Free Practice Questions for PRMIA 8008 Exam

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.

Expected value = $90 ($100 - 10%)

Value at 99% confidence level = $65

Therefore economic capital required at this level of confidence = $90 - $65 = $25.

Choice 'a' is the correct answer, the other choices are not.

(We can also look at it this way as explained in section III.B.6.2.2 of the handbook: Economic capital is designed to absorb unexpected losses, which are equal to total losses at a given confidence level minus expected losses. (Expected losses are to be covered by credit reserves). Total losses are $100-$65=$35, and expected losses are 10%*$100=$10, therefore economic capital should be $35-$10=$25.)

When assets are uncorrelated, variances are additive. But volatility (which is standard deviation) is not. In the given situation, the total variance of the portfolio will be equal to the the square root of the sum of the variances of the assets in the portfolio weighted by the square of their weights. Its volatility will be the square root of this variance. Thus Choice 'c' is the correct answer.

(This is because V(cA + dB) = c^2 V(A) + d^2 V(B) - refer tutorial on combining variances.)

Choice 'd' is incorrect as it describes the calculation of variance, not volatility. Also, the presence of a large number of uncorrelated assets does not create a portfolio with volatility equal to zero or that of the market. The other choices are therefore incorrect.

A standard model for representing asset returns in finance is the Geometric Brownian Motion process, and returns according to this model can be estimated by the expression given in Choice 'b'. Note that prices according to this model are log-normally distributed, and returns are normally distributed.

Time invariance refers to all time intervals being similar and identical, regardless of the effects of business cycles or other external events. 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.

Rating agencies generally provide transition probability matrices for a given period of time, say a year. The risk analyst may need to convert these into matrices for say 6 months, 2 years or whatever time horizon he or she is interested in. Simplifying assumptions that allow him to do so using simple matrix multiplication include these two assumptions - time invariance and the Markov property. Thus Choice 'c' is the correct answer. The other choices (normal distribution and zero skewness) are non-sensical in this context.

When a default occurs, the proportion of the exposure represented by the recovery rate is recovered. For example, if the recovery rate is 40% for a loan, the actual loss in the event of a default would be $60 for a $100 loan. In other words, the loss given default = 1 - recovery rate. Hence Choice 'd' is the correct answer. All other choices are incorrect.

Regardless of the approach being followed by a bank (ie, whether foundation IRB or advanced IRB), it must make its own estimates for the probability of default. Banks following the foundation IRB approach may use values set by the supervisor for the other three parameters, though those following the advanced IRB approach may use their own estimates for all four inputs. (This is also the difference between advanced IRB and the foundation IRB approaches.) Therefore Choice 'a' is the correct answer.

Also note the four difference elements that go as inputs to the internal ratings based approach in the choices provided.

All product pricing should reflect the cost of maintaining the liquidity required to support a product. This is regardless of the accounting treatment for the product, ie irrespective of whether the product is on or off balance sheet. Therefore statement I is incorrect.

The time horizon to consider for liquidity risk management is determined taking into account a number of factors, which include both the speed at which new sources of liquidity can be generated and any applicable regulatory requirements. Statement II is correct.

Managing collateral, both collateral received and collateral posted with counterparties, is an important aspect of liquidity risk management as liquidity problems often manifest themselves in the form of margin calls requiring collateral to be posted. Statement III is therefore correct.

The maturity period of the different sources of capital funding for a bank, for example equity capital, preferred shares, long term debt etc quite clearly has a significant impact on liquidity needs. Stable sources of funds such as equity or preferred capital, or debt that is not maturing shortly help the liquidity position. Statement IV is therefore correct.

Choice 'b' is the correct answer.

If you have not studied PCA prior to the preparing for the PRMIA exams, you will find the handbook to be a bit difficult to understand this topic. However, PRMIA have been asking questions about PCA on their exams so it is important to conceptually know what PCA is (and be able to answer the exam questions which are unlikely to ever require you to do a calculation).

Using PCA, a complex correlated system (eg, the rates in a term structure which are all correlated to each other) is effectively transformed into a 'principal component representation'. A principal component representation expresses each of the independent variables in the system as a linear representation based on 'principal components'. Principal components are derived from the eigenvectors of the correlation matrix. Remember that if you have a positive semi-definite correlation matrix (which will be an n x n square matrix), it will have 'n' eigenvectors, each with an eigenvalue. The eigenvectors will be orthogonal (ie perpendicular) to each other. The eigenvalues for each of the eigenvectors determine which are principal components - in descending order of the eignevalues. Therefore the eigenvector with the highest eigenvalue is the first principal component, the second highest value the second principal component and so on. If there are n variables in the system, then eigenvalue divided by n gives us the proportion of the variation explained by that particular principal component.

In the case of a PCA done on the term structure of interest rates, the first principal component is the 'trend' component, and under a principal component representation its coefficients are given by the first eigenvector. (By the way, remember the next two principal components are tilt and curvature respectively). If these coefficients are the same (they are, for an interest rate term structure), this means all rates move up or down when the value of the first principal component moves. Thust factor weights on the first component show whether there is common trend in the system. Statement I is correct.

The factors to be applied to the principal components are indeed obtained from the eigenvectors of the correlation matrix (and not the covariance matrix), and therefore statement II is correct.

PCA is used to reduce dimensionality, this is true and in fact one of the main reasons why PCA is used at all. Therefore statement III is correct.

Statement IV is false as it is the largest eigenvalues and not the smallest that determine the eigenvectors affecting most of the variation (through the principal components they represent).

Thus Choice 'b' is the correct answer.