8008 PRMIA PRM Certification - Exam III: Risk Management Frameworks, Operational Risk, Credit Risk, Counterparty Risk, Market Risk, ALM, FTP - 2015 Edition Free Practice Exam Questions (2025 Updated)

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.

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.

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.

This is easy to calculate as follows: At the 99% confidence level, the VaR=2.326 * Std Deviation (remember the z values at the 95% and 99% levels, the PRMIA exam may not give you these values). Thus the 1-day standard deviation is $250m/2.326, and the 250-day standard deviation is √250 * ($250m/2.326) = $1,699.4m.

Remember: if you know the VaR, you know the standard deviation. Once you know the standard deviation for any period of time, you can convert it into standard deviation for another period using the square root of time rule. You can also calculate the VaR at a different confidence level too.

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

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

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

One way to think about this question is this: we are provided with two pieces of information: if the portfolio is worth $100 to start with, it will be worth $95 at the end of year 1 and $85 at the end of year 2. What it is asking for is the probability of default in year 2, for the debts that have survived year 1. This probability is $10/$95 = 10.53%. Choice 'b' is the correct answer.

Note that marginal probabilities of default are the probabilities for default for a given period, conditional on survival till the end of the previous period. Cumulative probabilities of default are probabilities of default by a point in time, regardless of when the default occurs. If the marginal probabilities of default for periods 1, 2... n are p1, p2...pn, then cumulative probability of default can be calculated as Cn = 1 - (1 - p1)(1-p2)...(1-pn). For this question, we can calculate the probability of default for year 2 as [1 - (1 - 5%)(1 - 10.53%)] = 15%.

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.

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

There is more than one way to calculate returns. Absolute returns may be relevant for risk factors where the size of the movement is unrelated to its current value. For other risk factors, the returns might scale with the size of the existing value of the risk factor, eg equity prices. The right return definition needs to be adopted for each risk factor, therefore 'I' is a correct choice.

The risk analyst has a Choice 'b'etween parametric VaR, Monte Carlo, and historical simulation based VaR. 'II' therefore is one of the decisions that needs to be made (though historical simulation is the choice most often made).

The decision as to what to include in a portfolio is not a decision that is affected by choices made for VaR calculations. 'III' is therefore not a correct answer.

There are multiple ways to calculate volatility - including decisions on how long back in time to go for the data, and whether volatility clustering needs to be accounted for using EWMA or GARCH. Therefore 'IV' is a correct answer.

Under the contingent claims approach, credit risk is modeled as the value of a put option on the value of the firm's assets with a strike equal to the face value of the debt and maturity equal to the maturity of the obligation. The cost of credit risk is determined by the leverage ratio, the volatility of the firm's assets and the maturity of the debt. Cash flows are not a part of the equation. Therefore Choice 'a' is the correct answer.

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

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

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

Statement I is correct. Data is often divided into two sets - a 'training set' that is used to create and fine-tune the model while the 'control set' is used to prove that the model works on sample data. Back testing is then perfomed using actual data that becomes available over time, or may already be available as historical data.

Statement II is incorrect. A risk manager often spends a great deal of time in managing data, and ensuring that the data being used is accurate enough for the purpose it is being used for. A risk manager can expect to spend a good part of his or her team's time in cleansing data. While he or she can try to get the IT processes and systems to produce correct data in the first place so it requires minimal subsequent cleansing or validation, this task is likely to remain a key part of a risk manager's role for quite some time in the future given the challenges nearly all organizations face in managing risk data.

Statement III is correct. There was not enough granular data available on the underlying components of some of the derivative debt securities whose markets dried up during the crisis that began in 2007. This was because investors became increasingly unsure of what the value of these securities, such as CDOs was, leading to market seizure and firesale prices.

Statement IV is not correct. There is no easy solution to the lack of enough historical data, which is used to create as well as test models, and construct stress scenarios. Analytical approaches are not a good enough substitute for real market data. During the recent crisis, many instruments had rather short histories and there was not enough data available, and risk managers and portfolio managers relied upon analytical approaches to value and price them. Many of the assumptions that underpinned these approaches were untested in the real world and turned out to be incorrect.

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

When a derivative position is entered into, its mark-to-market value is generally close to zero (though the notional may be high). With the passage of time, the derivative's value fluctuates in an unpredictable way, creating a counterparty exposure that may be difficult to estimate and risk manage. Counterparty risk in such cases is estimated based on Potential Future Exposure, which may be calculated using either:

a) Take the mark-to-market at present, and add a certain percentage of the notional, or

b) Perform a Monte Carlo simulation, capturing the stochastic nature of the PFE.

Therefore I and II are valid choices. MLE and parametric estimation are not methods for calculating PFE.

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.

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.

EDFs are derived from the distance to default. The distance to default is the number of standard deviations that expected asset values are away from the default point, which itself is defined as short term debt plus half of the long term debt. Therefore debt levels affect the EDF. Similarly, asset values are estimated using equity prices. Therefore market capitalization affects EDF calculations. Asset volatilities are the standard deviation that form a place in the denominator in the distance to default calculations. Therefore asset volatility affects EDF too. The risk free rate is not directly factored in any of these calculations (except of course, one could argue that the level of interest rates may impact equity values or the discounted values of future cash flows, but that is a second order effect). Therefore Choice 'b' is the correct answer.

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.

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.

Any good risk measure has the property that it is sub-additive, which means the whole is less than the sum of the parts. In the case of VaR, sub-additivity arises due to the diversification effect, or said differently, due to the correlation between different assets being less than one. Therefore Choice 'd' is the correct answer.

Super-additivity is just the opposite of sub-additivity, ie, the whole is greater than the sum of the parts. Good risk measures do not have super-additivity. Therefore Choice 'b' is incorrect.

Choice 'c' states the same thing as Choice 'b' in different words, and is incorrect. Choice 'a' is non-sensical and incorrect.

Choice 'b', Choice 'c' and Choice 'a' correctly describe a bilateral close out netting as recommended by the ISDA. However Choice 'd' is not correct as it suggests individual settlement of transactions without netting which is the whole point of bilateral close out netting.