PRMIA 8010 - Operational Risk Manager (ORM) Exam

The cumulative probability of default for the security for the 5 years is [1 - (1 - probability of default upto year 4)*(1 - probability of default in year 5)]. An easier way to think about this is that the Probability of survival till year 5 = (Probability of survival till year 4 * Probability of survival during year 5). Using the relationship that probability of default = 1 - probability of survival, we can calculate the required probability in all cases.

In this case, the cumulative probability of default for the security for 5 years = 1 - (1 - 11.47%)*(1 - 5%) = 15.8695%, therefore Choice 'c' is the correct answer.

increasing the timing differences between the two legs of the transaction will increase settlement risk and not reduce it. Using escrow arrangements, such as central clearing houses to settle transactions (eg the DTCC in the United States) reduces settlement risk. Cash settlements based on netting arrangements reduce settlement risk, while physical delivery combined with gross cash payments increase it.

Therefore Choice 'a' is the correct answer.

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.

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

Ultimately, the objective of the operational risk severity estimation exercise is to calculate the 99.9th percentile loss over a one year horizon; and everything else we do with data, collecting loss information, modeling, curve fitting etc revolves around this objective. If we cannot estimate the 99.9th percentile loss accurately, then not much else matters. Therefore Choice 'a' is the correct answer.

Minimizing the combination of fitting and approximation errors is one of the things we do witha view to better estimating the operational loss distribution. Likewise, empirical loss data generally is range bound because corporations do not require employees to log losses less than an threshold, and high value losses are generally rare. This problemis addressed by extrapolating both large and small losses, something that impacts the performance of our model. Likewise, one of the objectives of scenario analysis is to fill data gaps by generating plausible scenarios. Yet while all these are real issues to address, the primary problem we are trying to solve is estimating the 0.999th quantile.

An interesting property that distinguishes the three most used distributions for modeling event frequency is that for a given mean, their variances differ. The ratio of variance to mean (the variance-mean ratio, calculated as variance/mean) can then be used to decide the kind of distribution to use. Both the variance and the mean can be estimated from available data points from the internal or external loss databases, or the scenario exercise.

The variance-mean ratio reflects how dispersed a distribution is. (In the PRMIA handbook, the variance to mean ratio has been described as the "Q-Factor".)

The Poisson distribution has its mean equal to its variance, and therefore the variance to mean ratio is 1. For the negative binomial distribution, this ratio is always greater than 1, which means there is greater dispersion compared to the mean - or more intervals with low counts as well as more intervals with high counts. For the binomial distribution, the variance to mean ratio is less than one, which means it is less dispersed than the Poisson distribution with values closer to the mean.

In a situation where operational risk events are seen as clustering together, ordependent, the variance will be higher and it would be more appropriate to use the negative binomial distribution.

Altman's Z-score, the Probit and the Logit models can all be used to assess the credit rating of an individual borrower. There is no such model as the 'distance todefault model', and therefore Choice 'a' is the correct answer.

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 change in the price of a security that follows a Weiner process isdetermined by its standard deviation and expected return. To get the price itself, we need to add this change in price to the current price. Therefore the future price in a Weiner process is determined by all three of current price, expected return and standard deviation.

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 managingrisk 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.