Free PRMIA Operational Risk Manager (ORM) Exam 8010 Exam Questions

Parametric VaR relies upon reducing a portfolio's positions to risk factors, and estimating the first order changes in portfolio values from each of the risk factors. This is called the delta approximation approach. Risk factors include stock index values, or the PV01 for interest rate products, or volatility for options. This approach can be quite accurate and computationally efficient if the portfolio comprises products whose value behaves linearly to changes in risk factors. This includes long and short positions in equities, commodities and the like.

However, where non-linear products such as options are involved and large moves in the risk factors are anticipated, a delta approximation based valuation may not give accurate results, and the VaR may be misstated. Therefore in such situations parametric VaR is not advised (unless it is extended to include second and third level sensitivities which can bring its own share of problems).

Parametric VaR also assumes that the returns of risk factors are normally distributed - an assumption that is violated in times of market stress. So if it is known that the risk factor returns are not normally distributed, it is not advisable to use parametric VaR.

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.

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 3 as =1 - (1-2%)*(1-3%)*(1-4%) = 8.74%

Statutory financial reporting is the responsibility of the Chief Financial Officer, not the Chief Risk Officer. The head of internal audit reports to the audit 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.

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 and n 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.

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).

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.

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.

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%)

The index option is affected by the spot value for the underlying index, as also the risk free interest rate, or the zero rate for the duration of the option. It is also affected by the volatility of the underlying. The 'strike price' is set and is fixed at the time the option is purchased, and therefore is not a risk factor.

Therefore other than IV, all other choices are valid risk factors that underlie an equity index option.

Other instruments may have other risk factors - for example, a long forex position will have the spot exchange rate as the only risk factor.

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.

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.

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.

This question requires the calculation of the credit VaR of the bonds - note that in the real exam the question may not refer to 'credit' VaR, but that can be inferred from the context, ie because the probability of default is provided, it can only be asking for the credit VaR. (Note the difference from the market risk VaR which is driven by interest rate changes affecting the value of the bonds - there are other questions addressing that calculation).

Credit VaR = Expected Value - Worst case portfolio value at the selected percentile (ie the confidence level)

Thus if we know the distribution of the portfolio value in the future, we can find out the value at the required percentile (in this case 99%), and the VaR will be the difference between this value and the expected value of the portfolio.

An important piece of information provided is that the defaults are independent, ie they are not correlated. This means joint probabilities of default or survival can be easily found by multiplying the relevant probabilities. The following outcomes are possible:

1. Both bonds default: Probability = 1% * 1% = 0.01%. Portfolio value = $0 (because both bonds have defaulted & there is zero recovery)

2. One bond defaults and the other survives: Probability = 2 * 1% * 99% = 1.98%. Portfolio value = $1m (because one bond survives with a value of $1m and the defaulted bond has a value of $0). (Note that because there are two ways in which this can happen, ie bond 1 defaults, bond 2 survives; and bond 1 survives, bond 2 defaults, we need to multiply the probability by 2).

3. Both bonds survive: Probability = 99% * 99% = 98.01%. Portfolio value = $2m.

Expected value is therefore $1.98m (which is equal to 2 * $1m * (1 - 1%), or alternatively can also be obtained by multiplying the probabilities in the above three outcomes with the value associated with each).

The future distribution of the value of the portfolio can be constructed from the three outcomes outlined above:

a. Upto the 98.01th percentile the value of the portfolio is $2m, and the VaR is zero (being greater than the expected value, so there is nothing to lose)

b. From the 98.01th percentile to the 99.99th percentile (98.01+ the next 1.98%), the value of the portfolio is $1m. VaR in this range is $0.98m (=$1.98m - $1m)

c. From the 99.99th to the 100th percentile the value of the portfolio is $0, and the VaR is $1.98m.

Since the question is asking for VaR at the 99% confidence level, it lies in the range in 'b' above, and therefore the VaR is $0.98m.

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