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

The commercial paper has greater credit risk as the entire notional is outstanding. On the forward contract, only the replacement value of the contract, which normally would be a mere fraction of the notional, would be at risk.

Therefore 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.

Top down approaches do not consider event frequency and severity, on the other hand they focus on high level available data such as total capital, income volatility, peer group information on risk capital etc. Bottom up approaches focus on severity and frequency distributions for events. Statement I is therefore not correct.

Top down approaches do indeed rely upon high level aggregate data and tend to infer operational risk capital requirements from these. Bottom up approaches look at more detailed firm specific information. Statement II is correct.

Scenario analysis requires estimating losses from risk scenarios, and allows incorporating the judgment and views of managers in addition to any data that might be available from internal or external loss databases. Statement III is correct. Therefore Choice ' b ' is the correct answer.

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 break close, also called a ' mutual put ' , gives either party the right to terminate a transaction at market price at a given date, or dates in the future. These are usually availed of in longer dated transactions, eg 10 years and over. For example, a 15-year swap might have a mutual put in year 5, and every 2 years thereafter.

All other choices are incorrect.

In statistics, which is relevant to risk management, a distinction is often drawn between ' frequentists ' and ' Bayesians ' . Frequentists rely upon data to draw conclusions as to probabilities. Bayesians consider conditional probabilities, ie, take into account what things are already known, and inject sometimes subjective a-priori probabilities into the calculations. Statement I describes Bayesians, and not frequentists. In reality however, the difference is merely academic. Risk managers use whichever technique best applies to the given situation without making it about ideology.

The difference between ' Knightian uncertainty ' and ' Risk ' is similarly academic. Knightian uncertainty refers to risk that cannot be measured or calculated. ' Risk ' on the other hand refers to things for which past data exists and calculations of exposure can be made. To give an example in the context of the financial world, the risk from a pandemic creating systemic failures from a failure of payment and settlement systems and the like is ' Knightian uncertainty ' , but the market risk from equity price movements can be modeled (albeit with limitations) and is calculable. Statement II is therefore correct.

Once a risk is identified, it can be mitigated, accepted, avoided or eliminated, or transferred by way of insurance. Therefore statement III is correct.

Confidence accounting is a conceptual idea that suggests that accounting statements make reference to ranges as opposed to point estimates in financial statements. For example, instead of saying that the pension obligation is $xx million, the company should say the pension obligation is in a range of $xx m - $yy m with a certain confidence level. Statement IV is therefore inaccurate.

Time invariance refers to all time intervals being similar and identical, regardless of the effects of business cycles or other external events. The Markov property is the assumption that there is no ratings momentum, and that transition probabilities are dependent only upon where the rating currently is and where it is going to. Where it has come from, or what the past changes in ratings have been, have no effect on the transition probabilities.

Rating agencies generally provide transition probability matrices for a given period of time, say a year. The risk analyst may need to convert these into matrices for say 6 months, 2 years or whatever time horizon he or she is interested in. Simplifying assumptions that allow him to do so using simple matrix multiplication include these two assumptions - time invariance and the Markov property. Thus Choice ' c ' is the correct answer. The other choices (normal distribution and zero skewness) are non-sensical in this context.

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

The current Basel rules for the basic VaR based charge for market risk capital set market risk capital requirements as the maximum of the following two amounts:

1. 99%/10-day VaR,

2. Regulatory Multiplier x Average 99%/10-day VaR of the past 60 days

The ' regulatory multiplier ' is a number between 3 and 4 (inclusive) calculated based on the number of 1% VaR exceedances in the previous 250 days, as determined by backtesting.

- If the number of exceedances is < = 4, then the regulatory multiplier is 3.

- If the number of exceedances is between 5 and 9, then the multiplier = 3 + 0.2*(N-4), where N is the number of exceedances.

- If the number of exceedances is > =10, then the multiplier is 4.

So you can see that in most normal situations the risk capital requirement will be dictated by the multiplier and the prior 60-day average VaR, because the product of these two will almost often be greater than the current 99% VaR.

The correct answer therefore is = max(200mm, 3*250mm) = $750mm.

Interestingly, also note that a 99% VaR should statistically be exceeded 1%*250 days = 2.5 times, which means if the bank ' s VaR model is performing as it should, it will still need to use a reg multiplier of 3.

If capital calculations are done in a standard way regardless of risk (as reflected by credit ratings), then it creates a perverse incentive for the lenders ' employees to lend to the riskiest borrowers that offer the highest expected returns as there is no incentive to ' save ' on economic capital requirements that are equal for both safe and unsafe borrowers. Therefore statement I is correct.

Given that the portfolio of such an institution is likely to then comprise poor quality borrowers, and economic capital would be based upon ' average ' expected ratings, it is likely to carry lower economic capital given its exposures. Therefore any such economic risk capital model is likely to understate economic capital requirements. Therefore statement IV is correct.

Statements II and III are incorrect and Choice ' b ' is the correct answer.

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.

The credit risk horizon for credit VaR is generally one year. Therefore Choice ' b ' is the correct answer.

The three pillars are minimum capital requirements, supervisory review and market discipline. National regulation is not a pillar described under the accord. Choice ' c ' is the correct answer.

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

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.

The correct answer is Choice ' c ' . The other choices do not refer to ' regulatory arbitrage ' .

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.

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.

Frequency modeling is performed using discrete distributions that have a positive integer as a resultant - this allows for the number of events per period of time to be modeled. Of the distributions listed above, Poisson, negative binomial and binomial can be used for modeling frequency distributions. The Poisson and negative binomial distributions are encountered the most in practice.

The gamma distribution is a continuous distribution and cannot be used for frequency modeling.

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.

If returns display mean reversion, then clearly daily volatilities will be greater than weekly volatility, both annualized using the square root of time rule. Mean reversion would imply that the deviation from the mean will be lower over a longer time period than a shorter time period, and therefore annualized volatility based on daily volatility will be greater.

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

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

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.

Model risk is the risk that a model built for estimating a variable will produce erroneous estimates. Model risk is caused by a number of factors, including:

a) Misspecifying the model: For example, using a normal distribution when it is not justified.

b) Model misuse: For example, using a model built to estimate bond prices to estimate equity prices

c) Parameter estimation errors: In particular, parameters that are subjectively determined can be subject to significant parameter estimation errors

d) Programming errors: Errors in coding the model as part of computer implementation may not be detected by end users

e) Data errors: Errors in data used for building the model may also introduce model risk

Therefore the correct answer is d, as all the choices are a source of model risk.

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.

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.

Statement I is incorrect. A transition matrix expresses the probabilities of moving to a given set of ratings at the end of a period (usually one year) conditional upon a given rating at the beginning of the period. It does not make a reference to an individual security and certainly not to the probability of migrating to other ratings during its entire lifetime.

Statement II is correct. Marginal default probabilities are the probability of default in a given year, conditional upon survival at the beginning of that year.

Statement III is incorrect. Cumulative probabilities of default will always be greater than the marginal probabilities of default - except in year 1 when they will be equal.

Statement IV is correct. LGD = 1 - Recovery Rate, therefore a low recovery rate implies higher LGD.

Statement I is not correct as VaR does not set an upper limit on losses. In this case, the bank expects the losses to exceed $253m 5% of the times, and the VaR number does not indicate any theoretical maximum amount of losses. Statement II is incorrect as there is a 95% (and not 5%) probability that the bank ' s losses will not exceed $253m Statement III is correct and describes VaR. Statement IV is incorrect, as regulatory capital is a more complex computation for which VaR is only one of the various input. Therefore Choice ' b ' is the correct answer.

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.

The z value at the 95% confidence level is 1.64. Since the variance is 0.16, the annual volatility is 40%. Therefore the daily volatility is 40% x √10/250 = 8%. The VaR therefore is 8% x 1.64 x $240m = $31,488,000

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

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.

Altman ' s Z-score, the Probit and the Logit models can all be used to assess the credit rating of an individual borrower. There is no such model as the ' distance to default model ' , and therefore Choice ' a ' is the correct answer.

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.

Operational risk as defined in Basel II specifically excludes strategic and reputational risk. Therefore Choice ' d ' is the correct answer.

Note that Basel II defines operational risk as follows:

Operational risk is defined as the risk of loss resulting from inadequate or failed internal processes, people and systems or from external events. This definition includes legal risk, but excludes strategic and reputational risk.

Marginal VaR of a component of a portfolio is the change in the portfolio VaR from a $1 change in the value of the component. It helps a risk analyst who may be trying to identify the best way to influence VaR by changing the components of the portfolio. Marginal VaR is also important for calculating component VaR (for VaR disaggregation), as component VaR is equal to the marginal VaR multiplied by the value of the component in the portfolio.

Marginal VaR is by definition the derivative of the portfolio value with respect to the component i. This is reflected in Choice ' a ' above. Using the definitions and relationships between correlation, covariance, beta and volatility of the portfolio and/or the component, we can show that the other two choices are also equivalent to Choice ' a ' .

Therefore all the choices present are correct.

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.

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.

Choice ' d ' is the correct answer. Settlement risk, as the name suggests, arises upon settlement when one of the parties delivers its obligation under the transaction and the other does not. Consider a EUR/USD FX forward contract maturing in a month. At maturity, one of the parties will deliver EURs and the other USDs. If one party fails to deliver, then it constitutes a very large risk to the other party. This risk is much larger than pre-settlement risk, because the amount at risk is the entire notional and not just the replacement value. Of course, settlement risk exists for a very short period of time, no more than a number or hours or a day.

There is no such thing as ' replacement risk ' , and credit risk is a larger category of which settlement risks is one component. Settlement risk is the most appropriate answer.

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.

A bank ' s stress testing programme in relation to firm wide stress tests should document the type, frequency and the purpose of the programme, as well as methodologies for defining scenarios and the remedial actions envisaged. Choice ' b ' is therefore a necessary attribute of a robust stress testing programme.

The programme should be supported by a robust systems infrastructure that allows the execution of periodic as well as ad-hoc stress tests at the right level (business unit, as well as firm-wide) at the right level of detail or granularity. Choice ' c ' also therefore is a valid choice.

A related element is data quality - without which no stress tests can be be credible.

Therefore all the choices listed are correct and Choice ' d ' is the correct answer.

If the current level of the S & P 500 is 2000, and a single day volatility is 1%, and the delta (ie change in portfolio value from a one point change) is $100, then the 1 day volatility for the portfolio in dollars is 2000 * 1% * $100 = $2,000.

At the 99% confidence level, the value of the inverse cumulative density function for the normal distribution is 2.33 (=NORMSINV(99%), in Excel). Therefore the 1 day VaR will be 2.33 * $2000 = $4,660. Extending it to 10 days using the square root of time rule, we get the 10 day VaR as equal to SQRT(10)*4660 = $14,736.

Since this method of calculating VaR relies upon a delta approximation of a risk factor (in this case the S & P500), it is the parametric approach to calculating VaR (the other methods being historical simulation, and Monte Carlo simulation).

The 2015 Handbook provides an excellent example of parametric (and other) VaR calculations in Chapter 3 of Volume III of Book 3. The spreadsheet used for the illustration can be downloaded from http://www.prmia.org/prm-exam/handbook-resources.

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.

Choice ' b ' is the correct answer. When two securities have a correlation of +1, they are effectively the same security. In such cases, the standard deviations of the two securities are additive, which means the VaRs can simply be added together to get the combined VaR. All the other choices are incorrect.

Choice ' c ' in particular would have been correct if the securities were completely uncorrelated, ie if they had a correlation of zero.

Choice ' a ' would have been correct if their correlation were -1.

Recovery rates vary a great deal from year to year, and are difficult to predict. Therefore statement III is true. Similarly, any attempt to predict these is hamstrung by a high standard error, which can be as high as the historical mean itself. The error does not cancel itself out due to the effect of the business cycle making the error directionally biased. Thus statement IV is false.

Statement II is true as these are all factors that make forecasting recovery rates for any credit risk model rather difficult. Statement I is false because recovery rates are difficult to predict and assumptions are not easy to make.

For operational risk modeling, both frequency and severity distributions need to be modeled. Modeling severity involves finding an analytical distribution, such as log-normal or other that approximates the distribution best represented by known data - whether from the internal loss database, the external loss database or scenario data. A ' risk functional ' is a measure of the deviation of the model distribution from the risk ' s actual severity distribution. It assigns a penalty value for the deviation, using a statistical measure, such as the KS distance (Kolmogorov-Smirnov distance).

The problem of finding the right distribution then becomes the problem of optimizing the risk functional. For example, if F is the model distribution, and G is the actual, or empirical severity distribution, and we are using the KS test, then the Risk Functional R is defined as follows:

Note that supx stands for ' supremum ' , which is a more technical way of saying ' maximum ' . In other words, we are calculating the maximum absolute KS distance between the two distributions. (Note that the KS distance is the max of the distance between identical percentiles of the two distributions using the CDFs of the two.)

Once the risk functional is identified, we can minimize it to determine the best fitting distribution for severity.

According to ISDA standard definitions, the legal claim for OTC derivatives is the current replacement value of the contract. Therefore Choice ' c ' is the correct answer. None of the other choices are correct.

Since the BHC always fails when the investment bank fails, the joint probability of default of the two is merely the probability of the investment bank failing, ie 0.05.

The probability of just the BHC failing, given that both the investment bank and the retail bank have survived will be equal to 0.11 - (0.05+0.05-0.05*0.05) = 0.0125. (The easiest way to understand this would be to consider a venn diagram, where the area under the largest circle is 0.11, and there are two intersecting circles inside this larger circle, each with an area of 0.05 and their intersection accounting for 0.05*0.05. We need to calculate the area outside of the two smaller circles, but within the larger circle representing the BHC).

Refer diagram below, please excuse the awful colors.

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.

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.

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.

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.

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.

Volatility clustering leads to levels of current volatility that can be significantly different from long run averages. When volatility is running high, institutions need to shed risk, and when it is running low, they can afford to increase returns by taking on more risk for a given amount of capital. An institution ' s response to changes in volatility can be either to adjust risk, or capital, or both. Accounting for volatility clustering helps institutions manage their risk and capital and therefore statements I and II are correct.

Regulatory requirements do not require volatility clustering to be taken into account (at least not yet). Therefore statement III is not correct, and neither is IV which is completely unrelated to volatility clustering.

When returns are non-normal and have fat tails, an assumption of normality in returns leads to underestimation of VaR at high confidence levels. At the same time, at lower confidence levels the normal distribution may give higher VaR estimates. Therefore Choice ' a ' is correct. The other choices are incorrect.

Also refer to the tutorial about VaR and heavy tails.

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

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.

Using the beta for VaR calculations is a significant simplification based on the CAPM and the assumption that any specific risks are diversified away. The one thing a risk model based on the CAPM does not consider is the specific risk of individual stocks, because, as mentioned, these are considered to be offsetting each other so that the portfolio only carries market risk reflected in the beta.

Therefore Choice ' c ' is not true and therefore the correct answer.

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

- reputational contagion,

- financial contagion,

- leveraging,

- double or multiple gearing,

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

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

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

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

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

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

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

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

This is a trick question, no great science to it. Remember that the ' present value of a basis point ' refers to PV01, which is the same as BPV (basis point value) referred to in the PRMIA handbook. In other textbooks, the same term is also variously called ' DV01 ' (dollar value of a basis point). Remember these other terms too.

PV01, or the present value of a basis point, is the change in the value of a bond (or other fixed income security) from a 1 basis point change in the yield. PV01 is calculated as (Price * Modified Duration/10,000).

Therefore Choice ' a ' is the correct answer.

Under the contingent claims approach, credit risk is evaluated as the value of the put on the firm ' s assets with a strike price equal to the face value of the debt and maturity equal to the maturity of the obligation. The Black Scholes model can then be used to value the put, and therefore an increase in volatility and the time to expiry (ie maturity) will increase the value of the debt. An increase in the risk free rate will actually reduce the value of the put, therefore statements I and III are correct and Choice ' b ' is the correct answer.

The current exposure is negative, so there is no immediate credit exposure. However, since the price of the derivative is volatile, we can reasonably expect the value to be greater than zero sometime in the future. This is a stochastic variable which will have a distribution, and not just a unique value, in the future that will represent the credit exposure. Since there is no unique value, a conservative approach is to pick a quintile of the distribution, and use that as the future value of the derivative contract, with the assurance that the probability of the credit exposure exceeding that quintile is known and has been consciously selected. This number can then be converted to a loan equivalent amount for credit risk purposes. Therefore Choice ' b ' is the correct answer. Choice ' a ' , Choice ' d ' and Choice ' c ' are incorrect for these reasons.

The binomial, Poisson and the negative binomial distributions can all be used to model the loss event frequency distribution. The omega distribution is not used for this purpose, therefore Choice ' a ' is the correct answer.

Also note that the negative binomial distribution provides the best model fit because it has more parameters than the binomial or the Poisson. However, in practice the Poisson distribution is most often used due to reasons of practicality and the fact that the key model risk in such situations does not arise from the choice of an incorrect underlying distribution.

Be wary of questions asking you to calculate VaR where the mean or expected returns are different from zero. The VaR formula of z-value times standard deviation needs to have an adjustment for the expected return [ie use VaR = z-value times standard deviation minus expected return]. In this case, the standard deviation for 1 day for the portfolio is =SQRT(1/250)*20%*$10m = $126,491. The VaR is therefore (2.326 * $126,491) - ($10,000,000 * 10% * 1/250) = $290,218.

The square root of time rule cannot be applied here because the returns across the periods are not independent. (Recall that the square root of time rule requires returns to be iid, independent and identically distributed.) Here there is a ' autocorrelation ' in play, which means one period ' s returns affect the returns of the other period.

VaR is merely a multiple of volatility, or standard deviation, using the factor for the desired confidence level. VaR across time periods can be combined using the square root of time rule, in fact if returns were independent we could have easily calculated the VaR for the 20-day period as equal to $100m*SQRT(20/10) = $141.4m

But in this case we need to account for the autocorrelation. We can do this akin to the way we combine the VaR of different assets that have a given correlation. Since we know that:

Variance (A + B) = Variance(A) + Variance(B) + 2*Correlation*StdDev(A)*StdDev(B).

The standard deviation, which the VaR is a multiple of, can be calculated by taking the square root of the variance.

Therefore the combined VaR over the two months will be equal to =SQRT( (100^2) + (100^2) + 2*0.2*100*100 )= $154.92m. All other answers are incorrect.

An error rate of 10 basis points means the number of errors expected in a day will be 15 (recall that 100 basis points = 1%). Therefore the total number of errors expected in a year will be 15 x 250 = 3750. Choice ' a ' is the correct answer.

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

Deterioration in the balance sheets of key counterparties is a concern for a liquidity manager even though it may not immediately affect a firm, and this is true because counterparty failures may lead to liquidity shortfalls for an institution for no fault of its own. It is important for a liquidity risk manager to watch the health of key counterparties where exposure is concentrated and take timely steps to reduce it should the health deteriorate.

Under times of liquidity stress, prepayments of loans extended will decline while withdrawals of demand deposits are likely to increase. Both will not decrease, and therefore Choice ' b ' is incorrect.

A bank is exposed to the undrawn portions of a line of credit extended to a borrower as the borrower, with superior information on its own finances, is likely to draw upon undrawn lines of credit thereby increasing the bank ' s exposure. Therefore Choice ' a ' is incorrect. Generally, a portion of the undrawn part is counted towards a liquidity outflow.

Longevity risk is the risk facing sellers of annuities that their clients will outlive their assumptions on their length of life, while mortality risk is the downside risk for an insurer that clients will die sooner than expected causing the reserves to fall short of what is needed. Therefore Choice ' d ' is not correct as the opposite is true.

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 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.

Choice ' c ' 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.

All the factors listed above contributed to systemic failure. Liquidity risk was not on the radar of regulators, and was a second priority for risk managers, and most of the focus was on capital adequacy as liquidity was thought to be an unlikely problem. Liquidity, regardless of capital adequacy, was the primary cause of failure of a number of institutions during the crisis.

Similarly, stress tests proved to be much milder than the shocks that were actually experienced, and the strategy of ' originate and distribute ' implied that the mortgage and other debt originators had no interest in any due diligence as they intended to package and sell the debt to other investors.

Therefore Choice ' d ' is the correct answer.

When two bonds that appear identical in every respect trade at different prices, the difference is often due to differences in liquidity between the two bonds (the less liquid bond will be cheaper and yield higher), and also due to the fact that ratings from the major rating agencies do not generally react to day to day changes in the market. The market ' s perception of the differences in the two credits will cause a divergence in the prices. This has been an extremely visible phenomenon during the credit crisis of 2007-2009, where fixed income security prices have changed sharply for many securities without any changes in external credit ratings.

Bonds carrying ' different market risk ' is meaningless, and so is the difference in convexity (because the calculated convexity would be identical for similar bonds).

Therefore Choice ' c ' is the correct answer.

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

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

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

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

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.

Stress testing is used for all the listed purposes. Therefore Choice ' a ' is the correct answer.

Measures of risk sensitivity include delta, gamma, vega, PV01, convexity and CR01, among others. They allow approximating the change in the value of a portfolio from a change (generally small) in one of the underlying risk factors.

Risk sensitivity measures are derivatives of the value of the portfolio, calculated with respect to the risk factor. Some risk sensitivity measures are second derivatives, and allow a more precise calculation of the change in the value of the portfolio. Many risk sensitivities are represented by Greek letter, but not all.

Delta (δ) is a measure of the change in portfolio value based on a 1% change in the value of the underlying. Gamma (γ) is a second order derivative that improves the calculation as part of a Taylor expansion. CR01 is a measure of the change due to a 1 basis point change in the credit spread. PL01 is not a measure of any kind of risk sensitivity, it does not mean anything.

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.

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

It is not generally sufficient to ensure the adequacy of liquidity across a group - ie it is not appropriate to just add up the sources and needs for liquidity across multiple entities in a group. This is because there can be restrictions on transferring liquidity between entities, particularly when the entities are located across borders. In cases where transfers of liquidity are permitted, there may be settlement delays in transferring funds from one entity to another. Therefore both statements I and II are incorrect.

Wholesale funding sources refers to the temporary interbank funding sources that need to be rolled over on very short intervals, often as short as overnight. These are not stable sources for long term funding. Statement III is therefore false.

Statement IV is correct as funding diversification refers to diversification of both funding sources and the duration for which the amounts are borrowed, ie tenor diversity.

Statement IV is the only correct statement and therefore Choice ' a ' 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.

In an interest rate swap, the parties agree to exchanging interest rate payments, with one party being a fixed interest rate payer and the other paying floating rates. The party receiving fixed rates and paying floating can be considered to be long a fixed rate bond and short a floating rate note. Therefore an IRS can be modeled as a combination of a fixed coupon bond and a floating rate note. Choice ' b ' is the correct answer.

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.

Strong management of collateral, both receivable and payable, is emerging as an area requiring significant investment by financial institutions and asset managers in IT infrastructures and business processes. A bank needs to make collateral calls daily, based upon the P & L of the previous day, and likewise receives collateral calls from its counterparties. Just like cash, a bank needs to make sure that it does not run out of collateral to post when a call is received. Interestingly, based upon the agreements between banks and their mutual understanding, only certain types of instruments often qualify as valid collateral - and in such cases even cash is not acceptable if the right type of bond or other agreed security is not available to post. The operational challenges of managing collateral increase manifold due to ' rehypothecation ' , ie when collateral received from one counterparty gets posted out as collateral where it is due. In such cases, the bank should have the mechanisms to receive the right assets back in a timely way in case rehypothecated assets are to be returned. The systems should be able to deal with delays, failures without impacting the ability of the bank to post collateral as needed. All of this requires major investments in IT and processes.

Statement I is not true as a bank is bound to post collateral to third parties when needed regardless of the failure of its counterparties to post collateral to it when owed. In the markets, failures by counterparties can and do happen, and a collateral management system needs to account for and keep a buffer for the fact that some collateral when due will not be received.

Statement II is not true as rehypothecation by counterparties of collateral posted increases the chances of the collateral not being received in time. The system should consider the need for liquidity to generate assets that can be posted as collateral when others have failed to return the collateral in a timely way.

Statement III is not correct as cash may not be acceptable to counterparties as collateral. From a practical point of view, they may not have the infrastructure to receive and account for cash as collateral. A Swiss bank, for example, may have an ' account ' to receive US t-bills as collateral but may not even have a US dollar account to receive cash. Even if it did, the volumes of transactions going back and forth may make tracking and reconciliations impossible. Thus a bank should always make sure that it has the right type of collateral available to post.

Statement IV is incorrect as well, as treasury issued instruments are also subject to haircuts. Their value also fluctuates in response to changes in yields, and therefore they are subject to haircuts as well.

Thus none of the statements are correct and Choice ' d ' is the correct answer.

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

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

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.

Remember that VaR is merely a multiple of the portfolio ' s standard deviation. The multiple is determined by the confidence level, and for a 99% confidence level this multiple is 2.3264 (=-NORMSINV(1%) in Excel). Therefore one standard deviation at this level of confidence would be equal to VaR/2.3264.

In addition to the Z-value at 99% confidence, you should also remember what the Z value is for a 95% level of confidence, as PRM questions may expect you to know these. The standard Windows calculator allowed in the exam does not allow you to calculate these, so it is safer to just remember these values.

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.

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

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

The Options Theoretic approach to calculating economic capital is a top-down approach that considers the value of capital as being equivalent to a call option with a strike price equal to the notional value of the debt - ie, the shareholders have a call option on the assets of the firm which they can acquire by paying the debt holders a value equal to their notional claim (ie the face value of the debt). Therefore Choice ' a ' is the correct answer and the other choices are incorrect.

The CDS rate is approximated by the [Loss given default x Default hazard rate]. Thus Choice ' b ' is the correct answer.

Note that this is also equal to the credit spread on the reference bond over the risk free rate. Therefore credit spreads and CDS rates are generally the same. Also, ' loss given default ' is nothing but (1 - Recovery rate). This can be substituted in the formula for the credit spread to get an alternative expression that directly refers to the recovery rate. Therefore all other choices are incorrect.

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

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

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

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

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

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

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

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

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

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

The beta distribution is commonly used to model recovery rates. It is a distribution for variables whose values lie between 0 & 1, and the parameters of the distribution can be estimated using the mean and standard deviation of the data. Therefore Choice ' a ' is correct and the others are wrong.

Refer to the tutorial on distributions for an Excel model of the beta 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.

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.

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.

Rating agencies target both accuracy and stability when they assign ratings. These two objectives can sometimes conflict, so a balance needs to be struck between the two. Rating agencies do not target any particular ' accuracy ratio ' or rankings. Therefore Choice ' c ' 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.

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.

The correct answer is choice ' a '

Recall the formula for calculating variance under EWMA. See below. Therefore the correct answer is =SQRT((1 - 0.93)*(LN(11/10))^2 + 0.93*((3.5%^2))) = 4.21%. Other answers are incorrect. Note that continuous returns are to be used, ie ln(11/10) and not discrete returns (=1/10) - though generally the difference between the two is small over short time periods. (If in the exam the answer doesn ' t exactly match, try using discrete returns.)

Note that events of default under the ISDA MA are caused by one of the parties that is considered ' at fault ' . In contrast, " termination events " are events for which no one is at fault, for example changes in legislation, illegality etc that still justify termination of the transactions under the contract.

The ISDA MA describes the following 8 types of events of default:

1. failure of pay or deliver

2. breach of agreement

credit support default

4. misrepresentation

5. default under specified transaction

6. cross default

7. bankruptcy

8. merger without assumption

All of the options presented in the question are events of default.

The immediate impact of the default would be to improve the liquidity available in the short term due to the pay out from the CDSs.

It is also important to consider the impact on liquidity from the occurence of a default even in situations where CDS protection may not have been purchased. In such cases, there may be a nearer term payout in the form of the recovery rate. Of course, recovery payments are generally not realized for longer periods of time as court cases linger on, but there is a good likelihood that a payment, albeit lower in total, is likely to be realized sooner than the maturity of the bond in cases where the bond is a longer term bond. At the same time, any interest payments, and the final principal payment, which may have been included in liquidity projections, will not occur.

The VaR in this case will be the top quintile of observations. In this case, since there are exactly 100 observations, this would mean the worst return would become the VaR. Therefore Choice ' b ' is the correct answer. Choice ' a ' and Choice ' c ' make no sense. This highlights that at higher confidence levels, fewer and fewer observations impact the VaR if we are using historical simulation based VaR.