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

Component VaR measures the proportion of total VaR that can be allocated to each asset in the portfolio. It is based upon the covariance matrix multiplied by the weights, and each row represents the component VaR for the asset in question. Since the total of such a matrix is the total VaR, component VaR is additive. Component VaR is used to assess the contribution of each asset in the portfolio to total risk and has the useful property of being additive so some sense can be made of the contribution of each asset to total risk.

Incremental VaR, conditional VaR and VaR are sub-additive by definition, and therefore not the correct answer.

p = k/N. If there are N observations of which K are upto T, then p = k/N allows us to have a continuous unbroken curve which gets increasingly weighted towards the distribution selected for the tail as we move towards the 'right', ie the higher values of losses.

The other choices are incorrect and mostly nonsensical.

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 exposure at default is the greatest for the certificate of deposit as the entire notional amount is exposed to the risk of default. The other choices represent derivatives for which the current replacement value, which would be far less than notional, would be the credit exposure.

Said another way - if the counterparty were to default, the entire money in the CD would be at risk, whereas for the derivative contracts it would only be the replacement value that would be at risk.

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.

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

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

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

Statement I is true. If a Monte Carlo simulation is based upon the same parameters as used for analytical VaR, and enough number of simulations are carried out, we would get the same results as with analytical VaR.

Statement II is false. We cannot use Monte Carlo simulations using parameters based upon a normal assumption when the underlying distribution is not normal. For example, if a return stream is based upon say a uniform distribution, we cannot use a simulation based upon drawings from a normal distribution even though we use the same mean and standard deviation.

Statement III is true. This is the advantage of historical simulations - no assumptions are necessary. (Historical simulations however often suffer from the great disadvantage of the paucity of data that would cover all possibilities.)

Statement IV is true. The results of historical simulations are limited to the data they are based upon.

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.

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.

The bank will not be able to recover the principal advanced on this loan if both the home buyer defaults, and the house value falls to less than $1m, ie the price moves adversely by more than $500k, which is $-500k/$150k = -3.33σ. (Note that 150k is the 1 year volatility in dollars, ie $1.5m * 10%).

The probability of both these things happening together is just the product of the two probabilities, one of which we know to be 5%. The other is also certainly a small number, and intuitively it is clear that the probability of both the things happening together will be less than 1%.

For a more precise answer, we can calculate the probability of the house price falling by 3.33 standard deviations by calculating the area under the standard normal curve to the left of -3.33σ. This indeed is a very small number (actually equal to NORMSINV(-3.33)=0.00043), which when multiplied by the probability of default of the home buyer at 5% is certainly going to be less than 1%. Therefore Choice 'b' is the correct answer.

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.

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.)

Top down approaches rely upon available data such as total capital, income volatility, peer group information etc and attempt to imply the capital attributable to operational risk. They do not consider firm specific scenarios or causal factors. Bottom up approaches on the other hand attempt to determine operational risk capital based upon an identification and quantification of firm specific risks. Bottom up approaches help determine a traditional loss distribution from which capital requirements can be determined at a given level of confidence.

Therefore Choice 'd' is the correct answer.

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 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.

If VaR is calculated based upon historical simulations, and these simulations are designed as to include all stress scenarios of interest, then VaR and stress tests can be a part of an integrated risk measurement system. Therefore it is not correct to say that stress tests are always separately modeled from VaR and II is false. I and III are true, and therefore Choice 'd' is the correct answer.

The default correlation between two obligors goes up if the joint probability of default between them increases. This is intuitive. Also consider the formula for the default correlation between two obligors

Default correlation = [P(1,2) - P1 * P2] / √P1*(1-P1)*P2*(1-P2); where P(1,2) is the joint probability of default between the two and P1 and P2 are their individual probabilities of default. Obviously, an increase in P(1,2) will cause the default correlation to increase.

Statement I is correct. Economic capital is the capital available to absorb unexpected losses, and credit ratings are also based upon a certain probability of default. Economic capital is often calculated at a level equal to the confidence required for the desired credit rating. For example, if the probability of default for a AA rating is 0.02%, then economic capital maintained at a 99.98% would allow for such a rating. Economic capital set at a 99.8% level can be thought of as the level of losses that would not be exceeded with a 99.8% probability.

Loss distributions are the product of the severity and frequency distributions, each of which are estimated separately. The total loss distribution is affected far more by the severity distribution than by the frequency distribution, therefore statement II is correct.

The Loss Distribution Approach (LDA) is one of the ways in which the requirements of the AMA can be satisfied, and not the other way round. Therefore statement III is incorrect.

Statement IV is correct as the total loss distribution is estimated using separate estimates of loss frequency and distributions.

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.)

When a derivative transaction is entered into, its value generally is close to zero. Over time, as the value of the underlying changes, the transaction acquires a positive or negative value. It is not possible to predict the future value of the transaction in advance, however distributional assumptions can be made and potential exposure can be measured in multiple ways. Of all the possible future exposures, it is generally positive exposures that are relevant to credit risk because that is the only situation where the bank may lose money from a default of the counterparty.

The maximum (generally a quantile eg, the 97.5th quantile) exposure possible over the time of the transaction is the 'Potential Future Exposure', or PFE.

The average of the distribution of positive exposures at a specified date before the longest trade in the portfolio is called 'Expected Exposure', or EE.

The expected positive exposure calculated as the weighted average of the future positive Expected Exposure across a time horize is called the EPE, or the 'Expected Positive Exposure'.

The price that would be received to sell an asset or paid to transfer a liability in an orderly transaction between market participants at the measurement date - is the 'fair value', as defined under FAS 157.

Therefore the corect answer is that EPE is the weighted average of the future positive expected exposure across a time horizon.

For the PRM exam, it is important to remember the z-multiples for both 99% and 95% confidence levels (these are 2.33 and 1.64 respectively).

The value at risk for an equity portfolio is its standard deviation multiplied by the appropriate z factor for the given confidence level. If we knew the standard deviation, VaR would be easy to calculate. The standard deviation can be derived using a correlation matrix for all the stocks in the portfolio, which is not a trivial task. So we simplify the calculation using the CAPM and essentially say that the standard deviation of the portfolio is equal to the beta of the portfolio multiplied by the standard deviation of the market.

Therefore VaR in this case is equal to Beta x Mkt Std Dev x Value x z-factor, and therefore Choice 'a' is the correct answer.

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.

Let the probability of default over a month be p. Therefore the probability of survival at the end of 12 months would be (1 - p)^12. Since the one year probability of default is 12%, we know that the probability of survival is 88%. Putting (1 - p)^12 = 88% and solving for p, we get p = 1.06%. Therefore Choice 'd' is the correct answer.

The actuarial or CreditRisk+ model considers default as an 'end of game' event modeled by a Poisson distribution. The annual number of defaults is a stochastic variable with a mean of μ and standard deviation equal to √μ.

The probability of n defaults is given by (μ^n e^-μ) /n!, and therefore in this case is equal to (=2^4 * exp(-2))/FACT(4)) = 0.0902.

Note that CreditRisk+ is the same methodology as the actuarial approach, and requires using the Poisson distribution.

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

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

Choice 'a' is the correct answer. Refer to the detailed loss event type classification under Basel II (see Annex 9 of the accord). You should know the exact names of all loss event types, and examples of each.

Marginal liquidity gap measures the expected net change in liquidity over, say, a day. It is just equal to the liquidity inflow minus liquidity outflow. The cumulative liquidity gap measures the aggregate change in liquidity from a point in time, in other words it is just the summation of the marginal liquidity gap for each of the days included in the period under consideration. The residual liquidity gap goes one step further and adds available 'opening balance' of liquidity to the cumulative liquidity gap to reveal the days or times when the net liquidity is most at risk.

Liquidity at Risk measures the expected time to survival at a certain confidence level applied to the firm's cash flows - and is not a measure of the liquidity gap.

Therefore Choice 'a' is the correct answer.

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

It does not consider Net Income to total assets, therefore Choice 'c' is the correct answer. This makes sense as net income is after interest and taxes, both of which are not relevant for considering the cash flows for debt servicing.

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.

The correct answer is Choice 'd'. 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).

Expected value = $90 ($100 - 10%)

Value at 99% confidence level = $65

Therefore economic capital required at this level of confidence = $90 - $65 = $25.

Choice 'a' is the correct answer, the other choices are not.

(We can also look at it this way as explained in section III.B.6.2.2 of the handbook: Economic capital is designed to absorb unexpected losses, which are equal to total losses at a given confidence level minus expected losses. (Expected losses are to be covered by credit reserves). Total losses are $100-$65=$35, and expected losses are 10%*$100=$10, therefore economic capital should be $35-$10=$25.)

The 10-day VaR is = $25m x SQRT(10) = $79.06m. Choice 'b' is the correct answer.

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

Choice 'd' is the correct answer.

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.

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.

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.

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.

The probability that the security would not default in the next 4 years is equal to the probability of survival at the end of the four years. In other words, =(1 - 3%)*(1 - 4%)*(1 - 4%)*(1 - 5%) = 84.93%. Choice 'd' is the correct answer.

This question requires the calculation of the credit VaR of the bonds - note that in the real exam the question may not refer to 'credit' VaR, but that can be inferred from the context, ie because the probability of default is provided, it can only be asking for the credit VaR. (Note the difference from the market risk VaR which is driven by interest rate changes affecting the value of the bonds - there are other questions addressing that calculation).

Credit VaR = Expected Value - Worst case portfolio value at the selected percentile (ie the confidence level)

Thus if we know the distribution of the portfolio value in the future, we can find out the value at the required percentile (in this case 99%), and the VaR will be the difference between this value and the expected value of the portfolio.

An important piece of information provided is that the defaults are independent, ie they are not correlated. This means joint probabilities of default or survival can be easily found by multiplying the relevant probabilities. The following outcomes are possible:

1. Both bonds default: Probability = 1% * 1% = 0.01%. Portfolio value = $0 (because both bonds have defaulted & there is zero recovery)

2. One bond defaults and the other survives: Probability = 2 * 1% * 99% = 1.98%. Portfolio value = $1m (because one bond survives with a value of $1m and the defaulted bond has a value of $0). (Note that because there are two ways in which this can happen, ie bond 1 defaults, bond 2 survives; and bond 1 survives, bond 2 defaults, we need to multiply the probability by 2).

3. Both bonds survive: Probability = 99% * 99% = 98.01%. Portfolio value = $2m.

Expected value is therefore $1.98m (which is equal to 2 * $1m * (1 - 1%), or alternatively can also be obtained by multiplying the probabilities in the above three outcomes with the value associated with each).

The future distribution of the value of the portfolio can be constructed from the three outcomes outlined above:

a. Upto the 98.01th percentile the value of the portfolio is $2m, and the VaR is zero (being greater than the expected value, so there is nothing to lose)

b. From the 98.01th percentile to the 99.99th percentile (98.01+ the next 1.98%), the value of the portfolio is $1m. VaR in this range is $0.98m (=$1.98m - $1m)

c. From the 99.99th to the 100th percentile the value of the portfolio is $0, and the VaR is $1.98m.

Since the question is asking for VaR at the 99% confidence level, it lies in the range in 'b' above, and therefore the VaR is $0.98m.

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

It is the cross-default clauses in debt agreements that generally provide that a default on one obligation is considered a credit event applying to all debts of the obligor, and therefore we are able to deal with credit risk at the borrower level, and not at the level of the individual security. It also helps avoid situations where borrowers can selectively default on some obligations while continuing to service others. Therefore Choice 'a' is the correct answer. The other choices are incorrect.

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.

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

Statutory financial reporting is the responsibility of the Chief Financial Officer, not the Chief Risk Officer. The head of internal audit reports to the audit committee of the board, not the CRO. Therefore statements I and II are incorect.

The CRO is generally expected to drive risk and compliance with related regulatory standards. Market risk, credit risk and operational risk groups report into the CRO, so statements III and IV are correct.

According to ISDA, a credit event is an event linked to the deteriorating credit worthiness of an underlying reference entity in a credit derivative. The occurrence of a credit event usually triggers full or partial termination of the transaction and a payment from protection seller to protection buyer. Credit events include

- bankruptcy,

- failure to pay,

- restructuring,

- obligation acceleration,

- obligation default and

- repudiation/moratorium.

A rating downgrade is not a credit event.

The credit spread is equal to the default rate times the loss given default, or stated another way, default rate times (1 - recovery rate). It is not equal to the default rate times the recovery rate. Therefore statement I is not correct.

When ratings are upgraded by rating agencies, the spread contracts and not widen. Therefore statement II is not correct.

Both recovery rates and probabilities of default are related to the business cycle, and they move in opposite directions. Economic recessions witness an increase in the default rate and a decrease in the recovery rate, and economic expansions result in a decrease in the default rate and an increase in the recovery rates when default does happen. Therefore statement III is correct.

Bond spreads incorporate both the risk of default, but also considerations of liquidity in the case of corporate bonds. Hence statement IV is correct.

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.

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

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.

Pre-settlement risk is the risk that one of the counterparties defaults prior to the date for the maturity of the transaction in question. This may be an unrelated default, in fact there may have been no default on that particular contract, but the party may have defaulted on its other obligations, or filed for bankruptcy. To deal with such cases and to protect the interests of both the parties, it is common to provide for immediate termination of positions and settlement based on the current replacement value of the contracts. Therefore statements I and II are correct.

Statement III is correct as well - the exposure from an OTC derivative contract derives from its current replacement value, and not the notional. If the current replacement value is negative, then the credit exposure is considered equal to zero.

Statement IV is correct as it is quite common to restate all exposures - those from credit lines, OTC derivatives etc - in loan equivalent terms prior to estimating credit risk.

Economic capital is a measure of the level of capital needed to maintain a desired credit rating. Regulatory capital is the amount of capital required to be held by regulation, and this may be quite different from economic capital. Book value is an accounting measure reflecting the assets minus liabilities as measured per accounting rules, this is often expressed per share. Shareholders' equity is a narrow term which is the amount of capital attributable to the shareholders and includes paid up capital and reserves but not long term debt or other non-equity funding.

Therefore Choice 'b' is the correct answer.