV
A
Explanation:
In a bankruptcy, equity ranks last. Preferred equity is one level above equity. Senior debt gets paid out first compared to junior debt, and secured debt is paid out first to the extent of the asset securing it (after which it counts as unsecured debt). Accounts payable and other short term liabilities are treated like unsecured creditors. Debtor-in-possession (DIP) financing ranks higher than any other asset as it is financing secured after the bankruptcy to continue the business.
Based on the above, statement I does not represent a correct ordering of seniority as equity is paid last. Similarly, DIP financing receives higher priority than even secured debt, and therefore statement IV is incorrect. Therefore the only correct statements are II and III and Choice ‘a’ is the correct answer.
Which of the following is the most accurate description of EPE (Expected Positive Exposure):
- A . The maximum average credit exposure over a period of time
- B . 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
- C . Weighted average of the future positive expected exposure across a time horizon.
- D . The average of the distribution of positive exposures at a specified future date
C
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.
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%
B
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.
Which of the following cannot be used as an internal credit rating model to assess an individual borrower:
- A . Distance to default model
- B . Probit model
- C . Logit model
- D . Altman’s Z-score
A
Explanation:
Altman’s Z-score, the Probit and the Logit models can all be used to assess the credit rating of an individual borrower. There is no such model as the ‘distance todefault model’, and therefore Choice ‘a’ is the correct answer.
Which of the following carry greater counterparty risk: a forward contract on a 10 year note, or a commercial paper carrying a AA credit rating with identical maturity and notional?
- A . The forward contract has greater credit risk as its future gains are unknown
- B . Credit risk can not be compared in these terms
- C . They both carry the same credit risk
- D . The commercial paper has greater credit risk as the entire notional is outstanding
D
Explanation:
The commercial paper has greater credit risk as the entire notional is outstanding. On the forward contract, only the replacement value of the contract, which normally would be a mere fraction of the notional, would be at risk.
Therefore Choice ‘d’ is the correct answer.
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 . 10.53%
- C . 10.00%
- D . 11.76%
B
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%.
For a loan portfolio, unexpected losses are charged against:
- A . Credit reserves
- B . Economic credit capital
- C . Economic capital
- D . Regulatory capital
B
Explanation:
Credit reserves are created in respect of expected losses, which are considered the cost of doing business. Unexpected losses are borne by economic credit capital, which is a part of economic capital. This question is a bit nuanced – and ‘economic capital’ would generally be a good answer as well. However, taking a rather beady eyed view of the terminology and distinguishing between ‘economic credit capital’ which is a subset of ‘economic capital’, we can say that ‘economic credit capital’ is a more appropriate Choice ‘a’s the question relates to credit losses.
When combining separate bottom up estimates of market, credit and operational risk measures, a most conservative economic capital estimate results from which of the following assumptions:
- A . Assuming that the resulting distributions have a correlation between 0 and 1
- B . Assuming that market, credit and operational risk estimates are perfectly positively correlated
- C . Assuming that market, credit and operational risk estimates are perfectly negatively correlated
- D . Assuming that market, credit and operational risk estimates are uncorrelated
B
Explanation:
Explanation
If the risks are considered perfectly positively correlated, ie assumed to have a correlation equal to 1, the standard deviations can simply be added together. This gives the most conservative estimate of combined risk forcapital calculation purposes. In practice, this is the assumption used most often.
If risks are uncorrelated, ie correlation is assumed to be zero, variances can be added or the standard deviation is the root of the sum of the squares of the individual standard deviations. This obviously gives a number lower than that given when correlation is assumed to be +1.
Similarly, assumptions of negative correlation, or any correlation other than +1 will give a standard deviation number that is smaller and thereforeless conservative. Choice ‘b’ is the correct answer.