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

Each of these represent valid techniques for performing stress testing and building stress scenarios. Therefore d is the correct answer. In practice, elements of each of these techniques is used depending upon the portfolio and the exact situation.

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.

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.

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.

Probability of the joint default of both A and B =

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

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

Solving, we get default correlation = 25%

The probability of default would make the expected value of the future cash flows from both the corporate bond and the risk free bond 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))

=> 5%*0 + (1 - 5%)*(1 + 12%) = (1 + Rf).

therefore Rf = 6.4%

(In reality investors would demand a 'credit risk premium' 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.)

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 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.

Some parts of this question draw upon contingent claims framework to the value of a firm. According to this framework, the relationship between the debt and equity holders of a firm can be viewed as follows: The equity holders have a call option on the assets of the firm with a strike price equal to the value of the debt, and the debt holders have sold them this call. This is so because should the value of the assets of the firm fall below the value of the debt, the equity holders can walk away by handing over the assets to the debt holders in full extinguishment of their claims. If the value of the firm's assets is greater than the value of debt, the equity holders will exercise their call option. At the same time, it is also possible to view the debtholders as holding an asset and having sold a put on the assets of the firm with a strike price equal to the value of the debt. If the value of the assets of the firm were to fall below the value of the debt, they will end up buying the assets at a price equal to the value of the debt.

An increase in the volatility of returns on the assets of a firm increases the volatility of the asset value. This means the likelihood that the asset value will go below the value of the debt of the firm will increase. Callable debt can be considered to be a summation of two separate securities: a regular debt, for which the firm pays interest and receives a principal loan; and a call option that the debt holders have sold to the firm allowing the firm to buy back the debt. In return, the firm pays an implied 'premium' to the debt holders who have agreed to buy the callable debt. Therefore the total payments by the company to callable debt holders is equal to the interest payments plus the premium payment for the option. An increase in asset volatility will increase the value of this option as it is likely that the assets will increase in value, and strengthen the company's credit, and lower its spread at which time it would like to repay the debt and refinance/roll over at the new lower rate. Therefore an increase in volatility will increase the 'premium' demanded by the callable debt holders, thereby increasing the total yield and lowering the value of the callable debt. Therefore Choice 'b' (An increase in the value of the callable debt of the firm) is incorrect.

An increase in asset volatility will decrease the value of the firm as it is now riskier than before (higher standard deviation, same expected returns). Therefore Choice 'a' (An increase in the value of the equity of the firm) is false too.

The value of the implicit put in the debt of the firm will increase and not decrease as the volatility of the underlying assets increases. Therefore Choice 'c' (A decrease in the value of the implicit put in in the debt of the firm) is incorrect too.

Choice 'd' (A decrease in the value of the non-callable debt issued by the firm) is correct because higher asset volatility will increase the riskiness of the company's debt, making the required yield higher and decreasing its value.

Under the contingent claims approach, a firm will default on its debt when the value of its assets fall to less than the face value of the debt. Debt holders can protect themselves against such an event by buying a put on the assets of the firm, where the strike price is equal to the value of the debt. In other words, Risky Debt + Put on the firm's assets = Risk free debt. This is because if the value of the assets is greater than the value of the debt, they will be paid in full. If the value of the assets is lower than the value of the debt, they will exercise the put and be paid in full.

Therefore the value of the put on the firm's assets with a strike equal to the value of the debt represents the cost of eliminating credit risk. Choice 'b' is the correct answer.

Note that it is improbable that a put on the firm's assets is available in real life to debt holders. However, the same effect can be synthetically achieved by using the shares of the firm as a proxy for its assets, and shorting an appropriate number of shares. Such a synthetic put will require frequent readjustments.

Generally, stress tests consider a shock or a severe scenario in order to determine the 'what-if' that circumstance were to materialize. They focus on the outcome based upon a set of shocks. In a reverse stress test, the outcome is assumed to be known (generally something as severe as bankruptcy, non-compliance with capital requirements etc), and the test is intended to work out what shocks or events would lead to such an outcome.

Reverse stress tests therefore start from a known stress test outcome (such as breaching regulatory captial ratios, illiquidity or insolvency) and then asking what events could lead to such an outcome for the bank. This can be quite a challenging task. Principle 9 laid out in the BCBS document on stress testing (May 2009) (which is part of the PRM syllabus effective March 1, 2010) lays down the expectations relating to reverse stress tests.

Therefore Choice 'a' is the correct answer. All the other choices are nonsensical.

All the listed variables are relevant to management monitoring the credit risk profile of an institution, therefore Choice 'd' is the correct answer.

The correct answer is choice 'a'

The correct order of steps to addressing data quality problems in an organization would include:

1. Assesing the current state

2. Designing the future state, and

3. Planning and implementation which would include identifying the gaps between the current and the desired future state, and implementation to address the gaps.

Therefore Choice 'a' is the correct answer.

Choice 'c' is incorrect because a gap analysis cannot be performed without understanding the 'as-is' (which results from understanding the current state).

Choice 'b' is non-sensical, and Choice 'd' is a flippant option (though often used in real life situations by management as an easy (and ineffective) way to escape accountability for difficult problems)

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

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

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

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

Choice 'd' represents a risk that does not arise from its holdings of mortgages. Therefore Choice 'd' is the correct answer.

All the other risks identified are correct - the bank faces interest rate, default and prepayment risks on its mortgages.

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.

An n x n positive definite square matrix will have n eigenvectors, and not n - 1. Therefore statement I is incorrect.

A correlation and covariance matrix are related to each other through the matrix of standard deviations. If the covariance matrix is represented by V, the correlation matrix by C and D is the diagonal matrix of standard deviations, then V = DCD. However, there is no simple relationship between the eigenvalues of the two matrices, and it is not possible to derive the eigenvalues for one given the eigenvalues for the other. Therefore statement II is false.

Principal components are uncorrelated to each other. That is correct, and in fact PCA is useful because of this being so. Statement III is therefore true.

PCA does not explain 100% of the variation in a system with just three components - statement IV is false. (Remember though that most (though not 100%) of the variation in a system of term structures is explained by the first three components - trend, tilt and curvature).

Thus Choice 'd' is the correct answer.

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

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

The initial issue price and issue size are irrelevant.

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.

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

A forward rate agreement allows one of the parties to borrow an amount at a rate for a length of time, all of which are agreed in advance. Consider a "3 x 6" FRA. This allows a fixed rate borrowing starting at 3 months till the end of 6 months. This is economically equivalent to holding a zero coupon bond till the end of 6 months, and being short another zero coupon bond till the end of 3 months (or the other way round, depending upon which end of the FRA you are on). Therefore Choice 'c' is the correct answer.

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.

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.

The correct answer is choice 'd'

For settlement of interbank payments, there are broadly two kinds of systems: RTGS (Real Time Gross Systems) and Deferred Net Systems (DNS). RTGS process payments in real time, settlement by settlement, and each transaction is settled by the a clearing institution (mostly the central bank) on a gross basis without regard for other settlements affecting the counterparty. DNS systems, on the other hand, allow for debiting or crediting the accounts of counterparties at periodic intervals after netting all payments paid or received since the last settlement. The exact timing of the payments does not matter so long as a bank has sufficient funding on a net basis at settlement time. Implicit in the DNS system is the extension of credit and liquidity by the central bank to the participating banks as it is possible for a bank to issue payment instructions even without having funds so long as they can arrange for such funds prior to settlement at the end of the day. In RTGS, a bank needs to have funds to make a payment at any point, and cannot make a payment against moneys expected to be received later intra-day. RTGS systems therefore need more liquidity on the part of the participants, and consume far more liquidity than DNS arrangements. Of course, the 'liquidity' of the DNS arrangement has a cost - which is that someone is taking up settlement risk, and invariably it is the central bank. If a bank under DNS fails to settle, its transactions have to be 'unwound', ie all payments made by it have to be rolled back. This can cause other banks to trip, causing further unwinding transactions. RTGS systems do not carry this risk. Therefore statement I is not correct as RTGS consume more liquidity than DNS arrangements.

Statement II is correct. US Fedwire or European TARGET are RTGS while CHIPS is a DNS based payment system.

Statement III is not correct. Current Basel requirements do not require any disclosure in respect of liquidity risk management. A consultative paper was issued by BIS in Dec 2009 for comments from members, but it is far from final. The BIS is still reacting to the liquidity issues that arose during the 2007-09 credit crisis.

Statement IV is not correct as a CFP is like a disaster recovery plan for liquidity, ie it helps a bank plan for and think about what steps would be taken to deal with a liquidity disaster situation. It does not provide any access to central bank financing.

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).

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

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

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.

CreditRisk+ treats default as a binary event, ignoring downgrade risk, capital structures of individual firms in the portfolio or the causes of default. It uses a single parameter, λ or the mean default rate, and derives credit risk based upon the Poisson distribution. 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.

A CFP is indeed a disaster recovery plan to deal with a liquidity crisis. Therefore statement I is correct.

A CFP should consider market stress conditions, including wide scale failures of payment and settlement systems. Statement II is not correct.

It is true that reputational damage may result if a firm has to activate its CFP - therefore the plan should consider internal and external communications, the timing of information release and the groups within the firm who need to know about the implementation of the plan. Reputational damage can only make any existing liquidity problems worse. Statement III is correct.

Sources of emergency funding should not include funding from the central bank - unless as part of a regular lending facility. Its role as a lender of last resort can not be considered in a CFP. Statement IV is incorrect.

Therefore only statements I and III are correct.

Right after inception' is incorrect as the interest rate swap (IRS) would be valued at close to zero right after inception and the credit risk would be minimum. Choice 'a' (ie 10 years, at maturity) is incorrect as at maturity there would be no more cash flows to exchange, and the replacement value of the contract would again be close to zero.

Therefore the worst time for the counterparty to default is somewhere between inception and maturity - in fact the range of possible outcomes for the contract increases with the passage of time, and we should find the worst time to default to be a later date. However, towards maturity, the value of the contract starts to go towards zero again, and the maximum value is reached around 7 years. 2 years is too early for the maximum to be reached for the 10 year IRS, and therefore choice a is the correct answer.

Credit VaR is the difference between the expected value of the portfolio and the value of the portfolio at the given confidence level. Therefore the credit VaR is $85m - $ 60m = $25m. Choice 'b' is the correct answer.

Note that economic capital and credit VaR are identical at a risk horizon of one year. Therefore if the question asks for economic capital, the answer would be the same.

[Again, an alternative way to look at this is to consider the explanation given in III.B.6.2.2: Credit Var = Q(L) - EL where Q(L) is the total loss at a given confidence interval, and EL is the expected loss. In this case Q(L) - $100-$60 = $40, and EL = $100-$85=$15. Therefore Credit VaR = $40-$15=$25.]

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.

In the univariate Gaussian model, each risk factor is modeled separately independent of the others, and the dependence between the risk factors is captured by the covariance matrix (or its equivalent combination of the correlation matrix and the variance matrix). Risk factors could include interest rates of different tenors, different equity market levels etc.

While this is a simple enough model, it has a number of limitations.

First, it fails to fit to the empirical distributions of risk factors, notably their fat tails and skewness. Second, a single covariance matrix is insufficient to describe the fine codependence structure among risk factors as non-linear dependencies or tail correlations are not captured. Third, determining the covariance matrix becomes an extremely difficult task as the number of risk factors increases. The number of covariances increases by the square of the number of variables.

But an inability to capture linear relationships between the factors is not one of the limitations of the univariate Gaussian approach - in fact it is able to do that quite nicely with covariances.

A way to address these limitations is to consider joint distributions of the risk factors that capture the dynamic relationships between the risk factors, and that correlation is not a static number across an entire range of outcomes, but the risk factors can behave differently with each other at different intersection points.

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

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

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.

According to the option pricing approach developed by Merton, the shareholders of a firm have a put on the assets of the firm where the strike price is equal to the face value of the firm's debt. This is just a more complicated way of saying that the debt holders are entitled to all the assets of the firm if these assets are insufficient to pay off the debts, and because of limited liability of the shareholders of a corporation this part payment will fully extinguish the debt.

A firm will default on its debt if the value of the assets falls below the face value of the debt. Therefore Choice 'a' is the correct answer. All other choices are incorrect.

(There are two ways to consider this sort of optionality, and I have mentioned only one for this question:

1. The equity holders can sell the assets of the firm to the debt holders at a price equal to the face value of the debt, ie a put. (ie they can extinguish their liability to the debt holders in full by handing them the assets of the firm, effectively selling them the assets at the value of the debt)

2. The equity holders have a long position in a call option where they can keep the assets of the firm by paying a price equal to the face value of the debt (ie, they can pay off the debt holders and keep the assets)

For this question, perspective 1 applies but you should be aware of the second one too as a question may reference that view point.)

With the passage of time, the range of possible values the FX contract can take increases. Therefore the maximum value of the contract, which is when the credit risk would be maximum, would be at maturity. (Note that this is different than an interest rate swap whose value at maturity approaches zero.) Therefore Choice 'a' is the correct answer and the others are incorrect.

As part of a reverse stress test, a firm has to identify and assess the scenarios most likely to cause it to fail, or in other words using the language used by the FSA in the UK, for its current business plan to become unviable. A firm's business plan should be considered to become unviable at the point that crystallizing risks cause the market to lose confidence it it, with the consequence that counterparties and other stakeholders are unwilling to transact with it or provide capital to the firm and, where releant, that existing counterparties may seek to terminate their contracts. Recent experience suggests that this point is reached well before a firm's regulatory capital is exhausted.

Large known losses, or negative EBITDA (earnings before interest , tax, depreciation and amortization) may be indicators or contribute to the loss of confidence, but do not of themselves make the current business plan unviable. Therefore Choice 'd' is the correct answer.

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.

Asset returns are relevant for credit risk models where a default is related to the value of the assets of the firm falling below the default threshold. When assessing credit risk for portfolios with multiple credit assets, it becomes necessary to know the asset correlations of the different firms. Since this data is rarely available, it is very common to approximate asset correlations using equity prices. Equity correlations are used as proxies for asset correlation, therefore Choice 'c' is the correct answer.

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.

According to a paper by the BCBS, here is an excellent summary of what happened. Based on this, Choice 'c' is the correct answer.

"At the outset of the crisis, mortgage default shocks played a part in the deterioration of market prices of collateralised debt obligations (CDOs). Simultaneously, these shocks revealed deficiencies in the models used to manage and price these products. The complexity and resulting lack of transparency led to uncertainty about the value of the underlying investment. Market participants then drastically scaled down their activity in the origination and distribution markets and liquidity disappeared. The standstill in the securitisation markets forced banks to warehouse loans that were intended to be sold in the secondary markets. Given a lack of transparency of the ultimate ownership of troubled investments, funding liquidity concerns were triggered within the banking sector as banks refused to provide sufficient funds to each other. This in turn led to the hoarding of liquidity, exacerbating further the funding pressures within the banking sector. The initial difficulties in subprime mortgages also fed through to a broader range of market instruments since the drying up of market and funding liquidity forced market participants to liquidate those positions which they could trade in order to scale back risk. An increase in risk aversion also led to a general flight to quality, an example of which was the high withdrawals by households from money market funds."

A fat tailed distribution has more weight in the tails, and therefore at a high level of confidence the VaR estimate will be higher for a distribution with heavier tails. At relatively lower levels of confidence however, the situation is reversed as the heavier tailed distribution will have a VaR estimate lower than a thinner tailed distribution.

A higher level of kurtosis implies a 'peaked' distribution with fatter tails. Among the given choices, a distribution with kurtosis equal to 8 will have the heaviest tails, and therefore a higher VaR estimate. Choice 'a' is therefore the correct answer. Also refer to the tutorial about VaR and fat tails.

When the economy is expanding, firms are less likely to default. Therefore the conditional probability of default, given an economic expansion, is likely to be lower than the unconditional probability of default. Therefore Choice 'a' is the correct answer and the other statements are incorrect.

I, III and IV represent situations where Monte Carlo simulations can be employed. I is not a situation where Monte Carlo can be used, as there is no basis available to simulate the returns. When no distribution assumption is possible, it may be advisable to use historical simulations. Therefore Choice 'd' is the correct answer, and the others are incorrect.

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.

An observed fact that the KMV approach relies upon is that firms do not default when their liabilities exceed assets, but when asset values are somewhere between short term liabilities and the total liabilities. In fact, the 'default point' in the KMV methodology is defined as the short term debt plus half of the long term debt. The difference between expected value of the assets in one year and this 'default point', when expressed in terms of standard deviation of the asset values, is called the 'distance-to-default'.

Therefore Choice 'd' is the correct answer. The other choices are incorrect.

According to Basel II, in any given year, negative capital charges (resulting from negative gross income) in any business line may offset positive capital charges in other business lines without limit. Therefore Choice 'b' is the correct answer.

For a number of processes, including many in finance, while a distribution such as the normal distribution is a good approximation of the distribution near the modal value of the variable, the same normal distribution may not be a good estimate of the tails. For this reason, the Pareto distribution is one of the distributions that is often used to model the tails of another distribution. Generally, if you have a set of observations, and you discard all observations below a threshold, you are left with what are called 'exceedances'. The threshold needs to be reasonably far out in the tail. If from each value of the exceedances you subtract the threshold value, the resulting dataset is estimated by the generalized Pareto distribution.

The Pareto distribution has a 'shape parameter'. The average of two Pareto distributions with tail parameters ξ1 and ξ2 (ξ is a Greek character, pronounced as 'sai' (saa-eee)), is the weighted average of ξ1 and ξ2 with weights proportional to the number of observations in the datasets underlying the distributions.

Credit enhancements come in two varieties: counterparty based, where the exercise of the credit enhancement requires a third party to pay, and this includes guarantees and CDS contracts. Asset based credit enhancements are based upon a physical asset in possession, and these include collateral and balances owed on other trades or transactions, and availed through close out netting arrangements.

Of the listed choices, I and III are asset based credit enhancements, and II and IV are third party based.