PRMIA 8008 PRM Certification - Exam III: Risk Management Frameworks, Operational Risk, Credit Risk, Counterparty Risk, Market Risk, ALM, FTP - 2015 Edition Exam Practice Test

Counterparty risk was difficult to gauge as it was impossible to know who the counterparty's counterparties were - this is true as the chain of financial transactions became excessively long with no central transparency of who owed who what. Bank A's credit depended upon the health of its counterparties, whose health in turn depended upon other counterparties. Thus Choice 'd' is a correct statement.

In an attempt to diversify, banks became more like each other - chasing yield, they piled into securitized products, and chasing diversification, they piled into different types of securitized products. The system as a whole became susceptible to small shocks in the assets underlying this vast edifice of structured products. Therefore Choice 'a' represents a correct statement.

Choice 'c' does not represent a correct statement. Central banks had little data on the interconnections between institutions. They were aware of the large volumes of OTC transactions, but had no data to figure out who was connected to who, and who had what kind of exposures.

Choice 'b' represents a correct statement. Most transactions, other than exchange cleared futures trades (which were a tiny fraction of all trades) were cleared on a bilateral basis. The existence of central counterparties (CCPs) could have limited the impact of the crisis significantly as market participants would not have lost trust in each other, and the 'collateral damage' that was witnessed from a fall in housing prices, and thereby mortgage assets, would have been more contained.

When we do a Monte Carlo simulation, the statistic we obtain (eg, the expected price) is an estimate of the real variable. The difference between the real value (which would be what we would get if we had access to the entire population) and that estimated by the Monte Carlo simulation is measured by the 'standard error', which is the standard deviation of the difference between the 'real' value and the simulated value (ie, the 'error').

As we increase the number of draws in a Monte Carlo simulation, the closer our estimate will be to the true value of the variable we are trying to estimate. But increasing the sample size does not reduce the error in a linear way, ie doubling the sample size does not halve the error, but reduces it by the inverse of the square root of the sample size. So if we have a sample size of 1000, going up to a sample size of 100,000 will reduce the standard error by a factor of 10 (and not 100), ie, SQRT(1/100) = 1/10. In other words, standard error is proportional to 1/√N, where N is the sample size.

Therefore Choice 'c' is correct and the others are incorrect.

The persistence parameter, β, is the coefficient of the most recent day's returns in GARCH 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 GARCH will never change in response to returns.

In the Standardized Approach, banks’ activities are divided into eight business lines: corporate finance, trading & sales, retail banking, commercial banking, payment & settlement, agency services, asset management, and retail brokerage. Therefore Choice 'c' is the correct answer.

This is a tricky question in the sense no risk management professional can be expected to know the answer to this one unless they have read Chapter 2 of the PRMIA handbook. So this question appears purely for the sake of something you would need to know purely for the sake of the exam.

PRMIA's handbook classifies governance sructures as reactive, preventative and active. Reactive structures involve monitoring signals after the event leading to corrective actions. Preventative structures are forward looking and anticipate issues before they arise. Active structures include considerations of operational efficiency and not just governance. All other answers are made up phrases and are incorrect.

In reality, corporations employ all structures together without worrying about the boundary between the three, and these distinctions do not exist except in textbooks.

Where a historical shock factor does not exist for a security, for example because the security is new or was only thinly traded earlier, or because a particular emerging market was immature at the time of the historical scenario being considered, it is inappropriate to leave the position unshocked. By and large, the general rule to be followed when carrying out stress testing is to leave no position unshocked. Therefore Choice 'b' is the correct answer.

Choice 'd', Choice 'a' and Choice 'c' all represent valid approaches to estimating a shock factor in such cases.

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 such an 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.

An interesting property that distinguishes the three most used distributions for modeling event frequency is that for a given mean, their variances differ. The ratio of variance to mean (the variance-mean ratio, calculated as variance/mean) can then be used to decide the kind of distribution to use. Both the variance and the mean can be estimated from available data points from the internal or external loss databases, or the scenario exercise.

The variance-mean ratio reflects how dispersed a distribution is. (In the PRMIA handbook, the variance to mean ratio has been described as the "Q-Factor".)

The Poisson distribution has its mean equal to its variance, and therefore the variance to mean ratio is 1. For the negative binomial distribution, this ratio is always greater than 1, which means there is greater dispersion compared to the mean - or more intervals with low counts as well as more intervals with high counts. For the binomial distribution, the variance to mean ratio is less than one, which means it is less dispersed than the Poisson distribution with values closer to the mean.

In a situation where operational risk events are seen as clustering together, or dependent, the variance will be higher and it would be more appropriate to use the negative binomial distribution.

Probability of the joint default of both A and B =

We know all the numbers except default correlation, and we can solve for it.

Default Correlation*SQRT(0.03*(1 - 0.03)*0.08*(1 - 0.08)) + 0.03*0.08 = 0.014.

Solving, we get default correlation = 25%

When a operational loss frequency distribution (which, for example, may be based upon a Poisson distribution) and a loss severity distribution (for example, based upon a lognormal distribution), it is assumed that the frequency of losses and the severity of the losses are completely independent and do not impact each other. Therefore statement II is correct, and the others are not valid assumptions underlying the operational loss distribution.

Choice 'd' is the correct answer, as laid down in the Basel II document. The other choices are incorrect.

The bank paid $7m for the bonds, and expected recovery is $3m (30% x $10m face). Therefore Bank B's loss is $4m ($7m - $3m). Choice 'b' is the correct answer. All other answers are incorrect.

A standard model for representing asset returns in finance is the Geometric Brownian Motion process, and returns according to this model can be estimated by the expression given in Choice 'b'. Note that prices according to this model are log-normally distributed, and returns are normally distributed.

Exposure for derivative instruments can vary significantly over the lifetime of the instrument, depending upon how the market moves. The potential future exposure represents the extremes, not the most likely outcome. The expected exposure is the most suitable measure for pricing the credit risk. Over time, as multiple transactions are entered into, the expectation (or the mean) will be realized - though individual transactions may have more or less by way of exposure.

The notional amount may not be relevant, though for loans it may be the most important contributor to the expected exposure. Mark-to-market will represent the exposure at a given point in time, but cannot be predicted nor be used to price the credit risk.

The economic capital required to avoid insolvency is just the asset VaR, ie $100. This means that if the worst case losses are realized, the institution would need to have a buffer equivalent to those losses which in this case will be $100, and this buffer is the economic capital.

The actual value of liabilities is not relevant as they are considered 'riskless' from the institution's point of view, ie they will be taken at full value. In this particular case, the institution has $200 in capital which is more than the economic capital required.

Therefore Choice 'c' is the correct answer.

The 'middle office' is a term used for the risk management function, therefore Choice 'd' is the correct answers. The other functions describe what the 'back office' does (IT, accounting). The 'front office' includes the traders.

All four data sources are expected to be utilized as inputs as appropriate for operational risk calculations under the advanced measurement approach. Of these, the last one, BEICF, is slightly different from the rest as it does not yield data points that become the basis of curve fitting or other statistical computions underlying capital calculations. It includes items such as KRIs, risk assessments etc and allow the risk manager to assess the qualitative aspects of loss data.

The recovery rate, the default hazard rate (also called the average default intensity) and the spread on debt are linked by the equation Hazard Rate = Spread/(1 - Recovery Rate). Therefore, the recovery rate implicit in the given data is = 1 - 8%/10% = 20%.

The risk analyst is using the block maxima approach. The data points that result will then be used to fit a GEV distribution.

Expected shortfall refers to the expected losses beyond a specified threshold. The peaks-over-threshold approach is an alternative approach to the block maxima approach, and involves considering exceedances above a threshold. Fourier transformation is not relevant in this context, and is a non-sensical option.

According to Basel II, where marking-to-market is not possible, banks may mark-to-model, where this can be demonstrated to be prudent. Marking-to-model is defined as any valuation which has to be benchmarked, extrapolated or otherwise calculated from a market input. When marking to model, an extra degree of conservatism is appropriate. Supervisory authorities will consider the following in assessing whether a mark-to-model valuation is prudent:

• Senior management should be aware of the elements of the trading book which are subject to mark to model and should understand the materiality of the uncertainty this creates in the reporting of the risk/performance of the business.

• Market inputs should be sourced, to the extent possible, in line with market prices. The appropriateness of the market inputs for the particular position being valued should be reviewed regularly.

• Where available, generally accepted valuation methodologies for particular products should be used as far as possible.

• Where the model is developed by the institution itself, it should be based on appropriate assumptions, which have been assessed and challenged by suitably qualified parties independent of the development process. The model should be developed or approved independently of the front office. It should be independently tested. This includes validating the mathematics, the assumptions and the software implementation.

• There should be formal change control procedures in place and a secure copy of the model should be held and periodically used to check valuations.

• Risk management should be aware of the weaknesses of the models used and how best to reflect those in the valuation output.

• The model should be subject to periodic review to determine the accuracy of its performance (e.g. assessing continued appropriateness of the assumptions, analysis of P&L versus risk factors, comparison of actual close out values to model outputs).

• Valuation adjustments should be made as appropriate, for example, to cover the uncertainty of the model valuation.

The model should be created independent of the front office, and not by it. Therefore statement III does not represent an appropriate choice. Choice 'a' is the correct answer.

Unexpected losses (UEL) for individual loans in a portfolio will always sum to greater than the total unexpected loss for the portfolio (unless all the loans are correlated in such a way that they default together). This is akin to the 'diversification effect' in market risk, in other words, not all the obligors would default together. So the UEL for the portfolio will always be less than the sum of the UELs for individual loans. Therefore statement III is true.This 'diversification effect' will be affected by the default correlations between the obligors, in cases where the probability of various obligors defaulting together is low, the UEL for the portfolio would be much less than the UEL for the individual loans. Hence statement IV is true.I and II are false for the reasons explained above.

Transition matrices are used for building distributions of the value of credit portfolios, and are the realized frequencies of migration from one credit rating to another over a period, generally one year. Therefore Choice 'd' is the correct answer.

Since they represent an actually observed set of values, they are not probabilities nor are they forward looking ex-ante estimates, though they are often used as proxies for probabilities. Choice 'a' and Choice 'c' are not correct. They include more than information on just defaults, therefore Choice 'b' is not correct.

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 to default model', and therefore Choice 'a' is the correct answer.

A non-financial firm such as a manufacturing company faces market risks similar to those faced by financial firms, except perhaps for not being exposed to risks from the equity markets. Non financial firms commonly face interest rate risks in respect of their debts, commodity price risks in respect of their inputs and products, and foreign currency risks in respect of their overseas operations. It is therefore not correct to say that the manufacturing firm does not face market risk because it does not take proprietary positions. While decisions on positions may not be actively taken, positions in foreign exchange (eg, through overseas debtors owing foreign currency, or liabilities in foreign currencies to overseas suppliers), commodities (through exposure to the need for raw material and inventory of finished goods) and interest rates (through debt financed, whether at fixed or floating rates) exist and create market risk much in the same way as they would for a proprietary position. Therefore statement I is incorrect.

While the firm faces market risks as an externality (as do financial firms for that matter, though often they seek such exposure to profit from their view on which way the externality will express itself), it is incorrect to say that these risks must be borne. They can be measured and hedged. Therefore statement II is incorrect.

The results of a manufacturing firm will include gains and losses arising from exposure to market risk, and will cloud the true profitability of the business. A firm with significant unhedged overseas sales may show vastly different results across time periods due to the FX gains and losses, making comparative assessment of profitability difficult. Therefore statement III is correct.

Market risks for a manufacturing firm may be directionally biased in terms of exposure, ie there may be a consistent 'long' position in a particular commodity that the firm produces, and a consistent 'short' position in the commodities consumed. In the same way, directional biases may exist in FX or interest rate exposures too. Regardless of the bias, the existence of market risk exposures increase the volatility of the income stream and make the firm more risky, even though the long term expected returns from such exposures is zero (ie, returns may be zero but standard deviation is not). Therefore statement IV is not correct as market risks form non financial firms do increase the overall risk of the firm.

Choice 'c' relates to operational risk and process capabilities, generally not a concern when evaluating market risk of a portfolio. Choice 'a', Choice 'b' and Choice 'd' represent real concerns for the risk manager when building stress tests for the value of a portfolio.

Choice 'a' is relevant because certain shocks may be inconsistent with each other, and therefore implausible. For example, an increase in futures prices may be inconsistent with without spot prices and/or interest rates increasing according to the no-arbitrage condition. Choice 'b' is relevant when modeling a covariance matrix in a stressed situation with higher correlations, as a hypothetical covariance matrix which is not positive semi-definite may give absurd results (negative variance). Choice 'd' is relevant as liquidity risks may affect the price that can be realized for positions held.

When modeling operational loss frequency distribution (which, for example, may be based upon a Poisson distribution) and a loss severity distribution (for example, based upon a lognormal distribution), it is assumed that the frequency of losses and the severity of the losses are completely independent and do not impact each other. Therefore Choice 'a' is correct, and the others are not valid assumptions underlying the operational loss modeling.

Once each of these distributions has been built, a random number is drawn from each to determine a loss scenario. The process is repeated many times as part of a Monte Carlo simulation to get a the loss distribution.

Banks using the basic indicator approach must hold 15% of the average annual gross income for the past three years, excluding any year that had a negative gross income. Therefore Choice 'd' is the correct answer.

The VaR for a spot FX position is merely a function of the standard deviation of the exchange rate. If V be the value of the position (in this case, EUR 15m x 1.5 = USD 22.5m), z the appropriate z value associated with the level of confidence desired, and σ be the standard deviation of the portfolio, the VaR is given by ZσV.

In this case, the 10-day standard deviation is given by SQRT(10/250)*16%. Therefore the VaR is =1.645*15*1.5*(16%*SQRT(10/250)) = USD 1.1844m. Choice 'c' is the correct answer.

An 'extreme value' will be a value that will lie in the tails. We need to determine the distribution that will have the least weight in the tails so that the probability of exceeding this tail value is minimum across the given choices.

The t-distribution, a distribution with kurtosis > 3 and a normal mixture distribution are all distributions with tails fatter than that for a normal distribution. A normal distribution will have the 'thinnest' tails among the choices and therefore the lowest probability of exceeding a given tail event value.

A note about the t-distribution: Leptokurtic distributions (those that have kurtosis>3, ie kurtosis greater than that for a normal distribution) generally appear to have higher peaks on their PDF graphs. The t-distribution is flatter, and actually appears lower than a normal distribution, which may make one think that it has a lower kurtosis and therefore should have thinner tails than a normal distribution. But that is not so, and the "visual" inspection test fails for inferring the kurtosis from just looking a the shape of the distribution. The kurtosis of a t-distribution is given by the formula {3 + 6/(d - 4)}, where d is the degrees of freedom and d > 4. Therefore the kurtosis of a t-distribution is always greater than 3 as "6/(d-4)" will always be a positive number being added to 3. Therefore there is no conflict between a t-distribution having fatter tails than a normal distribution as it has a higher kurtosis, even though it appears 'lower' on a graph when superimposed with a normal distribution.

Bank B's exposure is measured by the price it paid for the bonds, which in this case is $7m ($10m x 70/100). Hence Choice 'c' represents the correct answer.

(Note that the question is asking for 'exposure' and not the legal claim in the event of default. The legal claim in the event of default would be the full notional of $10m. )

The initial issue price and issue size are irrelevant.

The cumulative probability of default for the security for the 5 years is [1 - (1 - probability of default upto year 4)*(1 - probability of default in year 5)]. An easier way to think about this is that the Probability of survival till year 5 = (Probability of survival till year 4 * Probability of survival during year 5). Using the relationship that probability of default = 1 - probability of survival, we can calculate the required probability in all cases.

In this case, the cumulative probability of default for the security for 5 years = 1 - (1 - 11.47%)*(1 - 5%) = 15.8695%, therefore Choice 'c' is the correct answer.

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.

In the February of 2009, the Federal Reserve (which is the US central bank system) and other US banking regulators embarked on a simultaneous assessment of the capital held by the 19 largest US bank holding companies. This was an unprecedented exercise of a kind never undertaken before, and was known as the Supervisory Capital Assessment Program (SCAP). The purpose of the exercise was to determine the amount of additional capital (called the 'capital buffer') each of the institutions covered would need to ensure that it would have sufficient capital if the economy weakened more than was then expected. The idea was that these financial institutions would then raise additional capital equal to their respective capital buffers by the fourth quarter of 2009.

Statement I is false on two counts: firstl the SCAP was conducted by the US central bank and other regulators, and not the 'Treasury Department' (the Treasury Department in the US is the equivalent of the Ministry of Finance in may other countries). Second, the SCAP was a one time exercise, and not annual.

Statement II is correct. The regulators prescribed rates of losses on credit assets of different kinds and other macro-economic assumptions, and asked the banks to determine the extent of losses they would need to bear (in addition to calculating them independently too). Therefore the SCAP was a stress test where the scenario was prescribed by the regulators.

Statement III is false. Capital buffer under the SCAP referred to the additional capital the banks would need to have certain ratios of capital, and not 'excess' capital.

Statement IV is correct. The SCAP envisaged two capital targets: a Tier 1 capital ratio in excess of 6% at the end of 2010; and a Tier 1 common capital ratio in excess of 4%. Therefore both the total Tier 1 capital and Tier 1 common capital were targeted.

Therefore Choice 'c' is the correct answer.

The change in the price of a security that follows a Weiner process is determined 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.

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.]

This is easy to calculate as follows: At the 99% confidence level, the VaR=2.326 * Std Deviation (remember the z values at the 95% and 99% levels, the PRMIA exam may not give you these values). Thus the 1-day standard deviation is $250m/2.326, and the 250-day standard deviation is √250 * ($250m/2.326) = $1,699.4m.

Remember: if you know the VaR, you know the standard deviation. Once you know the standard deviation for any period of time, you can convert it into standard deviation for another period using the square root of time rule. You can also calculate the VaR at a different confidence level too.

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 - - may help clarify things further.

The EWMA and GARCH approaches to volatility clustering are independent of the method used to calculate VaR. Therefore Choice 'd' is the correct answer

If annual variance is 0.0256, then annual volatility (ie standard deviation) is √0.0256. Therefore the daily volatility will be √0.0256/√250 = 1.01%. The other choices are not correct.

In the case of mean reversion, the actual VaR would be lower than that estimated using the square root of time rule. This is because gains over a period would be followed by losses so that the price can revert to the mean. In such cases, the autocorrelation between subsequent periods is effectively negative. This means the combined VaR over the periods would be lower.

In the case of positive autocorrelation, the actual VaR would be higher than that estimated using the square root of time rule for exactly the opposite reason than that described for the mean-reverting case.

(Recall that Variance (A + B) = Variance(A) + Variance(B) + 2*Correlation*StdDev(A)*StdDev(B). In cases where correlation is zero, the variance can simply be added together (which is the case for iid observations). In cases where the correlation is negative, the combined variance (and therefore standard deviation and also VaR) will be lower; and where correlation is positive, the combined variance (and therefore standard deviation and also VaR) will be higher.)

Therefore statement II is correct, and so is statement III. Choice 'c' is the correct answer.

Basel II proposes three approaches to compute operational risk capital - the basic indicator approach (BIA), the standardized approach (SIA) and the advanced measurement approach (AMA). There is no operational risk approach called the factor based approach.

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 is asking 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%.

The term 'data quality' has multiple elements, ie, data in order to be considered of a high quality must have multiple attributes such as completeness, 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 not going 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 - and therefore Choice 'b' is the correct answer. The other choices address other aspects of data quality but not this, and therefore are not correct.

Monte Carlo VaR computations generally include the following steps:

1. Generate multivariate normal random numbers, based upon the correlation matrix of the risk factors

2. Based upon these correlated random numbers, calculate the new level of the risk factor (eg, an index value, or interest rate)

3. Use the new level of the risk factor to revalue each of the underlying assets, and calculate the difference from the initial valuation of the portfolio. This is the portfolio P&L.

4. Use the portfolio P&L to estimate the desired percentile (eg, 99th percentile) to get and estimate of the VaR.

Monte Carlo based VaR calculations rely upon full portfolio revaluations, as opposed to delta/delta-gamma approximations. As a result, they are also computationally more intensive. Because they are not limited by the range of instruments and the properties they can cover, they can capture a wide range of distributional assumptions for asset returns. They also tend to provide more robust estimates for the tail, including portions of the tail that lie beyond the VaR cutoff.

Therefore I and III are true, and the other two are not.

The 'degree' of a node in a network measures the number of links to other nodes. For the financial network, each market participant can be thought of as a node. The 'degree distribution' can be thought of as the histogram of the number of links for each node.

The financial network has a degree distribution with rather long tails - and therefore Choice 'd' is the correct answer. The other choices are incorrect. Long tailed networks have the property that they are robust when affected by random disturbances, but susceptible to targeted attacks, for example on key hubs.

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.)

Any stress test is conducted with a view to produce a dollar estimate of losses, therefore statement I is correct. However, these numbers do not come with any probabilities or confidence levels, unlike VaR, and statement III is incorrect. Stress testing can complement VaR, but not replace it, therefore statement II is not correct. Statement IV is correct as stress tests can be based on both actual historical events, or simulated factor shocks (eg, a factor, such as interest rates, moves by say 10-z).

Therefore Choice 'a' is correct.

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.)

This situation represents one of the paradoxes in estimating severity that one needs to be aware of - the improvement in controls reduces the weight of the body/middle of the distribution and moves it towards the tails (as the total probability under the curve must stay at 100%) and the distribution becomes more heavy tailed. As a result, the 99.9th percentile loss actually increases. instead of decreasing, creating a counterintuitive result. Therefore the correct answer is that the capital required will increase.

If scenario analysis produces such a result, the analyst must question if the 1 in 100 year loss severity is still accurate. If the new control has reduced the severity in the body of the distribution, the question as to why the more extreme losses have not changed should be raised.

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

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

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

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

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

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

In December 2009 the BIS came out with a new consultative document on liquidity risk. Given the events of 2007 - 2009, it has been clear that a key characteristic of the financial crisis was the inaccurate and ineffective

management of liquidity risk

The paper two separate but complementary objectives in respect of liquidity risk management: The first objective relates to the short-term liquidity risk profile of institution, and the second objective is to promote resiliency over longer-term time horizons. The paper identifies the following two ratios - you should be aware of these - though I am not sure if these will show up in the PRMIA exam:

1. Liquidity Coverage Ratio addresses the ability of an institution to survive an acute liquidity risk stress scenario lasting one month. It is calculated as follows:

Liquidity Coverage Ratio = Stock of high quality liquid assets/Net cash outflows over a 30-day time period

2. Net Stable Funding Ratio has been developed to capture structural issues related to funding choices.

Net Stable Funding Ratio = Available amount of stable funding/Required amount of stable funding

Both ratios should be equal to or greater than 1. The statement contains detailed definitions of what is included or excluded from each of the terms used in the calculations for each of the ratios. In addition, the standard also describes the what the 'acute' scenario should include (things such as a 3 notch credit downgrade, reduction in retail deposits etc)

Therefore Choice 'b' is the correct answer. Book Value to Share Price and Earnings Per Share are accounting measures unrelated to liquidity.

Choice 'c' is the correct answer as Monte Carlo simulations are not used to generate stress scenarios. They are applicable to VaR calculations under certain situations, and are not used for stress tests. The other three represent valid approaches to stress testing.

Any good risk measure has the property that it is sub-additive, which means the whole is less than the sum of the parts. In the case of VaR, sub-additivity arises due to the diversification effect, or said differently, due to the correlation between different assets being less than one. Therefore Choice 'd' is the correct answer.

Super-additivity is just the opposite of sub-additivity, ie, the whole is greater than the sum of the parts. Good risk measures do not have super-additivity. Therefore Choice 'b' is incorrect.

Choice 'c' states the same thing as Choice 'b' in different words, and is incorrect. Choice 'a' is non-sensical and incorrect.