8008 PRM Certification - Exam III: Risk Management Frameworks, Operational Risk, Credit Risk, Counterparty Risk, Market Risk, ALM, FTP - 2015 Edition Questions and Answers

A computation of Altman's Z-score considers the following ratios:

- Working capital to total assets

- Retained earnings to total assets

- EBIT to total assets

- Market cap to debt

- Sales to total assets

Nearly all the numbers above are accounting measures derived straight from the balance sheet or the income statement. Market capitalization is a market driven number. Therefore Choice 'c' is the correct answer as the Altman credit risk score considers both accounting and market based measures.

Altman's score, though computationally straightforward and intuitively easy to understand, was introduced in the late sixties and has been very accurate in predicting corporate bankruptcies, which is why it continues to be used extensively.

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.

Once the frequency distribution has been determined (for example, using the binomial, Poisson or the negative binomial distributions) and the severity distribution has also been determined (for example, using the lognormal, gamma or other functions), the loss distribution can be produced by a Monte Carlo simulation using successive drawings from each of these two distributions. It is assumed that the severity and frequency are independent of each other. The resulting distribution gives a distribution showing the losses for operational risk, from which there Op Risk VaR can be determined using the appropriate percentile.Therefore Choice 'b' is the correct answer.

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 GEV distribution.

Least squares and maximum likelihood are methods that are used for curve fitting, and they have a variety of applications across risk management.

The stresses on liquidity that happened as part of the credit crisis beginning 2007-08 led to drying up of trading and liquidity crisis in the corporate bond markets, the auction rate securities markets, the wholesale (interbank lending) markets, the money markets, the markets for structured products, and even the otherwise liquid futures and forwards markets (as there was no liquidity available to fund the financing of futures). The one market that was not affected was the market for treasuries, in fact the flight to quality ensured that this market was very liquid (even though stressed from a pricing perspective as yields plummetted).

Therefore Choice 'a' is the correct answer.

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.

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.

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.

All the above listed reasons are valid explanations as to why an institution level stress test cannot be estimated by merely summing up the results of the stress tests of the individual desks.

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

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.

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 is more 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 correct answer.

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.

VaR calculations look at the lower part of the distribution of future portfolio values, for example, if the desired confidence level is 95%, the cut-off for the VaR calculation will be at the bottom 5%; similarly at 1% for a 99% confidence level. The number of observations that will end up in these bottom ranges will be few and sparse, and therefore their accuracy will generally be lower than, say, the average where observations are more likely to be concentratred. If the shape of the distribution of future portfolio values is not symmetrical and has a long tail to the left, then this problem gets further exacerbated as there may be even fewer and less reliable simulated numbers at the 5% or 1% quintiles. Thus the shape of the distribution will affect the accuracy of a VaR estimate. The distribution for a short option position, for example, will have a long tail to the left, and the VaR number will be quite significantly affected by a few simulations. On the other hand, for a long option position where the long tail is to the right, and we are interested in the left tail which is better defined and ends at zero we are more likely to get a better VaR estimate. Therefore Statement I is correct.

The number of simulations carried out directly affects the standard error, which is inversely proportional to the square root of the sample size (ie the number of simulations). THe accuracy of the VaR estimate can be increased by increasing the sample size (or reduced by reducing the sample size). Therefore Statement II is correct.

The confidence level selected for the VaR estimate also affects the accuracy of the estimate. To intuitively understand this, consider this extreme example where the desired confidence level is 99.9% and there are 1000 observations. Therefore the VaR will be determined by the last value in the sample, and will therefore be quite fickle and dependent upon what chance produces as the lowest value in the simulation. But if for the same sample the confidence level desired were to be 90%, there would be 100 observations beyond the 90% cut-off and this would be a much more stable and accurate number. Therefore the confidence level selected for the VaR estimate is also a determinant of the accuracy of the VaR estimate derived from the simulation. Statement III is correct.

Thus all statements are correct and Choice 'b' 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 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 2 subordinated 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.

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.

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.)

Suppose during a historical event interest rates rose from 2% to 2.25%. This can be understood as a change of either 25 basis points, or a change of 12.5%. When applied to the current portfolio when interest rates are 0.50%, we may model this 'shock' as either a rise to 0.75%, or 0.5625% (ie a rise of 12.5% over existing levels). The former is called an absolute shock, and the latter a relative shock.

I is true as relative shocks can never change the sign of a risk factor. Yet interest rate changes are modeled as absolute changes as relative shocks can get artificially amplified or attenuated if the current level of interest rates is too different from those that existed during the crisis being modeled. Therefore II is true. III and IV are false as volatility is modeled as a relative shock and spreads are modeled as absolute shocks.

This is an example of pipeline and warehousing risk. Generally there is a lag between acquiring assets and securitizing them due to the legal work to be done, the work to be done by the ratings agencies and in finding investors. During this period, the bank is exposed to the underlying assets purchased, and this is the 'pipeline and warehousing' risk as these assets are in the pipeline and warehoused for intended subsequent sale. Generally this period tends to be short. However, during the credit crisis this became a significant source of risk as many banks were left exposed to risk they had intended to get rid of, but could not do so as the market dried up. The other choices are all incorrect.

Note that pipeline and warehousing risk is also known as 'securitzation risk'. It means that funding from securitization cannot be relied upon as a matter of fact.

Three parameters define economic credit capital: the risk horizon, ie the time horizon over which the risk is being assessed; the confidence level, ie the quintile of the loss distribution; and the definition of credit losses, ie whether mark-to-market losses are considered in addition to default-only losses. The probability of default is not a parameter within the control of the risk manager, but an input into the capital calculation process that he has to estimate. Therefore Choice 'c' is the correct answer.

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.

Risks such as abrupt changes to a firm's business model 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.

Under the CreditPortfolio View approach, the credit rating transition matrix is adjusted for the state of the economy in a way as to increase the probability of defaults when the economy is not doing well, and vice versa. Therefore Choice 'a' is the correct answer. The other choices represent nonsensical options.

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.

The second order approximation of the VaR of an options position is given by [Option delta x Underlying's VaR - Option gamma/2 x (Underlying's VaR)^2]. Therefore, a higher gamma reduces VaR and a lower gamma increases VaR. Hence Choice 'b' is the correct answer.

Error rates are generally modeled using the Poisson distribution. Recall that the Poisson distribution has only one parameter - λ - 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.

The $10m cash flow due in 6 months is equivalent to a bond with a present value of 10m/(1.05)^0.5 =$9,759,000. Essentially, the question requires us to calculate the VaR of a bond.

The VaR of a fixed income instrument is given by Duration x Interest Rate x Volatility of the interest rate x z-factor corresponding to the confidence level.

In this case, since the question requires us to calculate the value "closest to" the correct answer, we can use an estimate for the modified duration of the bond as equal to 0.5 years/(1+r) = 0.5/1.05 = 0.47 years. The VaR would be given by 0.5 * 5% * 15% * 2.326 * sqrt(1/250) * 9,759,000 = $5,384 which is closest to $5,500. Therefore Choice 'a' is the correct answer. Note that we have to multiply by sqrt(1/250) as the given volatility is annual and the question is asking for daily VaR. All other answers are incorrect.

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.

A high score under the probit and logit models indicates a higher default risk, while under Altman's methodology it indicates a lower default risk. Therefore Choice 'd' is the correct answer.

Ex-ante VaR calculations can differ from actual realized P&L due to a large number of reasons. I, II and III represent some of them. Mean reversion however has nothing to do with VaR estimates differing from actual P&L. 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.

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.

The credit migration approach to assessing portfolio credit risk involves obtaining a distribution of future portfolio values from the ratings migration matrix. First, the frequencies in the matrix are used as probabilities, and expected future values of the securities belonging to each rating category are calculated. These are then discounted to the present using the discount rate appropriate to the 'future' rating category. This gives us a forward distribution of the value of each security in the portfolio. These are then combined using the default correlations between the issuers. The default correlation between the issuers is often proxied using asset returns, and recognizing that default occurs when asset values fall below a certain threshold. A distribution for the future value of the portfolio is generated using simulation, and from this distribution the Credit VaR can be calculated.

Thus, we need the migration matrix, the risk horizon from which the present values need to be calculated, and the forward yield curve or the discount curve for each rating category for the risk horizon. Thus, Choice 'd' is the correct answer.

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.

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. Statement I 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 context of 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 $xx m - $yy m with a certain confidence level. Statement IV is therefore inaccurate.

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.

The correct answer is choice 'a'

Recall the following summary of the GARCH model. The long term variance in a GARCH model is given by ω/(1 - α - β). In this case, this works out to =SQRT(0.001/(1 - 0.05 - 0.93)) * SQRT(250) = 3.54%. Yesterday's volatility of 1% is irrelevant to the question.

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.

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 derivative transaction 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 the underlying 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 risk and 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.

Statement I is correct. Data is often divided into two sets - a 'training set' that is used to create and fine-tune the model while the 'control set' is used to prove that the model works on sample data. Back testing is then perfomed using actual data that becomes available over time, or may already be available as historical data.

Statement II is incorrect. A risk manager often spends a great deal of time in managing data, and ensuring that the data being used is accurate enough for the purpose it is being used for. A risk manager can expect to spend a good part of his or her team's time in cleansing data. While he or she can try to get the IT processes and systems to produce correct data in the first place so it requires minimal subsequent cleansing or validation, this task is likely to remain a key part of a risk manager's role for quite some time in the future given the challenges nearly all organizations face in managing risk data.

Statement III is correct. There was not enough granular data available on the underlying components of some of the derivative debt securities whose markets dried up during the crisis that began in 2007. This was because investors became increasingly unsure of what the value of these securities, such as CDOs was, leading to market seizure and firesale prices.

Statement IV is not correct. There is no easy solution to the lack of enough historical data, which is used to create as well as test models, and construct stress scenarios. Analytical approaches are not a good enough substitute for real market data. During the recent crisis, many instruments had rather short histories and there was not enough data available, and risk managers and portfolio managers relied upon analytical approaches to value and price them. Many of the assumptions that underpinned these approaches were untested in the real world and turned out to be incorrect.

Therefore Choice 'c' is the correct answer and the rest are incorrect.

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.

Total expected losses which are average and anticipated are equal to the sum of expected losses in the underlying exposures. Total unexpected losses, which are the excess of worst case losses at a certain confidence level over the expected losses, benefit from the diversification effect and are lower than the sum of unexpected losses of the underlying exposures. Therefore Choice 'c' is the correct answer. The other choices are incorrect.

A situation where a firm has more liabilities than assets does not necessarily imply default, so long as the firm is able to pay its obligations when they come due. Therefore, short term debts have a greater bearing on a firm's default than longer term debt. However, this is not to say that merely having enough to pay off the short term debts (ie debts due within one year) is enough to avoid default. Over time, the long term debt will also be turning to short term debt, and it may not be possible for the firm to roll over its liabilities without lenders considering the long term debt. The KMV approach considers the entire short term debt and half of the long term debt as the critical value of assets below which default will be triggered. Therefore Choice 'c' is the correct answer.

Incremental VaR is the change in portfolio VaR resulting from a change in a single position. This is accurately described by VaR_(p+a) - VaR_p. The other answers are incorrect, and describe other concepts.

It is important to know and understand the ideas behind MVaR (marginal VaR), CVaR (component VaR) and iVaR (incremental VaR), and the differences between them.

The CCAR is a supervisory mechanism adopted by the US Federal Reserve Bank to assess capital adequacy for bank holding companies it supervises. It was not a concept introduced by the international Basel framework.

The other three were indeed rules introduced by Basel 2.5, which was ultimately subsumed into Basel III.

Stressed VaR is just the standard 99%/10 day VaR, calculated with the assumption that relevant market factors are under stress.

The Incremental Risk Charge (IRC) is an estimate of default and migration risk of unsecuritized credit products in the

trading book. (Though this may sound like a credit risk term, it relates to market risk - for example, a bond rated A being downgraded to BBB. In the old days, the banking book where loans to customers are held was the primary source of credit risk, but with OTC trading and complex products the trading book also now holds a good deal of credit risk. Both IRC and CRM account for these.)

While IRC considers only non-securitized products, the CRM (Comprehensive Risk Model) considers securitized products such as tranches, CDOs, and correlation based instruments.

The IRC, SVaR and CRM complement standard VaR by covering risks that are not included in a standard VaR model. Their results are therefore added to the VaR for capital adequacy determination.

Statement I is true, the quantiles of the averaged models are equal to the geometric average of the quantiles of the original models.

Statement II is correct, the number of data points from which model parameters are estimated must be greater than the number of parameters. So if a distribution, say Poisson, has one parameter, we need at least two data points to estimate the parameter. Other complex distributions may have multiple parameters for shape, scale and other things, and the minimum number of observations required will be greater than the number of parameters.

Statement III is true, if the ILD data and scenarios cover the same risk, they are essentially different perspectives on the same risk, and therefore should be combined as weighted averages.

But if they cover completely different risks, the models will need to be added together, not averaged - which is why Statement IV is true.

The minimum multiplication factor specified under Basel II is 3. Therefore the correct answer is Choice 'a'. The exact requirements are laid down below.

Each bank must meet, on a daily basis, a capital requirement expressed as the higher of (i) its previous day’s value-at-risk number measured according to the parameters specified in this section and (ii) an average of the daily value-at-risk measures on each of the preceding sixty business days, multiplied by a multiplication factor.

The multiplication factor will be set by individual supervisory authorities on the basis of their assessment of the quality of the bank’s risk management system, subject to an absolute minimum of 3. Banks will be required to add to this factor a “plus” directly related to the ex-post performance of the model, thereby introducing a built in positive incentive to maintain the predictive quality of the model. The plus will range from 0 to 1 based on the outcome of so-called “backtesting.”

The number of futures contracts to sell are equal to $10m x 1.1/$50,000 = 220. Liquidating his portfolio would reduce the beta to zero, but would also get rid of the bets he wants to play on. Therefore Choice 'c' is the correct answer.

(Note that futures and spot prices generally move together allowing futures positions to be used for hedging the risk against movement in spot prices. However there is a basis risk between spot and futures, therefore the a perfect hedge is never possible with futures. If interest rates move a great deal, spot and futures prices may diverge. Of course, this risk is generally quite low but may become amplified with large leveraged portfolios. Just something to be aware of.)

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.

The Earnings Volatility approach to calculating economic capital is a top down approach that considers economic capital as being the capital required to make for the worst case fall in earnings, and calculates EC as equal to the worst case decrease in earnings capitalized at the rate of return expected of the firm. The worst case decrease in earnings, or the earnings-at-risk can only be stated at a given confidence level, and is equal to the Expected Earnings less Earnings under the worst case scenario.

The term 'group risk' has been defined in the FSA document 08/24 on stress testing as the risk that a firm may be adversely affected by an occurrence (financial or non-financial) in another group entity or an occurrence that affects ther group as a whole. These risks may occur through:

- reputational contagion,

- financial contagion,

- leveraging,

- double or multiple gearing,

- concentrations and large exposures (particularly intra-group).

Thus, the insurance sector may be considered a group, and a firm may suffer just because another group firm has had losses or reputational issues.

The FSA statement goes on to identify some elements of group risk as follows:

- intra-group exposures (credit or operational exposures through outsourcing or service arrangements, as well as more standard business exposures);

- concentration risks (from credit, market or insurance risks which could put a strain on capital resources across entities simultaneously);

- contagion (reputational damage, operational or financial pressures); and

- complex group structures (with dependencies, complex split of responsibilities and accountabilities).

Therefore Choice 'a' is the correct answer and the rest of the choices are incorrect.

First of all, if prices are lognormally distributed, that implies the returns (which are equal to the log of prices) are normally distributed. To say that prices are lognormally distributed is just another way of saying that returns are normally distributed.

Since the correlation between the two securities is zero, this means their variances can be added. But standard deviations, or volatilities cannot be added (they will be the square root of sum of variances). VaR is nothing but a multiple of standard deviation, and therefore it is not additive if correlations are anything other than 1 (ie perfect positive, which would imply we are dealing with the same asset). Therefore VaR(A+B)=SQRT(VaR(A)^2 + VaR(B)^2). This implies the combined VaR of a portfolio with these two securities will be less than the sum of VaRs of the two individual securities.

Thus Choice 'c' is the correct answer and the other choices are wrong.