Pass the PRMIA PRM Certification 8010 Questions and answers with CertsForce

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%)

All the reasons and risks presented above are valid reasons for using scenario analysis, except V and VI - ie, the need to reduce the complexity of calculations is not a valid reason for using scenario analysis. Similarly, making operational risk capital estimates match management's desired capital allocation targets is also not a valid reason. Capital calculations are intended to provide adequate capital for managing the risk from operations, regardless of what management may desire them to be.

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.

The easiest way to answer this question is to ignore the joint probability of default as thatis irrelevant to expected losses. The joint probability of default impacts the volatility of the losses, but not the expected amount. One way to think about it is to think of asset portfolios, where diversification reduces risk (ie standard deviation) butthe expected returns are nothing but the average of the expected returns in the portfolio. Just as the expected returns of the portfolio are not affected by the volatility or correlations (these affect standard deviation), in the same way the joint probability of default does not affect the expected losses. Therefore the expected losses for this portfolio are simply $1m x 10% + $1m x 15% = $250,000.

This can also be seen from the lens of a joint probability distribution as follows:

There are four possibilities for this portfolio:

- Only loan A defaults: loss of $1m: 9% probability

- Only loan B defaults: loss of $1m: 14% probability

- Both loan A and B default: loss of $2m: 1% probability

- Neither A nor B default: loss of $0m: 76% probability

Therefore the expected losses on the portfolio are ($1m x 9%) + ($1m x 14%) + ($2m x 1%) + ($0m x 76%) = $250,000.

(Notes: How is the above table calculated? The totals (10%, 90%, 15% and 85%) are filled in first. The top left cell (both A & B default) is given as 1%. We can now calculate the rest of the cells as the totals are known.)

The correct answer is choice 'a'

The correct order of steps to addressing data quality problems in an organization would include:

1. Assesing the current state

2. Designing the future state, and

3. Planning and implementation which would include identifying the gaps between the current and the desired future state, and implementation to address the gaps.

Therefore Choice 'a' is the correct answer.

Choice 'c' is incorrect because a gap analysis cannot be performed without understanding the 'as-is' (which results from understanding the current state).

Choice 'b' is non-sensical, and Choice 'd' is a flippant option (though often used in real life situations by management as an easy (and ineffective) way to escape accountability for difficult problems)

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.

All of the properties described are the properties of a 'coherent' risk measure.

Monotonicity means that if a portfolio's future value is expected to be greater than that of another portfolio, its risk should be lower than thatof the other portfolio. For example, if the expected return of an asset (or portfolio) is greater than that of another, the first asset must have a lower risk than the other. Another example: between two options if the first has a strike price lower thanthe second, then the first option will always have a lower risk if all other parameters are the same. VaR satisfies this property.

Homogeneity is easiest explained by an example: if you double the size of a portfolio, the risk doubles. The linear scaling property of a risk measure is called homogeneity. VaR satisfies this property.

Translation invariance means adding riskless assets to a portfolio reduces total risk. So if cash (which has zero standard deviation and zero correlation with other assets) is added to a portfolio, the risk goes down. A risk measure should satisfy this property, and VaR does.

Sub-additivity means that the total risk for a portfolio should be less than the sum of its parts. This is a property that VaR satisfies most of thetime, but not always. As an example, VaR may not be sub-additive for portfolios that have assets with discontinuous payoffs close to the VaR cutoff quantile.

Extreme value theory focuses on the extreme and rare events, and in the case of VaR calculations, it is focused on the right tail of the lossdistribution. In very simple and non-technical terms, EVT says the following:

1. Pull a number of large iid random samples from the population,

2. For each sample, find the maximum,

3. Then the distribution of these maximum values will follow a GeneralizedExtreme Value distribution.

(In some ways, it is parallel to the central limit theorem which says that the the mean of a large number of random samples pulled from any population follows a normal distribution, regardless of the distribution of the underlying population.)

Generalized Extreme Value (GEV) distributions have three parameters: ξ (shape parameter), μ (location parameter) and σ (scale parameter). Based upon the value of ξ, a GEV distribution may either be a Frechet, Weibull or a Gumbel. These arethe only three types of extreme value distributions.

By assuming the assets to be independent, we are reducing the correlation from a positive number to zero. Reducing asset correlations reduces the combined standard deviation of the assets, and therefore reduces economic capital. Therefore Choice 'b' is the correct answer.

Note that this question could also be phrased in terms of the impact on VaR estimates, and the answer would still be the same. Both VaR and economic capital are a multiple of standard deviation, and if standard deviation goes down, both VaR and economic capital estimates will reduce.

Marginal VaR of a component of a portfolio is the change in the portfolio VaR from a $1 change in the value of the component. It helps a risk analyst who may be trying to identify the best way to influence VaR by changingthe components of the portfolio. Marginal VaR is also important for calculating component VaR (for VaR disaggregation), as component VaR is equal to the marginal VaR multiplied by the value of the component in the portfolio.

Marginal VaR is by definitionthe derivative of the portfolio value with respect to the component i. This is reflected in Choice 'a' above. Using the definitions and relationships between correlation, covariance, beta and volatility of the portfolio and/or the component, we can show that the other two choices are also equivalent to Choice 'a'.

Therefore all the choices present are correct.