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.