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

Survivorship bias is the tendency for failed companies, funds, investments and even entire markets (eg Russian stock market returns after the Communist revolution) to be excluded from performance studies because they no longer exist. Survivorship bias results in past results looking better than they actually were as data points relating to failures are not included.

A risk manager needs to be aware of survivorship bias when basing risk analysis on historical data and should question if failures (eg failed funds, delisted companies etc) have been included in the data he or she is relying upon.

Losses due to credit risk include the loss of value from credit migration and default events (which can be considered a migration to the 'default' category). Therefore Choice 'd' is the correct answer. Changes in spreads or interest rates are examples of market risk events.

[Discussion: It may be argued that losses from spreads changing could be categorized as credit risk and not market risk. The distinction between credit and market risk is never really watertight.

The reason I have called it market risk in this question is because spreads can change due to two reasons: first, due to the individual issuer going down in their credit rating (whether issued or perceived, as we have witnessed in Europe sovereign debt), and second due to the spread for the overall category changing due to macro fundamentals with nothing changing for the individual issuer. For example the spread between municipal bonds and treasuries may be small during boom times and may expand during recessions - regardless of how the individual issuer has been doing. Clearly, the first case is credit risk and the second is probably market risk.

A change in overall corporate bond spreads is something I would consider akin to a rate change - which is why I have called it as not a part of credit risk. But an alternative perspective may not be incorrect either.]

The credit worthiness of the retail customer is certainly a factor for the bank to consider as it will need to price the loan to cover the expectation of default. At the same time, it will need to look at other loans in its portfolio as to avoid unacceptable concentration risk. A corollary of the same theme is that the bank will need to take a portfolio view of the loan request and consider its contribution to total portfolio risk. Therefore all the choices are appropriate considerations for the bank and Choice 'd' is the correct answer.

The actuarial model considers defaults to follow a Poisson distribution with a given mean per period, and these are binary in nature, ie a default happens or it does not happen. The model does not consider the loss of value from credit downgrades, and focuses only on defaults. The model also does not consider default correlations between obligors. Therefore Choice 'c' is the correct answer.

The other choices are not true statements that would apply to the actuarial approach.

Managing liquidity requires understanding and providing for two things: the amount of liquidity needed to pay for all current obligations (in both normal and stressed scenarios), and determining the time horizon over which this liquidity should be available. The first is essentially a function of the business of the firm, and the assets and liabilities resulting from operations. The second considers other factors such as the speed with which new cash can be borrowed (eg, from the repo markets), the consequences are of running out of liquidity (eg, maybe only an overdrawn fee as opposed to bankruptcy), etc. In other words, liquidity risk management answers two questions: how much, and for how long.

This question asks for identifying the factors that affect the 'how much' part. Choice 'd', Choice 'c' and Choice 'b' do affect the determination of the liquidity needs of the firm. Choice 'a' does not affect the liquidity needs, but the 'how long' part. Choice 'a' is therefore the correct answer.

Concentration risk in a credit portfolio arises due to a high degree of correlation between the default probabilities of the issuers of securities in the portfolio. For example, the fortunes of the issuers in the same industry may be highly correlated, and an investor exposed to multiple such borrowers may face 'concentration risk'.

A low degree of correlation, or independence of individual defaults in the portfolio actually reduces or even eliminates concentration risk.

The fact that issuers are from the same country may not necessarily give rise to concentration risk - for example, a bank with all US based borrowers in different industries or with different retail exposure types may not face practically any concentration risk. What really matters is the default correlations between the borrowers, for example a lender exposed to cement producers across the globe may face a high degree of concentration risk.

Stress testing provides an independent and complementary perspective to other risk management tools such as value-at-risk and economic capital. Both are tools that serve similar purposes but are not interchangeable. Stress testing, no matter how exhaustively done, can not replace other tools such as those based on analytical or historical models. It can provide a useful sense check to validate models and assumptions, but is not a replacement for traditional techniques. Therefore statement I is false.

Stress testing can certainly help identify risks with new products for which historical data may be limited, and analytical models may be based upon many unproven assumptions. It can help challenge the risk characteristics of new products where stress situations have not been observed in the past. Therefore statement II is correct.

ICAAP stands for the 'internal capital adequacy assessment process' performed by a bank (remember the acronym and its expansion). Stress testing is an integral part of a firm's ICAAP, and not distinct. It is one of the elements of the internal process. Therefore statement III is false.

Statement IV is correct as stress testing is indeed a powerful tool that can communicate risks throughout the organization as the stress scenarios are easier to comprehend than arcane statistical models. They are also easier to explain to regulators, and are a powerful communication tool.

Thus Choice 'c' is the correct answer.

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.

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.

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 be low.

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

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

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

Thus Choice 'c' is the correct answer.

Over the past decade or so, systemic risk has been increased by vastly increasing network complexities resulting from greater interconnectivity between institutions as well as countries. Therefore statement I is incorrect.

Statement II is incorrect and statement III is correct because the average path length between institutions, or their degree of separation where they are not directly dealing with each other but through other counterparties to which they are exposed (analogous to 6 degrees of separation, or the 'small world' property), has shrunk and not increased.

Statement IV correctly describes knife edge dynamics, which is another way of waying that the financial network displays a tipping point property.

This question emphasizes the difference between primary and secondary risks. Primary risks are the risks consciously undertaken, ie the risks whose premium the investor is trying to earn. Secondary risks are risks that accompany the primary risks that the investor will either hedge, or will ignore if they are small. It is important to watch out for secondary risks because they could become significant and offset the returns being sought even if the investor's market view is proved correct.

An investor in market index futures is betting that the index will rise. Index futures prices are largely driven by the spot value of the index, but are also affected by costs of carry. In particular, futures prices will be driven by interest rates, expected dividends, and any other factors that may cause the basis between spot and futures prices to diverge. These risks are secondary risks.

In this question, Choice 'd' represents the primary risk, and Choice 'a', Choice 'b' and Choice 'c' are all secondary risks. Therefore Choice 'd' is the correct answer.

Since the business units are perfectly correlated, we can get the combined EC as equal to the sum of the individual EC estimates. Therefore Choice 'a' is the correct answer.

When assets are uncorrelated, variances are additive. But volatility (which is standard deviation) is not. In the given situation, the total variance of the portfolio will be equal to the the square root of the sum of the variances of the assets in the portfolio weighted by the square of their weights. Its volatility will be the square root of this variance. Thus Choice 'c' is the correct answer.

(This is because V(cA + dB) = c^2 V(A) + d^2 V(B) - refer tutorial on combining variances.)

Choice 'd' is incorrect as it describes the calculation of variance, not volatility. Also, the presence of a large number of uncorrelated assets does not create a portfolio with volatility equal to zero or that of the market. The other choices are therefore incorrect.

Parametric VaR relies upon reducing a portfolio's positions to risk factors, and estimating the first order changes in portfolio values from each of the risk factors. This is called the delta approximation approach. Risk factors include stock index values, or the PV01 for interest rate products, or volatility for options. This approach can be quite accurate and computationally efficient if the portfolio comprises products whose value behaves linearly to changes in risk factors. This includes long and short positions in equities, commodities and the like.

However, where non-linear products such as options are involved and large moves in the risk factors are anticipated, a delta approximation based valuation may not give accurate results, and the VaR may be misstated. Therefore in such situations parametric VaR is not advised (unless it is extended to include second and third level sensitivities which can bring its own share of problems).

Parametric VaR also assumes that the returns of risk factors are normally distributed - an assumption that is violated in times of market stress. So if it is known that the risk factor returns are not normally distributed, it is not advisable to use parametric VaR.

Monte Carlo simulations can be effectively used in all cases where an analytical estimate of the VaR cannot be made for any reason - which may include complexity of portfolios, discontinuities or non-linearity in returns or just the plain unavailability of closed form analytical models. Therefore Choice 'd' is the correct answer.

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.

A LIBOR based loan requires cash to move from the lender to the borrower in the amount of the notional. The Overnight Index Swap requires only the exchange of interest payments, and therefore represents less risk.

Therefore the LIBOR based loan is a riskier exposure.

The LIBOR is generally higher than the OIS. In fact, the difference between the two, the LIBOR-OIS spread, is a standard measure of the risk premium in the market that goes up when the risk of default by counterparty banks is considered high. This is because when the market perceives the risk of default to be high, the participants need a risk premium to take on the default risk which is considerably lesser with the OIS.

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.

While conceptually VaR is a fairly straightforward concept, a number of decisions need to be made to select between the different choices available for the exact mechanism to be used for the calculations.

The Basel framework requires banks to estimate VaR at the 99% confidence level over a 10 day horizon. Yet this is a decision that needs to be explicitly made and documented. Therefore 'I' is a correct choice.

At various stages of the calculations, portfolio values need to be determined. The valuation can be done using a 'full valuation', where each position is explicitly valued; or the portfolio(s) can be reduced to a handful of risk factors, and risk sensitivities such as delta, gamma, convexity etc be used to value the portfolio. The decision between the two approaches is generally based on computational efficiency, complexity of the portfolio, and the degree of exactness desired. 'II' therefore is one of the decisions that needs to be made.

The decision as to disclosing the VaR in financial filings comes after the VaR has been calculated, and is unrelated to the VaR calculation system a bank needs to set up. 'III' is therefore not a correct answer.

Though the Basel framework requires a 10-day VaR to be calculated, it also allows the calculation of the 1-day VaR and and scaling it to 10 days using the square root of time rule. The bank needs to decide whether it wishes to scale the VaR based on a 1-day VaR number, or compute VaR for a 10 day period to begin with. 'IV' therefore is a decision to be made for setting up the VaR system.

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.

The question is asking for the probability of default over a 6 month period when the probability of annual default is known. If we let the 6 month probability of defaut be 'd', then the probability of survival at the end of 1 year would be (1 - d)^2. This we know is equal to 1 - 3% = 0.97. Therefore we can calculate 'd' to be equal to 1.51%. Choice 'c' is the correct answer, the others are incorrect.

Note that an exam question may ask for probability of the security having survived after 6 months, in which case the answer might be 1 - 1.51%. Also note that such questions will always require you to use the probability of survival (1 - probability of default) for doing the calculations. That is because the probabilities of survival can be multiplied over periods of time, but not probabilities of default as the first default in any period is the 'game-over' event after which neither survival nor defaults mean anything. Therefore you generally always have to get the probability of survival till a point in time, and use that for any other calculations.

If the hedge performs as expected, then any P&L on the long bond position will be offset by identical losses (or gains) on the hedge.

Since hedges are never perfect, and some residual risk such as basis risk, the inability to enter into an unrounded number of futures contracts will remain. However, the bulk of the risk would be mitigated, and the investor will be able to avoid any losses but will also forgo any gains. Therefore choice b is the correct answer and the rest are incorrect.

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.

Choice 'a' is the correct answer. The other choices represent non-sensical statements.

There are multiple ways to incorporate scenario analysis for modeling operational risk capital - and the exact approach used depends upon the quantity of loss data available, and the quality of scenario assessments. Generally:

- If there is no past loss data available, scenarios are the only practical means to model operational risk loss distributions. Both frequency and severity estimates can be modeled based on scenario data.

- If there is plenty of past data available, scenarios can be used as a modifier for estimates that are based solely on data (for example, consider the MAX of the loss estimates at the desired quantile as provided by the data, and as indicated by scenarios)

- If high quality scenario data is available, and there is sufficient past data, one could mix scenario assessments with the loss data and fit the combined data set to create the loss distribution. Alternatively, both could be fitted with severity estimates and then the two severities could be parametrically combined.

In short, there is considerable flexibility in how scenarios can be used.

Statement I is therefore correct, and so is statement II as both indicate valid uses of scenarios.

Statement III is not correct because it may be okay to create severity estimates based on scenario data alone.

Statement IV is not correct because while using scenarios as modifiers to other means of estimation is acceptable, that is not the only use of scenarios.

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.

Statement I is correct as credit VaR calculations often use a one year time horizon. This is primarily because the cycle in respect of credit related activities, such as loan loss reviews, accounting cycles for borrowers etc last a year.

Statement II is false. There are two ways in which loss assessments in respect of credit risk can be made: default mode, where losses are considered only in respect of default, and no losses are recognized in respect of the deterioration of the creditworthiness of the borrower (which is often expressed through a credit rating transition matrix); and the mark-to-market mode, where losses due to both defaults and credit quality are considered. The default mode is used for the loan book where the institution has lent moneys and generally intends to hold the loan on its books till maturity. The mark to market mode is used for traded securities which are not held to maturity, or are held only for trading.

Statement III is correct. The confidence interval, or the quintile of losses used for maintaining credit ratings tends to be very high as the possibility of the institution's default needs to be remote.

Statement IV is correct too, for the reasons explained earlier.

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 bullet bond is a bond that pays coupons covering interest during the life of the bond and the principal at maturity. An amortizing loan pays the interest as well as a part of the principal with every payment. Therefore, the exposure of the amortizing loan continually reduces, and approaches zero towards the end of its life. The bullet bond will always have a higher exposure at any time during its life when compared to an equivalent amortizing loan. Hence Choice 'd' is the correct answer.

Simulations of liquidity needs can be of various types: historical simulations, where the current positions are subjected to the kind of liquidity shocks experienced in the past; static simulations, where a static view of current positions, counterparty credit position, and the business is considered; and dynamic simulations where all factors are dynamically changed including counterparty credit standing, changes to the current portfolio and behavioural aspects of the business. Choice 'b' is incorrect as dynamic simulations require no such assumptions.

Liquidity risk is often thought of in terms of market liquidity risk and funding liquidity risk. Market liquidity risk relates to the the liquidity for a particular type of asset drying up. For example, during the 2007-2009 crisis a large number of corporate bonds and structured products became extremely illiquid. Market liquidity risk manifests itself in the form of higher bid offer spreads, higher pricde impact, and a reduction in the normal market size (ie, the 'normal' size of a trade for which a dealer quote is valid for). Therefore Choice 'd' is correct. Similarly, Choice 'a' is incorrect as adverse price impact results from market liquidity risk and not funding liquidity risk.

Market liquidity risk applies to the entire market and all its participants. It is not idiosyncratic. Therefore Choice 'c' is incorrect too. Funding liquidity risk on the other hand applies to an individual institution that is under liquidity stress in the sense of not being able to meet its obligations such as margin or collateral calls because of a lack of liquid assets. Thus it is funding liquidity that is idiosyncratic. Market liquidity risk often leads to funding liquidity risks materializing as firms are unable to get to the funds they were relying upon due to assets becoming illiquid.

For a dataset with 250 observations, the top 2% of the losses will be the top 5 observations. Expected shortfall is the average of the losses beyond the VaR threshold. Therefore the correct answer is (20 + 19 + 19 + 17 + 16)/5 = 18.2m .

Note that Expected Shortfall is also called conditional VaR (cVaR), Expected Tail Loss and Tail average.

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 be low.

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

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

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

Thus Choice 'c' is the correct answer.

The key to pricing loans is to make sure that the prices cover expected losses. The correct measure of expected losses is the mean, and not the median. To the extent the median is different from the mean, the loans would be over or underpriced.

The loss curve for credit defaults is a distribution skewed to the right. Therefore its mode is less than its median which is less than its mean. Since the median is less than the mean, the bank is pricing in fewer losses than the mean, which means over the long run it is underestimating risk and underpricing its loans. Therefore Choice 'd' is the correct answer.

If on the other hand for some reason the bank were overpricing risk, its loans would be more expensive than its competitors and it would lose market share. In this case however, this does not apply. Loan pricing decisions are driven by the rate of defaults, and not the other way round, therefore any pricing decisions will not reduce the rate of default.

Netting is the ability to set just the net balances when amounts are both owed and due. Netting can take many forms. Payment netting is netting between counterparties that owe moneys to each other in the same currency under the same transaction (or master agreement). Closeout netting is when parties settle a net amount for the value of all outstanding transactions upon the occurrence of an event of default such as bankruptcy. Multiateral netting involves a third party that sets off exposures across counterparties that owe moneys to each other.

Closeout netting under the ISDA master agreement enables a party to terminate transactions early if an Event of Default or Termination Event occurs in respect of the other party. It involves the calculation and netting of the termination values of all transactions to produce a single amount payable between the parties. Closeout netting is therefore the correct answer.

When VaR is based on an assumption of normality with a static mean and volatility, it means anything that violates these assumptions will introduce model error. Volatility clustering implies a non-static volatility. Heavy tails imply non-normality of the shape of the distribution. Autocorrelation of squared returns implies that returns are not independent and identically distributed. Therefore all of these introduce model error. Choice 'd' is therefore the correct answer.

Explanation

If the risks are considered perfectly positively correlated, ie assumed to have a correlation equal to 1, the standard deviations can simply be added together. This gives the most conservative estimate of combined risk for capital calculation purposes. In practice, this is the assumption used most often.

If risks are uncorrelated, ie correlation is assumed to be zero, variances can be added or the standard deviation is the root of the sum of the squares of the individual standard deviations. This obviously gives a number lower than that given when correlation is assumed to be +1.

Similarly, assumptions of negative correlation, or any correlation other than +1 will give a standard deviation number that is smaller and therefore less conservative. Choice 'b' is the correct answer.

Statement I is true - capital adequacy indeed is a reference to the ability of the firm to stay a 'going concern'. (Going concern is an accounting term that means the ability of the firm to continue in business without the stress of liquidation.)

Statement II is not true because even though the stated objective of regulatory capital requirements is similar to the purposes for which economic capital is calculated, regulatory capital calculations are based upon a large number of ad-hoc estimates and parameters that are 'hard-coded' into regulation, while economic capital is generally calculated for internal purposes and uses an institution's own estimates and models. They are rarely identical.

Statement II is not true as the purpose of economic capital is to provide a buffer against unexpected losses. Expected losses are covered by the P&L (or credit reserves), and not capital.

Statement IV is incorrect as even though economic capital may be calculated at very high confidence levels, that is never 100% which would require running a 'risk-free' business, which would mean there are no profits either. The level of confidence is set at a level which is an acceptable balance between the interests of the equity providers and the debt holders.

The three pillars under Basel II are minimum capital requirements, supervisory review process and market discipline. Therefore statement I is false. The other two statements are accurate. Therefore Choice 'd' is the correct answer.

EVT, when used in the context of operational risk measurement, focuses on tail events and attempts to build a distribution of losses beyond what is covered by VaR. Statements I, II and II are correct. Statement IV describes conditional VaR (CVAR) and not EVT.

Choice 'c' is the correct answer.

Choice 'a' is the correct answer. Exposures such as those to a line of credit of which only a part (or none) may be drawn at the time of assessment present a difficulty when attempting to quantify credit risk. It is not correct to take the entire amount of the line as the exposure at default, and likewise the current exposure is likely to be too aggressively low a number to consider.

While the borrower has an information advantage in that he would be aware of the deterioration in credit standing before the bank and would probably draw cash prior to default, it is unlikely that the entire amount of the line of credit would be drawn in all cases. In some cases, none may be drawn. In other cases, the bank would become aware of the situation and curtail or cancel access to the credit line in a timely fashion.

Therefore a fixed proportion of existing credit lines is considered a reasonable approximation of the exposure at default against credit lines.

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 first two formulae describe component VaR. The last formula is the formula for Marginal VaR. Therefore I and II is the correct answer.

Component VaR is a VaR decomposition technique that allows the total VaR for a portfolio to be broken down and attributed to the components of a portfolio. The total of the component VaR for each constituent of a portfolio is equal to the VaR for the portfolio. This property is extremely useful as opposed to the standalone VaR for each constituent taken alone as it can be used for allocating trading budgets.

The Basel II framework allows the use of the basic indicator approach, the standardized approach and the advanced measurement approaches for operational risk. There is no approach called the 'internal measurement approach' permitted for operational risk. Choice 'a' is therefore the correct answer.

A PRNG (pseudo random 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.

Collateral, limits to avoid credit exposure concentrations, termination rights based upon credit ratings, third party guarantees and credit derivatives are all tools or instruments that financial institutions use to manage their credit risk. A cumulative accuracy plot measures the accuracy of ratings, and is not a tool for managing credit risk. Therefore Choice 'b' represents the correct answer.