PRMIA 8010 - Operational Risk Manager (ORM) Exam

All four data sources are expected to be utilized as inputs as appropriate for operational risk calculations under the advanced measurement approach. Of these, the last one, BEICF, is slightly different from the rest as it does not yield data points that becomethe basis of curve fitting or other statistical computions underlying capital calculations. It includes items such as KRIs, risk assessments etc and allow the risk manager to assess the qualitative aspects of loss data.

Choice 'c' correctly describes Altman's z-score. All other choices are incorrect.

Probability of the joint default of both A and B =

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

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

Solving, we get default correlation = 25%

The correct answer is choice 'b'

Both statements are accurate. Basel IIrequires pooled probabilities of default to be applied to risk buckets that contain similar exposures. Also, stress testing is mandatory for both market and credit risk.

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 unexpectedlegal 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 examplea 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 difference between the yields oncorporate bonds and the risk free rate is called the corporate bond spread. Widening of the spread means that corporate bonds yield more, and their yield curve shifts upwards, driving down bond prices. The increase in the spread is a consequence of the market risk from holding these interest rate instruments, which is a part of market risk. If the reduction in the value of the portfolio were to be caused by a change in the credit rating of the bonds held, it would have been a loss arising due to credit risk. Counterparty risk and liquidity risk are not relevant for this question. Therefore Choice 'c' is the correct answer.

Counterparty risk was difficult to gauge as it was impossible to know who the counterparty's counterparties were - this is true as the chain of financial transactions became excessively long with no central transparency of who owed who what. Bank A's credit depended upon the health of its counterparties, whose health in turn depended upon other counterparties. Thus Choice 'd' is a correct statement.

In an attempt to diversify, banks became more like each other - chasing yield, they piled into securitized products, and chasing diversification, they piled into different types of securitized products. The system as a whole became susceptible to small shocks in the assets underlying this vast edifice of structured products. Therefore Choice 'a' represents a correct statement.

Choice 'c' does not represent a correct statement. Central banks had little data on the interconnections between institutions. They were aware of the large volumes of OTC transactions, but had no data to figure out who was connected to who, and who had what kind of exposures.

Choice 'b' represents a correct statement. Most transactions, other than exchange cleared futures trades (which were atiny fraction of all trades) were cleared on a bilateral basis. The existence of central counterparties (CCPs) could have limited the impact of the crisis significantly as market participants would not have lost trust in each other, and the 'collateral damage' that was witnessed from a fall in housing prices, and thereby mortgage assets, would have been more contained.

A recap would be in order here: calculating operational risk capital is a multi-step process.

First, we fit curves to estimate the parameters to our chosen distribution types for frequency (eg, Poisson), and severity (eg, lognormal). Note that these curves are fitted at the UoM level - which is the lowest level of granularity at which modeling is carried out. Since there are many UoMs, there are are many frequency and severity distributions. However what we are interested in is the loss distribution for the entire bank from which the 99.9th percentile loss can be calculated. From the multiple frequency and severity distributions we have calculated, this becomes a two step process:

- Step 1: Calculate the aggregate loss distribution for each UoM. Each loss distribution is based upon and underlying frequency and severity distribution.

- Step 2: Combine the multiple loss distributions after considering the dependence between the different UoMs. The 'dependence' recognizes that the various UoMs are not completely independent, ie the loss distributions are not additive, and that there is a sort of diversification benefit in the sense that not all types of losses can occur at onceand the joint probabilities of the different losses make the sum less than the sum of the parts.

Step 1 requires simulating a number, say n, of the number of losses that occur in a given year from a frequency distribution. Then n losses are picked from theseverity distribution, and the total loss for the year is a summation of these losses. This becomes one data point. This process of simulating the number of losses and then identifying that number of losses is carried out a large number of times to get the aggregate loss distribution for a UoM.

Step 2 requires taking the different loss distributions from Step 1 and combining them considering the dependence between the events. The correlations between the losses are described by a 'copula', andcombined together mathematically to get a single loss distribution for the entire bank. This allows the 99.9th percentile loss to be calculated.

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.

Credit risk is the risk from a borrower defaulting on moneys lent. Counterparty risk, on the other hand, is the risk that a counterparty to a derivativetransaction will be unable to pay at the time the transaction is in-the-money.

Credit risk therefore relates more to the banking book, counterparty risk relates more to the trading book. Credit risk and counterparty risk differ in that for counterparty risk, the amount at risk fluctuates for counterparty risk depending upon the value of the underlying derivative. Counterparty risk generally starts at zero, for most swaps and other derivatives are near zero value at inception. Over time, as the prices of theunderlying instruments move, one party ends up owing money to the other. A deterioration in the financial situation of the party owing moneys may lead to a loss to the other party, resulting in counterparty risk. Counterparty risk can also arise from stock lending operations and repo trades.

Credit risk on the other hand is the traditional risk of default by a borrower, or a bank's customer who has taken a loan or has an overdraft or other credit facility.

Statement I is therefore incorrect as credit riskand counterparty risks are different.

Statement II is correct as counterparty risk is 'contingent' in the sense it arises only if the transaction with the counterparty ends up being in-the-money, and the counterparty defaults.

Statement III is incorrect. The statement describes credit risk.

Statement IV is incorrect, as the exposure is known for moneys lent. Derivative exposures for the future are difficult to estimate, they can even turn from moneys owed to moneys due as the value of the underlying changes.