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)

When VaR is based on an assumption of normality with a static mean and volatility, it means anything that violates these assumptions will introduce model error. Volatility clustering implies a non-static volatility. Heavy tails imply non-normality of the shape of the distribution. Autocorrelation of squared returns implies that returns are not independent and identically distributed. Therefore all of these introduce model error. Choice 'd' is therefore the correct answer.

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

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.

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 marginal probability of default for year 2 by solving the equation [1 - (1 - 20%)(1 - P2) = 45%] for P2. Solving, we get the marginal probability of default during year 2 as 31.25%. Since this is the annual marginal probability of default, we will need to convert it to a monthly number, which we can do by solving the following equation where M1 is the monthly marginal probability of default.

1 - 31.25% = (1 - M1)^12, implying M1 = 3.07%

Probability of the joint default of both A and B =

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

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

Solving, we get default correlation = 25%

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

Of the listed choices, I and III are asset based credit enhancements, and II is third party based. Cash reserves are not credit enhancements (unless held as collateral).

The square root of time rule can be used to convert, say a 1-day VaR to a 10-day VaR, by multiplying the known number by the square root of time to get the VaR over a different time horizon. However, there are key assumptions that underlie the application of this rule, and statements I to IV correctly state those assumptions.

Statements V and VI are not correct, because the application of the square root of time rule requires the absence of serial correlations, and also the absence of volatility clustering (ie independence). Therefore Choice 'c' is the correct answer.

The square root of time rule is also applied to convert volatility or standard deviation for one period to the volatility for a different time period. Remember that VaR is just a multiple of volatility, and therefore the assumptions that apply to the square root of time rule for VaR also apply to the same rule when used in the context of volatilities or standard deviation.

Performance measurement at a very basic level involves comparing the return earned to the capital invested to earn that return. Risk adjusted performance measures (RAPMs) come in various varieties - and the key difference between RAPMs and traditional measures such as return on equity, return on assets etc is that RAPMs account for the risk undertaken. They may do so by either adjusting the return, or the capital, or both. They are classified as RAROCs (risk adjusted return on capital), RORACs (return on risk adjusted capital) and RARORACs (risk adjusted return on risk adjusted capital).

A computation of Altman's Z-score considers the following ratios:

- Working capital to total assets

- Retained earnings to total assets

- EBIT to total assets

- Market cap to debt

- Sales to total assets

Nearly all the numbers above are accounting measures derived straight from the balance sheet or the income statement. Market capitalization is a market driven number. Therefore Choice 'c' is the correct answer as the Altman credit risk score considers both accounting and market based measures.

Altman's score, though computationally straightforward and intuitively easy to understand, was introduced in the late sixties and has been very accurate in predicting corporate bankruptcies, which is why it continues to be used extensively.

The probabilities of default of the two bonds are independent (as indicated by a zero default correlation). The various possible states of the portfolio are as follows:

First bond defaults, and the second does not: Probability * Loss = 0.03*0.92 * $50m = $1.38m

Second bond defaults, and the first does not: Probability * Loss = 0.97*0.08 * $50m = $3.88m

Both bonds default: Probability * Loss = 0.03*0.08 * $100m = $0.24m

Thus total expected loss on this portfolio = $5.5m. Since recovery rates are not provided, those should be assumed to be zero.

There is an easier way to solve this as well: default correlation does not affect expected losses, but their volatility. You can calculate the expected losses of the two bonds and add them up, ie, $50m*0.03 + $50m *0.08 = $5.5m

The correct definition of CVA is LGD * EPE * PD. All other answers are incorrect.

CVA reflects the adjustment for counterparty default on derivative and other trading book transactions. This reflects the credit charge, that neeeds to be reduced from the expected value of the transaction to determine its true value. It is calculated as a product of the loss given default, the probability of default and the average weighted exposure of future EPEs across the time horizon for the transaction.

The future exposures need to be discounted to the present, and occasionally the equations for CVA will state that explicitly. Similarly, in some more advanced dynamic models the correlation between EPE and PD is also accounted for. The conceptual ideal though remains the same: CVA=LGD*EPE*PD.

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 choices provided.

The peaks-over-threshold model is used when losses over a given threshold are recorded, as is often the case when using data based on external public sources where only large loss events tend to find a place. The generalized Pareto distribution is also used when attempting to model loss severity using EVT. Lognormal mixtures and generalized hyperbolic distributions are not used as extreme value distributions.

Choice 'd' is the correct answer.

The probability 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.)

When modeling 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 Choice 'a' is correct, and the others are not valid assumptions underlying the operational loss modeling.

Once each of these distributions has been built, a random number is drawn from each to determine a loss scenario. The process is repeated many times as part of a Monte Carlo simulation to get a the loss distribution.

All product pricing should reflect the cost of maintaining the liquidity required to support a product. This is regardless of the accounting treatment for the product, ie irrespective of whether the product is on or off balance sheet. Therefore statement I is incorrect.

The time horizon to consider for liquidity risk management is determined taking into account a number of factors, which include both the speed at which new sources of liquidity can be generated and any applicable regulatory requirements. Statement II is correct.

Managing collateral, both collateral received and collateral posted with counterparties, is an important aspect of liquidity risk management as liquidity problems often manifest themselves in the form of margin calls requiring collateral to be posted. Statement III is therefore correct.

The maturity period of the different sources of capital funding for a bank, for example equity capital, preferred shares, long term debt etc quite clearly has a significant impact on liquidity needs. Stable sources of funds such as equity or preferred capital, or debt that is not maturing shortly help the liquidity position. Statement IV is therefore correct.

Choice 'b' is the correct answer.

Let the probability 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.

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.

Pre-settlement risk is the risk that one of the counterparties defaults prior to the date for the maturity of the transaction in question. This may be an unrelated default, in fact there may have been no default on that particular contract, but the party may have defaulted on its other obligations, or filed for bankruptcy. To deal with such cases and to protect the interests of both the parties, it is common to provide for immediate termination of positions and settlement based on the current replacement value of the contracts. Therefore statements I and II are correct.

Statement III is correct as well - the exposure from an OTC derivative contract derives from its current replacement value, and not the notional. If the current replacement value is negative, then the credit exposure is considered equal to zero.

Statement IV is correct as it is quite common to restate all exposures - those from credit lines, OTC derivatives etc - in loan equivalent terms prior to estimating credit risk.