PRMIA 8010 Operational Risk Manager (ORM) Exam Exam Practice Test

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 thanthe 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 ofthe 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 usingthe 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.

Monte Carlo VaR computations generally include the following steps:

1. Generate multivariate normal random numbers, based upon thecorrelation 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 rangeof 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.

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

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

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

Offsetting trades with other counterparties will not reduce credit exposure to a given counterparty. All other choices represent means of reducing credit risk. Therefore Choice 'c' is the correct answer.

Exposure for derivative instruments can vary significantly over the lifetimeof the instrument, depending upon how the market moves. The potential future exposure represents the extremes, not the most likely outcome. The expected exposure is the most suitable measure for pricing the credit risk. Over time, as multiple transactionsare entered into, the expectation (or the mean) will be realized - though individual transactions may have more or less by way of exposure.

The notional amount may not be relevant, though for loans it may be the most important contributor to the expected exposure. Mark-to-market will represent the exposure at a given point in time, but cannot be predicted nor be used to price the credit risk.

The probability that only none of the three bonds will default is equal to the probability of all surviving. Since default correlation is zero, we can simply multiply the probabilities of survival. Therefore the correct answer is 94% = (1 - 1%) * (1 - 2%) * (1 - 3%)

According to the Basel II framework, Tier 1 capital, also called core capital or basic equity, includes equity capital and disclosed reserves.

Tier 2 capital, also called supplementary capital, includes undisclosed reserves, revaluation reserves, general provisions/general loan-loss reserves, hybrid debt capital instruments and subordinated term debt.

Tier 3 capital, or short term subordinated debt, is intended only to cover market risk but only at the discretion of their national authority.

All the reasons and risks presented above are valid reasons for using scenario analysis, except V and VI - ie, the need to reduce the complexity of calculations is not a valid reason for using scenario analysis. Similarly, making operational risk capital estimates match management's desired capital allocation targets is also not a valid reason. Capital calculations are intended to provide adequate capital for managing the risk from operations, regardless of what management may desire them to be.

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.

A recap would be in order here: calculating operational risk capital is a multi-step process.

First, we fit curves to estimate the parameters to our chosen distribution types for frequency (eg, Poisson), and severity (eg, lognormal). Note that these curves are fitted at the UoM level - which is the lowest level of granularity at which modeling is carried out. Since there are many UoMs, there are are many frequency and severity distributions. However what we are interested in is the loss distribution for the entire bank from which the 99.9th percentile loss can be calculated. From the multiple frequency and severity distributions we have calculated, this becomes a two step process:

- Step 1: Calculate the aggregate loss distribution for each UoM. Each loss distribution is based upon and underlying frequency and severity distribution.

- Step 2: Combine the multiple loss distributions after considering the dependence between the different UoMs. The 'dependence' recognizes that the various UoMs are not completely independent, ie the loss distributions are not additive, and that there is a sort of diversification benefit in the sense that not all types of losses can occur at onceand the joint probabilities of the different losses make the sum less than the sum of the parts.

Step 1 requires simulating a number, say n, of the number of losses that occur in a given year from a frequency distribution. Then n losses are picked from theseverity distribution, and the total loss for the year is a summation of these losses. This becomes one data point. This process of simulating the number of losses and then identifying that number of losses is carried out a large number of times to get the aggregate loss distribution for a UoM.

Step 2 requires taking the different loss distributions from Step 1 and combining them considering the dependence between the events. The correlations between the losses are described by a 'copula', andcombined together mathematically to get a single loss distribution for the entire bank. This allows the 99.9th percentile loss to be calculated.

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 ratherdifficult. Statement I is false because recovery rates are difficult to predict and assumptions are not easy to make.

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

Assuming time invariance and the Markov property, it is easy to calculate the transition matrix for any time period as P^n, where P is the given transition matrix for one period andn the number of time periods that we need to compute the new transition matrix for.

However, when the new time period is less than the time period the matrix is available for, the only way to deriving a transition matrix for a partial period is to numerically calculate a matrix M such that M^n = P. Therefore Choice 'b' is the correct answer. Taking cube roots of a matrix is not a possible operation, dividing by 3 gives a matrix meaningless in this context, and P x P x P will give us the transition matrix for 3 years, not 1/3rd of a year.

This situation represents one of the paradoxes in estimating severity that one needs to be aware of - the improvement in controls reduces the weight of the body/middle of the distribution and moves it towards the tails (as the total probability under the curve must stay at 100%) and the distribution becomes more heavy tailed. As a result, the 99.9th percentile loss actually increases. instead of decreasing, creating a counterintuitive result. Therefore the correct answer is that the capital required will increase.

If scenario analysis produces such a result, the analyst must question if the 1 in 100 year loss severity is still accurate. If the new control has reduced the severity in the body of the distribution, the question as to why the more extreme losses have not changed should be raised.

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

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

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

A default hazard rate is the rate of default in a continuous time setting. This question is asking for probability of survival at the end of 5 years. The formula to calculate the probability of survival at the end of t years where the default hazard rate is λ is e^(-λ *t) (or in Excel,=exp(-λ*t). Therefore the correct answer is Choice 'd'.

(It may be tempting to infer that if the probability of survival at the end of 1 year is 90% (1 - 10%), then the probability of survival in 5 years would be 90%^5. However this reasoning is not correct for the reason that the given rate is not the discrete rate of default, but the hazard rate which is nothing but the continuously compounded rate of default.)

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 thedistributions 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 distributionand cannot be used for frequency modeling.

According to the Basel II framework, Tier 1 capital, also called core capital or basic equity, includes equity capital and disclosed reserves.

Tier 2 capital, also called supplementary capital, includes undisclosed reserves, revaluation reserves, general provisions/general loan-loss reserves, hybrid debt capital instruments and subordinated term debt issued originally for 5 years or longer.

Tier 3 capital, or short term subordinated debt, is intended only to cover market risk but only at the discretion of their national authority. This only includes short term subordinated debt originally issued for 2 or more years.

An interesting thing to note is the difference between 'subordinated term debt' under Tier 2 and the 'short term subordinated debt' under Tier 3. The distinction is based upon the years to maturity at the time the debt was issued. The remaining time to maturity is not relevant. For the subordinated term debt included under Tier 2, the amount that can be counted towards capital is reduced by 20% for every year when the debt is due within 5 years. This takes care of the time to maturity problem for Tier 2subordinated debt. For Tier 3 short term subordinated debt, this is not an issue because debt will only qualify for Tier 3 if it has a lock-in clause stipulating that the debt is not required to be repaid if the effect of such repayment is to take the bank below minimum capital requirements.

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

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

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

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

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

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

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

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

Regardless of the approach being followed by a bank (ie, whether foundation IRB or advanced IRB), it must make its own estimates for the probability of default. Banks following the foundation IRB approach may use values set by the supervisor for the other three parameters, though those following the advanced IRB approach may use their own estimates for all four inputs.(This is also the difference between advanced IRB and the foundation IRB approaches.) Therefore Choice 'a' is the correct answer.

Also note the four difference elements that go as inputs to the internal ratings based approach in the choicesprovided.

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

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

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

For EVT, we use the block maxima or the peaks-over-threshold methods. These provide us the data points that can be fitted to a GEVdistribution.

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

Theprobability of default would make the future cash flows from both the bonds identical. If p be the probability of default, the cash flows from the risky corporate bond would be

= (cash flows in the event of default x probability of default) + (cash flows without default x (1 - probability of default))

=> p*0 + (1 - p)*(1 + 8.5%) = (1 - p)*1.085.

The cash flows from the treasury bond would be 1.04. These two should be equal, ie,

1.04 = (1- p)*1.085, implying p = 4.15%.

(Note: The above is a simplification intended for the exam. In reality investors would demand a 'credit risk premium' for the corporate bond over and above the expected default loss rate. They are unlikely to be happy with just being compensated with exactly the expected default loss rate plus the risk-fre rate because the expected default loss rate itself is uncertain. They would demand some premium over and above what the default rate alone might mathematically imply above the risk free rate. In this question, this credit risk premium is ignored.)

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

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

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

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.

Assuming timeinvariance and the Markov property, it is easy to calculate the transition matrix for any time period as P^n, where P is the given transition matrix for one period and n the number of time periods that we need to compute the new transition matrix for. ThusChoice 'b' is the correct answer.

Choice 'c' is the correct answer. 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. ('Herstatt risk' refers to settlement risk, and is irrelevant.)

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 suchan 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.

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

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

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

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

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