8010 Operational Risk Manager (ORM) Exam Questions and Answers

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

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 canbe 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 waysin 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% confidencelevel, 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 actuarial or CreditRisk+ model considers default as an 'end of game' event modeled by a Poisson distribution. The annual number of defaults is a stochastic variable with a mean of μ and standard deviation equal to √μ.

The probability of n defaults is given by (μ^n e^-μ) /n!, and therefore in this case is equal to (=2^4 * exp(-2))/FACT(4)) = 0.0902.

Note that CreditRisk+ is the same methodology as the actuarial approach, and requires using thePoisson distribution.

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.

Basel II proposes three approaches to compute operational risk capital - the basic indicator approach(BIA), the standardized approach (SIA) and the advanced measurement approach (AMA). There is no operational risk approach called the factor based approach.

Choice'a' is the correct answer. Exposures such as those to a line of credit of which only a part (or none) may be drawn at the time of assessment present a difficulty when attempting to quantify credit risk. It is not correct to take the entire amount of the line as the exposure at default, and likewise the current exposure is likely to be too aggressively low a number to consider.

While the borrower has an information advantage in that he would be aware of the deterioration in credit standing before the bank and would probably draw cash prior to default, it is unlikely that the entire amount of the line of credit would be drawn in all cases. In some cases, none may be drawn. In other cases, the bank would become aware of the situation and curtail or cancel access to the credit line in a timely fashion.

Therefore a fixed proportion of existing credit lines is considered a reasonable approximation of the exposure at default against credit lines.

In a bankruptcy, equity ranks last. Preferred equity is one level above equity. Senior debt gets paid outfirst compared to junior debt, and secured debt is paid out first to the extent of the asset securing it (after which it counts as unsecured debt). Accounts payable and other short term liabilities are treated like unsecured creditors. Debtor-in-possession(DIP) financing ranks higher than any other asset as it is financing secured after the bankruptcy to continue the business.

Based on the above, statement I does not represent a correct ordering of seniority as equity is paid last. Similarly, DIP financingreceives higher priority than even secured debt, and therefore statement IV is incorrect. Therefore the only correct statements are II and III and Choice 'a' 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.

Model risk is the risk that a model built for estimating a variable will produce erroneous estimates. Model risk is caused by a number of factors, including:

a) Misspecifying the model: For example, using a normal distribution when it is not justified.

b) Model misuse: For example, using a model built to estimate bond prices to estimate equity prices

c) Parameter estimation errors: In particular, parameters that are subjectively determined can be subject to significant parameter estimation errors

d) Programming errors: Errors in coding the model as part of computer implementation may not be detected by end users

e) Data errors: Errors in data used for building the model may also introduce model risk

Therefore the correct answer is d, as all the choices are a source of model risk.

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. Riskfactors 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.

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.

Refer to the detailed loss event type classification under Basel II (see Annex 9 of the accord). You should know the exact names of all loss event types, and examples of each.

The probability that only one of thethree bonds will default is equal to the sum of the probabilities of the three scenarios where one bond defaults and the other two survive. This probability is given by 1%*(1 - 2%)*(1 - 3%) + (1 - 1%)*2%*(1 - 3%) + (1 - 1%)*(1 - 2%)*3% = 5.7818%. Choice 'c' is the correct answer.

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

It does not consider Net Income to total assets, therefore Choice 'c' is the correct answer. This makes sense as net income is after interest and taxes, both of which are not relevant for considering the cash flows for debt servicing.

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.

The probability that the security would not default in the next 4 years is equal to the probability of survival raised to the power four. In other words, =(1 -3%)^4 = 88.53%. Choice 'b' is the correct answer.

Concentration risk in a credit portfolio arises due to a high degree of correlation betweenthe default probabilities of the issuers of securities in the portfolio. For example, the fortunes of the issuers in the same industry may be highly correlated, and an investor exposed to multiple such borrowers may face 'concentration risk'.

A low degreeof correlation, or independence of individual defaults in the portfolio actually reduces or even eliminates concentration risk.

The fact that issuers are from the same country may not necessarily give rise to concentration risk - for example, a bank withall US based borrowers in different industries or with different retail exposure types may not face practically any concentration risk. What really matters is the default correlations between the borrowers, for example a lender exposed to cement producersacross the globe may face a high degree of concentration risk.

A LIBOR based loan requires cash to move from the lenderto the borrower in the amount of the notional. The Overnight Index Swap requires only the exchange of interest payments, and therefore represents less risk.

Therefore the LIBOR based loan is a riskier exposure.

The LIBOR is generally higher than the OIS. In fact, the difference between the two, the LIBOR-OIS spread, is a standard measure of the risk premium in the market that goes up when the risk of default by counterparty banks is considered high. This is because when the market perceives the risk of default to be high, the participants need a risk premium to take on the default risk which is considerably lesser with the OIS.

Under theCreditPortfolio View approach, the credit rating transition matrix is adjusted for the state of the economy in a way as to increase the probability of defaults when the economy is not doing well, and vice versa. Therefore Choice 'a' is the correct answer.The other choices represent nonsensical options.

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 tothe actuarial approach.

The current Basel rules for the basic VaR based charge formarket risk capital set market risk capital requirements as the maximum of the following two amounts:

1. 99%/10-day VaR,

2. Regulatory Multiplier x Average 99%/10-day VaR of the past 60 days

The 'regulatory multiplier' is a number between 3 and 4 (inclusive) calculated based on the number of 1% VaR exceedances in the previous 250 days, as determined by backtesting.

- If the number of exceedances is <= 4, then the regulatory multiplier is 3.

- If the number of exceedances is between 5 and 9, then the multiplier = 3 + 0.2*(N-4), where N is the number of exceedances.

- If the number of exceedances is >=10, then the multiplier is 4.

So you can see that in most normal situations the risk capital requirement will be dictated by the multiplier and the prior 60-dayaverage VaR, because the product of these two will almost often be greater than the current 99% VaR.

The correct answer therefore is = max(200mm, 3*250mm) = $750mm.

Interestingly, also note that a 99% VaR should statistically be exceeded 1%*250 days = 2.5times, which means if the bank's VaR model is performing as it should, it will still need to use a reg multiplier of 3.

The binomial, Poisson and the negative binomialdistributions can all be used to model the loss event frequency distribution. The omega distribution is not used for this purpose, therefore Choice 'a' is the correct answer.

Also note that the negative binomial distribution provides the best model fit because it has more parameters than the binomial or the Poisson. However, in practice the Poisson distribution is most often used due to reasons of practicality and the fact that the key model risk in such situations does not arise from the choice of an incorrect underlying distribution.

Top down approaches rely upon available data such as total capital, income volatility, peer group information etc and attempt to imply the capital attributable to operational risk. They do not consider firm specific scenarios or causal factors. Bottom up approaches on the other hand attempt to determine operational risk capital based upon an identification and quantification of firm specific risks. Bottom up approaches help determine a traditional loss distribution from which capital requirements can be determined at a given level of confidence.

Therefore Choice 'd' is the correct answer.

The greatest model risk when calculating operational risk capital comes fromincorrect assumptions about correlations between different operational risks for which standalone risk calculations have been made. Generally, the correlation can be expected to be positive, and would therefore vary between 0 and 1. These two values determine the 'bounds' between which the total operational risk capital would lie, and these bounds are generally quite far apart. Therefore the total value of the operational risk capital is very sensitive to the value chosen for the correlation, and this is the source of the biggest model risk under the AMA.

With the passage of time, the range of possible values the FX contract can take increases. Therefore the maximumvalue 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.

The probability of default would make the expected value of the future cash flows from both the corporate bond and the risk free bond 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))

=> 5%*0 + (1 - 5%)*(1 + 12%) = (1 + Rf).

therefore Rf = 6.4%

(In reality investors would demand a 'credit risk premium' 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.)

According to a paper by the BCBS, here is an excellent summary of what happened. Based on this, Choice 'c' is the correct answer.

"At the outset of the crisis, mortgage default shocks played a part in the deterioration of marketprices of collateralised debt obligations (CDOs). Simultaneously, these shocks revealed deficiencies in the models used to manage and price these products. The complexity and resulting lack of transparency led to uncertainty about the value of the underlying investment. Market participants then drastically scaled down their activity in the origination and distribution markets and liquidity disappeared. The standstill in the securitisation markets forced banks to warehouse loans that were intended to be soldin the secondary markets. Given a lack of transparency of the ultimate ownership of troubled investments, funding liquidity concerns were triggered within the banking sector as banks refused to provide sufficient funds to each other. This in turn led to the hoarding of liquidity, exacerbating further the funding pressures within the banking sector. The initial difficulties in subprime mortgages also fed through to a broader range of market instruments since the drying up of market and funding liquidity forced market participants to liquidate those positions which they could trade in order to scale back risk. An increase in risk aversion also led to a general flight to quality, an example of which was the high withdrawals by households from money market funds."

The first two formulae describe component VaR. The last formula is the formula for Marginal VaR. Therefore I and II is the correct answer.

Component VaR is a VaR decomposition technique that allows the total VaR for a portfolio to be broken down and attributed to the components of a portfolio. The total of the component VaR for each constituent of a portfolio is equal to the VaR for the portfolio. This property is extremely useful as opposed to the standalone VaR for each constituent taken alone as it can be used for allocating trading budgets.

The persistence parameter, λ, is the coefficient of the prior day's variance in EWMA calculations. A higher value of the persistence parameter tends to 'persist' the prior value of variance for longer. Consider an extreme example - if the persistence parameter is equal to 1, the variance under EWMA will never change in response to returns.

1 - λ is the coefficient of recent market returns. As λ is lowered, 1 - λ increases,giving a greater weight to recent market returns or shocks. Therefore, as λ is lowered, the model will react faster to market shocks and give higher weights to recent returns, and at the same time reduce the weight on prior variance which will tend to persist for a shorter period.

The distance to default is the number of standard deviations that expected asset values are away from the default point. The expression in Choice 'd' represents distance to default. Choice 'd' is the correct answer. The other choices are incorrect.

Conditional default probabilitiesare modeled as a logit function under CreditPortfolio view. That ensures the resulting probabilities are 'well behaved', ie take a value between 0 and 1. The probability may be expressed as = 1/ (1 + exp(I)), where I is a country specific index taking various macro economic factors into account.

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.

Since the business units are perfectly correlated, we can get the combined EC as equal to the sum of the individual EC estimates.Therefore Choice 'a' is the correct answer.