Explanation
The three pillars are minimum capital requirements, supervisory review and market discipline. National regulation is not a pillar described under the accord. Choice 'c' is the correct answer.

Explanation
This is a tricky question in the sense no risk management professional can be expected to know the answer to this one unless they have read Chapter 2 of the PRMIA handbook. So this question appears purely for the sake of something you would need to know purely for the sake of the exam.
PRMIA's handbook classifies governance sructures as reactive, preventative and active. Reactive structures involve monitoring signals after the event leading to corrective actions. Preventative structures are forward looking and anticipate issues before they arise. Active structures include considerations of operational efficiency and not just governance. All other answers are made up phrases and are incorrect.
In reality, corporations employ all structures together without worrying about the boundary between the three, and these distinctions do not exist except in textbooks.

Explanation
Bank B's exposure is measured by the price it paid for the bonds, which in this case is $7m ($10m x 70/100).
Hence Choice 'c' represents the correct answer.
(Note that the question is asking for 'exposure' and not the legal claim in the event of default. The legal claim in the event of default would be the full notional of $10m. ) The initial issue price and issue size are irrelevant.

Explanation
An n x n positive definite square matrix will have n eigenvectors, and not n - 1. Therefore statement I is incorrect.
A correlation and covariance matrix are related to each other through the matrix of standard deviations. If the covariance matrix is represented by V, the correlation matrix by C and D is the diagonal matrix of standard deviations, then V = DCD. However, there is no simple relationship between the eigenvalues of the two matrices, and it is not possible to derive the eigenvalues for one given the eigenvalues for the other. Therefore statement II is false.
Principal components are uncorrelated to each other. That is correct, and in fact PCA is useful because of this being so. Statement III is therefore true.
PCA does not explain 100% of the variation in a system with just three components - statement IV is false.
(Remember though that most (though not 100%) of the variation in a system of term structures is explained by the first three components - trend, tilt and curvature).
Thus Choice 'd' is the correct answer.

Explanation
When we do a Monte Carlo simulation, the statistic we obtain (eg, the expected price) is an estimate of the real variable. The difference between the real value (which would be what we would get if we had access to the entire population) and that estimated by the Monte Carlo simulation is measured by the 'standard error', which is the standard deviation of the difference between the 'real' value and the simulated value (ie, the 'error').
As we increase the number of draws in a Monte Carlo simulation, the closer our estimate will be to the true value of the variable we are trying to estimate. But increasing the sample size does not reduce the error in a linear way, ie doubling the sample size does not halve the error, but reduces it by the inverse of the square root of the sample size. So if we have a sample size of 1000, going up to a sample size of 100,000 will reduce the standard error by a factor of 10 (and not 100), ie, SQRT(1/100) = 1/10. In other words, standard error is proportional to 1/N, where N is the sample size.
Therefore Choice 'c' is correct and the others are incorrect.