PRMIA 8010 Dumps

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.

Measures of risk sensitivity include delta, gamma, vega, PV01, convexity and CR01, among others. They allow approximating the change in the value of a portfolio from achange (generally small) in one of the underlying risk factors.

Risk sensitivity measures are derivatives of the value of the portfolio, calculated with respect to the risk factor. Some risk sensitivity measures are second derivatives, and allow a more precise calculation of the change in the value of the portfolio. Many risk sensitivities are represented by Greek letter, but not all.

Delta (δ) is a measure of the change in portfolio value based on a 1% change in the value of the underlying. Gamma (γ) is asecond order derivative that improves the calculation as part of a Taylor expansion. CR01 is a measure of the change due to a 1 basis point change in the credit spread. PL01 is not a measure of any kind of risk sensitivity, it does not mean anything.

A recap would be in order here: calculating operational risk capital is a multi-step process.

First, we fit curves to estimate the parameters to our chosen distribution types for frequency (eg, Poisson), and severity (eg, lognormal). Note that these curves are fitted at the UoM level - which is the lowest level of granularity at which modeling is carried out. Since there are many UoMs, there are are many frequency and severity distributions. However what we are interested in is the loss distribution for the entire bank from which the 99.9th percentile loss can be calculated. From the multiple frequency and severity distributions we have calculated, this becomes a two step process:

- Step 1: Calculate the aggregate loss distribution for each UoM. Each loss distribution is based upon and underlying frequency and severity distribution.

- Step 2: Combine the multiple loss distributions after considering the dependence between the different UoMs. The 'dependence' recognizes that the various UoMs are not completely independent, ie the loss distributions are not additive, and that there is a sortof diversification benefit in the sense that not all types of losses can occur at once and the joint probabilities of the different losses make the sum less than the sum of the parts.

Step 1 requires simulating a number, say n, of the number of losses that occur in a given year from a frequency distribution. Then n losses are picked from the severity distribution, and the total loss for the year is a summation of these losses. This becomes one data point. This process of simulating the number of losses andthen identifying that number of losses is carried out a large number of times to get the aggregate loss distribution for a UoM.

Step 2 requires taking the different loss distributions from Step 1 and combining them considering the dependence between the events. The correlations between the losses are described by a 'copula', and combined together mathematically to get a single loss distribution for the entire bank. This allows the 99.9th percentile loss to be calculated.

Credit risk is the risk from a borrower defaulting on moneys lent. Counterparty risk, on the other hand, is the risk that a counterparty to a derivativetransaction will be unable to pay at the time the transaction is in-the-money.

Credit risk therefore relates more to the banking book, counterparty risk relates more to the trading book. Credit risk and counterparty risk differ in that for counterparty risk, the amount at risk fluctuates for counterparty risk depending upon the value of the underlying derivative. Counterparty risk generally starts at zero, for most swaps and other derivatives are near zero value at inception. Over time, as the prices of theunderlying instruments move, one party ends up owing money to the other. A deterioration in the financial situation of the party owing moneys may lead to a loss to the other party, resulting in counterparty risk. Counterparty risk can also arise from stock lending operations and repo trades.

Credit risk on the other hand is the traditional risk of default by a borrower, or a bank's customer who has taken a loan or has an overdraft or other credit facility.

Statement I is therefore incorrect as credit riskand counterparty risks are different.

Statement II is correct as counterparty risk is 'contingent' in the sense it arises only if the transaction with the counterparty ends up being in-the-money, and the counterparty defaults.

Statement III is incorrect. The statement describes credit risk.

Statement IV is incorrect, as the exposure is known for moneys lent. Derivative exposures for the future are difficult to estimate, they can even turn from moneys owed to moneys due as the value of the underlying changes.

Regardless of the approach being followed by a bank (ie, whether foundation IRB or advanced IRB), it must make its own estimates for the probability of default. Banks following the foundation IRB approach may use values set by the supervisor for the other three parameters, though those following the advanced IRB approach may use their own estimates for all four inputs.(This is also the difference between advanced IRB and the foundation IRB approaches.) Therefore Choice 'a' is the correct answer.

Also note the four difference elements that go as inputs to the internal ratings based approach in the choicesprovided.

When a default occurs, the proportion of the exposure represented by therecovery rate is recovered. For example, if the recovery rate is 40% for a loan, the actual loss in the event of a default would be $60 for a $100 loan. In other words, the loss given default = 1 - recovery rate. Hence Choice 'd' is the correct answer. Allother choices are incorrect.

By assuming the assets to be independent, we are reducing the correlation from a positive number to zero. Reducing asset correlations reduces the combined standard deviation of the assets, and therefore reduces economic capital. Therefore Choice 'b' is the correct answer.

Note that this question could also be phrased in terms of the impact on VaR estimates, and the answer would still be the same. Both VaR and economic capital are a multiple of standard deviation, and if standard deviation goes down, both VaR and economic capital estimates will reduce.

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.

There ismore than one way to calculate returns. Absolute returns may be relevant for risk factors where the size of the movement is unrelated to its current value. For other risk factors, the returns might scale with the size of the existing value of the risk factor, eg equity prices. The right return definition needs to be adopted for each risk factor, therefore 'I' is a correct choice.

The risk analyst has a Choice 'b'etween parametric VaR, Monte Carlo, and historical simulation based VaR. 'II' therefore is one of the decisions that needs to be made (though historical simulation is the choice most often made).

The decision as to what to include in a portfolio is not a decision that is affected by choices made for VaR calculations. 'III' is therefore not a correctanswer.

There are multiple ways to calculate volatility - including decisions on how long back in time to go for the data, and whether volatility clustering needs to be accounted for using EWMA or GARCH. Therefore 'IV' is a correct answer.

increasing the timing differences between the two legs of the transaction will increase settlement risk and not reduce it. Using escrow arrangements, such as central clearing houses to settle transactions (eg the DTCC in the United States) reduces settlement risk. Cash settlements based on netting arrangements reduce settlement risk, while physical delivery combined with gross cash payments increase it.

Therefore Choice 'a' is the correct answer.

The correct answer is Choice 'c'. The following is a brief description of the major approaches available to model credit risk, and the analysis that underlies them:

1. CreditMetrics: based on the credit migration framework. Considers the probability of migration to other credit ratings and the impact of such migrations on portfolio value.

2. CreditPortfolio View: similar to CreditMetrics, but adds the impact of the business cycle to the evaluation.

3. The contingent claims approach: uses option theory by considering a debt as a put option on the assets of the firm.

4. KMV's EDF (expected default frequency) based approach: relies on EDFs and distance to default as a measure of credit risk.

5. CreditRisk+: Also called the 'actuarial approach', considers default as a binary event that either happens or does not happen. This approach does not consider the loss of value from deterioration in credit quality (unless the deterioration implies default).

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.

Choice 'c' is the correct answer. 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. ('Herstatt risk' refers to settlement risk, and is irrelevant.)

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 ofconfidence 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 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.

High frequency and low severity risks, for example the risks of fraud losses for a credit card issuer, may have high expected losses, but low unexpected losses. In other words, we can generally expect these losses tostay within a small expected and known range. The capital requirement will be the worst case losses at a given confidence level less expected losses, and in such cases this can be expected to be low.

On the other hand, medium severity medium frequency risks, such as the risks of unexpected legal claims, 'fat-finger' trading errors, will have low expected losses but a high level of unexpected losses. Thus the capital requirement for such risks will be high.

It is also worthwhile mentioning high severity andlow frequency risks - for example a rogue trader circumventing all controls and bringing the bank down, or a terrorist strike or natural disaster creating other losses - will probably have zero expected losses & high unexpected losses but only at very highlevels of confidence. In other words, operational risk capital is unlikely to provide for such events and these would lie in the part of the tail that is not covered by most levels of confidence when calculating operational risk capital.

Note that risk capital is required for only unexpected losses as expected losses are to be borne by P&L reserves. Therefore the operational risk capital requirements for a low severity high frequency risk is likely to be low when compared to other risks that are lower frequency but higher severity.

Thus Choice 'c' is the correct answer.

Incremental capital (or incremental VaR, depending upon the context), is a measure of the change in the capital (or VaR) requirements if a certain change is made to a portfolio.It uses the 'before' and 'after' approach, ie find out what the capital requirement or VaR will be without the change, and what it will be after the change. The difference is the incremental capital or incremental VaR. It helps measure the change in risk as a result of a particular action, eg a change in a position.

Marginal capital or VaR on the other hand is a method to break down the capital requirement or the VaR so that it can be assigned to individual positions within the portfolio. The total of marginal capital or marginal VaR for all the positions in a portfolio adds up to the total capital requirements or total VaR. Note that marginal VaR is also called component VaR.

Therefore incremental capital is the correct answer to this question. The other choices are incorrect. In the exam, the question may be phrased differently, so try to keep in mind the different between incremental and marginal capital, which can be a bit confusing given what these terms mean in plain English.

Statement I is correct. The financial system proved to be stable against small shocks and disturbances, or shocksof a particular type (eg, the dotcom crash, the wars in the Persian Gulf); but rather fragile against other types of shocks, including disturbances to key market participants caused by a worsening of mortgage defaults.Statement II is incorrect. Financialinnovation, in particular the slicing and dicing of 'risk' through securitization, significantly increased interrelationships, dependence on the same risk factors, and the complexity of the system as a whole.Statement III is incorrect. A distinction is sometimes made between risk that is knowable, measureable, and quantifiable through parameters; and uncertainty, where the parameters are not known at all. The latter is called 'Knightian uncertainty' after the name of the scholar who came up with the distinction between the two.Statement IV is correct. Feedback effects had the greatest impact on liquidity which was tended to be hoarded, and on asset prices that tumbled as market participants tried to sell assets to become more liquid.Thus, choice is a the correct answer.

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.

Risks such as abrupt changes to a firm's businessmodel caused by legislation, or the introduction of capital controls in foreign countries where a firm in invested, geo-political risks etc are not modelable in the traditional sense. These risks cannot be modeled using VaR. Therefore statement I is correct.

VaR indeed does not consider liquidity risk, it is only concerned with the standard deviation of portfolio returns. Statement II is a valid criticism.

Statement III is not correct, as VaR can consider historical price movements.

Statement IV is correct,as VaR does not consider systemic risk or the risk of contagion.

Since the BHC always fails when the investment bank fails, the joint probability of default of the two is merely the probability of the investment bank failing, ie 0.05.

The probability of just the BHC failing, given that both the investment bank and the retail bank have survived will be equal to 0.11 - (0.05+0.05-0.05*0.05) = 0.0125. (The easiest way to understand this would be to consider a venn diagram, where the area under the largest circle is 0.11, and there are two intersecting circles inside this larger circle, each with an area of 0.05 and their intersection accounting for 0.05*0.05. We need to calculate the area outside of the two smaller circles, but within the larger circle representing the BHC).

Refer diagram below, please excuse the awful colors.

Frequency modeling is performed using discrete distributions that have a positive integer as a resultant - this allows for the number of events per period of time to be modeled. Of thedistributions listed above, Poisson, negative binomial and binomial can be used for modeling frequency distributions. The Poisson and negative binomial distributions are encountered the most in practice.

The gamma distribution is a continuous distributionand cannot be used for frequency modeling.

The exact formula for VaR is = -(Zα σ + μ), where Z α is the z-multiple for the desired confidence level, and μ is the mean return. Now Zα is always a negative number, or at least will certainly be provided the desired confidence level is greater than 50%, and μ 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 -Zασ, 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 -Zασ= 250,000 (as μ=0), and therefore -Zασ - μ = 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.

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.

Tier 3 capital, or short term subordinated debt, is intended only to cover market risk but only at the discretion of their national authority.

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.

The binomial, Poisson and the negative binomialdistributions 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.

The peaks-over-threshold model is used when lossesover a given threshold are recorded, as is often the case when using data based on external public sources where only large loss events tend to find a place. The generalized Pareto distribution is also used when attempting to model loss severity using EVT.Lognormal mixtures and generalized hyperbolic distributions are not used as extreme value distributions.

Choice 'd' is the correct answer.

All of the distributions referred to in the question can be used to model the loss severity distribution for op risk.Therefore Choice 'c' is the correct answer.

The total variance of the system is 100^2 + 40^2 + 30^2 = 12500 (as variance = volatility squared). The first factor alone has a variance of 10,000, or 80%. Therefore only the first factor will be included in the final analysis, and the rest will be ignored.

Interestingly, this example highlights one of the limitations of PCA. Obviously, the second and third factors are material when considering volatility, though the effect of squaring them to get the variance makes them appear less important than they are.

The change in the price of a security that follows a Weiner process isdetermined by its standard deviation and expected return. To get the price itself, we need to add this change in price to the current price. Therefore the future price in a Weiner process is determined by all three of current price, expected return and standard deviation.

Choice 'b' is the correct answer. All other answers are incorrect.

Refer to the detailed loss event type classification underBasel II (see Annex 9 of the accord). You should know the exact names of all loss event types, and examples of each.

Odds are the ratio between the probability of the occurence of an event to the probability that the event does not occur.

If odds are H, then p = H/(1 + H) and H = p/(1-p). In this case the odds are 1:5, or 1/5, therefore the correct answer is Choice 'a', equal to (1/5)/(1 + 1/5) = 1/6 = 16.67%. All other choices are incorrect.

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.

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:

1. Pull a number of large iid random samples from the population,

2. For each sample, find the maximum,

3. Then the distribution of these maximum values will follow a GeneralizedExtreme Value distribution.

(In some ways, it is parallel to the central limit theorem which says that the the mean of a large number of random samples pulled from any population follows a normal distribution, regardless of the distribution of the underlying population.)

Generalized Extreme Value (GEV) distributions have three parameters: ξ (shape parameter), μ (location parameter) and σ (scale parameter). Based upon the value of ξ, a GEV distribution may either be a Frechet, Weibull or a Gumbel. These arethe only three types of extreme value distributions.

The term 'data quality' has multiple elements, ie, data in order to be considered of a high quality must have multiple attributes such ascompleteness, timeliness, auditability etc. Because this is not an exact science, every expert or text book will have a different view of what goes into data quality. For our purposes however, we will stick to what the PRMIA study material specifies, and according to the study material the following are the elements that can be considered attributes that make for quality data:

1. Integration

2. Integrity

3. Completeness

4. Accessibility

5. Flexibility

6. Extensibility

7. Timeliness

8. Auditability

I am notgoing to describe each of these here as that would be repetitive of the study material, but suffice it to say that the break-down of a number into its constituents should tie to the aggregate total. If that is not true, then the data lacks integrity - andtherefore Choice 'b' is the correct answer. The other choices address other aspects of data quality but not this, and therefore are not correct.

If capital calculations are done in a standard way regardless of risk (as reflected by credit ratings), then it creates a perverse incentive for the lenders' employees to lend to the riskiest borrowers that offer the highest expected returns as there is no incentive to 'save' on economic capital requirements that are equal for both safe and unsafe borrowers. Therefore statement I is correct.

Given that the portfolio of suchan institution is likely to then comprise poor quality borrowers, and economic capital would be based upon 'average' expected ratings, it is likely to carry lower economic capital given its exposures. Therefore any such economic risk capital model is likely to understate economic capital requirements. Therefore statement IV is correct.

Statements II and III are incorrect and Choice 'b' is the correct answer.

Internal loss data isgenerally the highest quality as it is relevant, and is 'real' as it has occurred to the organization. External loss data suffers from a significant limitation that the risk profiles of the banks to which the data relates is generally not known due to anonymization, and may likely may not be applicable to the bank performing the calculations. Therefore, replacing external loss data with external loss data is not a good idea. Statement IV is therefore incorrect.

All other approach described are valid approaches for the risk analyst to consider and implement. Therefore statements I, II and III are correct and IV is not.