Free 8010 Practice Test Questions and Answers (2026) | Cert Empire Practice Questions

The credit migration approach to assessing portfolio credit risk involves obtaining a distribution of

future portfolio values from the ratings migration matrix. First, the frequencies in the matrix are used

as probabilities, and expected future values of the securities belonging to each rating category are

calculated. These are then discounted to the present using the discount rate appropriate to the

'future' rating category. This gives us a forward distribution of the value of each security in the

portfolio. These are then combined using the default correlations between the issuers. The default

correlation between the issuers is often proxied using asset returns, and recognizing that default

occurs when asset values fall below a certain threshold. A distribution for the future value of the

portfolio is generated using simulation, and from this distribution the Credit VaR can be calculated.

Thus, we need the migration matrix, the risk horizon from which the present values need to be

calculated, and the forward yield curve or the discount curve for each rating category for the risk

horizon. Thus, Choice 'd' is the correct answer.

According to the Basel II framework, Tier 1 capital, also called core capital or basic equity, includes

equity capital and disclosed reserves.

Tier 2 capital, also called supplementary capital, includes undisclosed reserves, revaluation reserves,

general provisions/general loan-loss reserves, hybrid debt capital instruments and subordinated

term debt.

Tier 3 capital, or short term subordinated debt, is intended only to cover market risk but only at the

discretion of their national authority.

The Earnings Volatility approach to calculating economic capital is a top down approach that

considers economic capital as being the capital required to make for the worst case fall in earnings,

and calculates EC as equal to the worst case decrease in earnings capitalized at the rate of return

expected of the firm. The worst case decrease in earnings, or the earnings-at-risk can only be stated

at a given confidence level, and is equal to the Expected Earnings less Earnings under the worst case

scenario.

Choice 'a' is the correct answer. 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.

Statement I is true - component VaR for individual assets in the portfolio add up to the total VaR for

the portfolio. This property makes component VaR extremely useful for risk disaggregation and

allocation.

Stateent II is incorrect, the incremental VaRs for the positions in a portfolio do not add up to the

portfolio VaR, in fact their sum would be greater.

Statement III is correct. Marginal VaR for an asset or position in the portfolio is by definition the

change in the VaR as a result of a $1 change in that position. Incremental VaR is the change in the VaR

for a portfolio from a new position added to the portfolio - and if that position is $1, it would be

identical to the marginal VaR.

Statement IV is correct, VaR is sub-additive due to the diversification effect. Adding up the VaRs for

all the positions in a portfolio will add up to more than the VaR for the portfolio as a whole (unless all

the positions are 100% correlated, which effectively would mean they are all identical securities

which means the portfolio has only one asset).

Statement V is in incorrect. As explained for Statement I above, component VaR adds up to the VaR

for the portfolio.

Total expected losses which are average and anticipated are equal to the sum of expected losses in

the underlying exposures. Total unexpected losses, which are the excess of worst case losses at a

certain confidence level over the expected losses, benefit from the diversification effect and are

lower than the sum of unexpected losses of the underlying exposures. Therefore Choice 'c' is the

correct answer. The other choices are incorrect.

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.

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.

Choice 'c' is the correct answer. The Markov property is the assumption that there is no ratings

momentum, and that transition probabilities are dependent only upon where the rating currently is

and where it is going to. Where it has come from, or what the past changes in ratings have been,

have no effect on the transition probabilities. ('Herstatt risk' refers to settlement risk, and is

irrelevant.)

p = k/N. If there are N observations of which K are upto T, then p = k/N allows us to have a

continuous unbroken curve which gets increasingly weighted towards the distribution selected for

the tail as we move towards the 'right', ie the higher values of losses.

The other choices are incorrect and mostly nonsensical.

All the factors listed above contributed to systemic failure. Liquidity risk was not on the radar of

regulators, and was a second priority for risk managers, and most of the focus was on capital

adequacy as liquidity was thought to be an unlikely problem. Liquidity, regardless of capital

adequacy, was the primary cause of failure of a number of institutions during the crisis.

Similarly, stress tests proved to be much milder than the shocks that were actually experienced, and

the strategy of 'originate and distribute' implied that the mortgage and other debt originators had no

interest in any due diligence as they intended to package and sell the debt to other investors.

Therefore Choice 'd' is the correct answer.

Once we have a number of distributions in the model space, the task is to select the "best"

distribution that is likely to be a good estimate of true severity. We have a number of distributions to

pick from, an empirical dataset (from internal or external losses), and we can estimate the

parameters for the different distributions. We then have to decide which distribution to pick, and

that generally requires considering both approximation and fitting errors.

There are three methods that are generally used for selecting a model:

1. The cross-validation method: This method divides the available data into two parts - the training

set, and the validation set (the validation set is also called the 'testing set'). Parameter estimation for

each distribution is done using the training set, and differences are then calculated based on the

validation set. Though the temptation may be to use the entire data set to estimate the parameters,

that is likely to result in what may appear to be an excellent fit to the data on which it is based, but

without any validation. So we estimate the parameters based on one part of the data (the training

set), and check the differences we get from the remaining data (the validation set).

2. Complexity penalty method: This is similar to the cross-validation method, but with an additional

consideration of the complexity of the model. This is because more complex models are likely to

produce a more exact fit than simpler models, this may be a spurious thing - and therefore a 'penalty'

is added to the more complex models as to favor simplicity over complexity. The 'complexity' of a

model may be measured by the number of parameters it has, for example, a log-normal distribution

has only two parameters while a body-tail distribution combining two different distributions may

have many more.

3. The bootstrap method: The bootstrap method estimates fitting error by drawing samples from the

empirical loss dataset, or the fit already obtained, and then estimating parameters for each draw

which are compared using some statistical technique. If the samples are drawn from the loss dataset,

the technique is called a non-parametric bootstrap, and if the sample is drawn from an estimated

model distribution, it is called a parametric bootstrap.

4. Using goodness of fit statistics: The candidate fits can be compared using MLE based on the KS

distance, for example, and the best one selected. Maximum likelihood estimation is a technique that

attempts to maximize the likelihood of the estimate to be as close to the true value of the parameter.

It is a general purpose statistical technique that can be used for parameter estimation technique, as

well as for deciding which distribution to use from the model space.

All the choices listed are the correct answer.

Credit reserves are created in respect of expected losses, which are considered the cost of doing

business. Unexpected losses are borne by economic credit capital, which is a part of economic

capital. Therefore Choice 'c' is the correct answer.

An observed fact that the KMV approach relies upon is that firms do not default when their liabilities

exceed assets, but when asset values are somewhere between short term liabilities and the total

liabilities. In fact, the 'default point' in the KMV methodology is defined as the short term debt plus

half of the long term debt. The difference between expected value of the assets in one year and this

'default point', when expressed in terms of standard deviation of the asset values, is called the

'distance-to-default'.

Therefore Choice 'd' is the correct answer. The other choices are incorrect.

The default correlation between two obligors goes up if the joint probability of default between

them increases. This is intuitive. Also consider the formula for the default correlation between two

obligors

Default correlation = [P(1,2) - P1 * P2] / √P1*(1-P1)*P2*(1-P2); where P(1,2) is the joint probability of

default between the two and P1 and P2 are their individual probabilities of default. Obviously, an

increase in P(1,2) will cause the default correlation to increase.

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%)

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 market

prices 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 sold in 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 Basel II framework allows the use of the basic indicator approach, the standardized approach

and the advanced measurement approaches for operational risk. There is no approach called the

'internal measurement approach' permitted for operational risk. Choice 'a' is therefore the correct

answer.

The difference between the yields on corporate 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.

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 once and 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 the severity 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', and combined together mathematically to get a single loss distribution for the entire bank.

This allows the 99.9th percentile loss to be calculated.