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)

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.

This problem can be solved by combining the variance of the returns from the two consecutive periods in the same way as one would combine the variance of different assets that have a given correlation. In such cases we know that:

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

The standard deviation can be calculated by taking the square root of the variance.

Therefore the combined volatility over the two months will be equal to =SQRT((5%^2) + (5%^2) + 2*0.3*5%*5%) = 8.062%. All other answers are incorrect.

If you have not studied PCA prior to the preparing for the PRMIA exams, you will find the handbook to be a bit difficult to understand this topic. However, PRMIA have been asking questions about PCA on their exams so it is important to conceptually know what PCA is (and be able to answer the exam questions which are unlikely to ever require you to do a calculation).

Using PCA, a complex correlated system (eg, the rates in a term structure which are all correlated to each other) is effectively transformed into a 'principal component representation'. A principal component representation expresses each of the independent variables in the system as a linear representation based on 'principal components'. Principal components are derived from the eigenvectors of the correlation matrix. Remember that if you have a positive semi-definite correlation matrix (which will be an n x n square matrix), it will have 'n' eigenvectors, each with an eigenvalue. The eigenvectors will be orthogonal (ie perpendicular) to each other. The eigenvalues for each of the eigenvectors determine which are principal components - in descending order of the eignevalues. Therefore the eigenvector with the highest eigenvalue is the first principal component, the second highest value the second principal component and so on. If there are n variables in the system, then eigenvalue divided by n gives us the proportion of the variation explained by that particular principal component.

In the case of a PCA done on the term structure of interest rates, the first principal component is the 'trend' component, and under a principal component representation its coefficients are given by the first eigenvector. (By the way, remember the next two principal components are tilt and curvature respectively). If these coefficients are the same (they are, for an interest rate term structure), this means all rates move up or down when the value of the first principal component moves. Thust factor weights on the first component show whether there is common trend in the system. Statement I is correct.

The factors to be applied to the principal components are indeed obtained from the eigenvectors of the correlation matrix (and not the covariance matrix), and therefore statement II is correct.

PCA is used to reduce dimensionality, this is true and in fact one of the main reasons why PCA is used at all. Therefore statement III is correct.

Statement IV is false as it is the largest eigenvalues and not the smallest that determine the eigenvectors affecting most of the variation (through the principal components they represent).

Thus Choice 'b' 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.

The minimum variance hedge ratio answers the question of how much of the hedge to buy to hedge a given position. It minimizes the combined volatility of the primary and the hedge position. The minimum variance hedge ratio is given by the expression [ σ(x) / σ(y) ] * ρ(x,y)]. Effectively, this is the same as the beta of the primary position with respect to the hedge.

In this case, the hedge ratio is = 10%/9% * 0.9 = 1

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 to the actuarial approach.

The CCAR is a supervisory mechanism adopted by the US Federal Reserve Bank to assess capital adequacy for bank holding companies it supervises. It was not a concept introduced by the international Basel framework.

The other three were indeed rules introduced by Basel 2.5, which was ultimately subsumed into Basel III.

Stressed VaR is just the standard 99%/10 day VaR, calculated with the assumption that relevant market factors are under stress.

The Incremental Risk Charge (IRC) is an estimate of default and migration risk of unsecuritized credit products in the

trading book. (Though this may sound like a credit risk term, it relates to market risk - for example, a bond rated A being downgraded to BBB. In the old days, the banking book where loans to customers are held was the primary source of credit risk, but with OTC trading and complex products the trading book also now holds a good deal of credit risk. Both IRC and CRM account for these.)

While IRC considers only non-securitized products, the CRM (Comprehensive Risk Model) considers securitized products such as tranches, CDOs, and correlation based instruments.

The IRC, SVaR and CRM complement standard VaR by covering risks that are not included in a standard VaR model. Their results are therefore added to the VaR for capital adequacy determination.

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.

In the Standardized Approach, banks’ activities are divided into eight business lines: corporate finance, trading & sales, retail banking, commercial banking, payment & settlement, agency services, asset management, and retail brokerage. Therefore Choice 'c' is the correct answer.

When calculating volatility weighted VaR, returns are adjusted by a factor equal to the current volatility divided by the historical volatility, ie the volatility that existed during the time period the returns were earned. If the current volatility is greater than the historical volatility (also called contemporary volatility), then it has the effect of increasing the magnitude of any past returns (whether positive or negative). This in turn increases the VaR.

Consider an example: if the current volatility is 2%, and a return of -5% was earned at a time when the volatility was 0.8%, then the volatility weighted return would be 12.5% (=-5% x 2%/0.8%). Clearly, this has the effect of increasing the VaR.

Choice 'd' is therefore the correct answer.

When we do a Monte Carlo simulation, the statistic we obtain (eg, the expected price) is an estimate of the real variable. The difference between the real value (which would be what we would get if we had access to the entire population) and that estimated by the Monte Carlo simulation is measured by the 'standard error', which is the standard deviation of the difference between the 'real' value and the simulated value (ie, the 'error').

As we increase the number of draws in a Monte Carlo simulation, the closer our estimate will be to the true value of the variable we are trying to estimate. But increasing the sample size does not reduce the error in a linear way, ie doubling the sample size does not halve the error, but reduces it by the inverse of the square root of the sample size. So if we have a sample size of 1000, going up to a sample size of 100,000 will reduce the standard error by a factor of 10 (and not 100), ie, SQRT(1/100) = 1/10. In other words, standard error is proportional to 1/√N, where N is the sample size.

Therefore Choice 'c' is correct and the others are incorrect.

GARCH is a mean reverting model of volatility, with a steady state mean that the model reverts to in the absence of market shocks. EWMA is not mean reverting and volatility under EWMA stays constant in the absence of shocks. Therefore statement I is correct.

Both EWMA and GARCH models are designed to address volatility clustering, which explains much of the non-normality of returns. When returns are standardized to the volatility calculations under either of these methods, the returns appear far closer to the normal distribution than non-standardized returns. (If it were not to, then there would have been no point in using these techniques.) Statement II is correct.

Steady state variance under GARCH is defined as ω / (1 - α - β), where α and β are the two parameters (called the reaction and persistence coefficient respectively). Clearly, it is affected by more than just the persistence coefficient, therefore statement III is not correct.

Sub-additivity is a very desired property in risk measures. It implies the sum of the parts is greater than the whole. In the case of risk measures, the whole is smaller than the sum of the parts due to diversification. Statement IV is true.

Therefore the correct answer is Choice 'c'

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%)

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

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

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

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

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

When a operational loss frequency distribution (which, for example, may be based upon a Poisson distribution) and a loss severity distribution (for example, based upon a lognormal distribution), it is assumed that the frequency of losses and the severity of the losses are completely independent and do not impact each other. Therefore statement II is correct, and the others are not valid assumptions underlying the operational loss distribution.

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.

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

Banks using the basic indicator approach must hold 15% of the average annual gross income for the past three years, excluding any year that had a negative gross income. Therefore Choice 'd' is the correct answer.

The exact formula for VaR is = -(Zα σ + μ), where Z α is the z-multiple for the desired confidence level, and μ is the mean return. Now Zα is always a negative number, or at least will certainly be provided the desired confidence level is greater than 50%, and μ is often assumed to be zero because generally for the short time periods for which market risk VaR is calculated, its value is very close to zero.

Therefore in practice the formula for VaR just becomes -Zασ, and since Z is always negative, we normally just multiply the Z factor without the negative sign with the standard deviation to get the VaR.

For this question, there are two ways to get the answer. If we use the formula, we know that -Zασ= 250,000 (as μ=0), and therefore -Zασ - μ = 250,000 - 10,000 = $240,000.

The other, easier way to think about this is that if the mean changes, then the distribution's shape stays exactly the same, and the entire distribution shifts to the right by $10,000 as the mean moves up by $10,000. Therefore the VaR cutoff, which was previously at -250,000 on the graph also moves up by 10k to -240,000, and therefore $240,000 is the correct answer.

The other choices are intended to confuse by multiplying the z-factor for the 99% confidence level with 10,000 etc.

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)