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Quiz Updated PRMIA - Exam 8011 Lab Questions
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PRMIA Credit and Counterparty Manager (CCRM) Certificate Exam Sample Questions (Q93-Q98):
NEW QUESTION # 93
Which of the following is true in relation to Principal Component Analysis (PCA)?
I. An n x n positive definite square matrix will have n-1 eigenvectors
II. The eigenvalues for a correlation matrix can be derived from the corresponding values for the covariance matrix III. Principal components are uncorrelated to each other IV. PCA is useful as it allows 100% of the variation in a complex system to be explained by the first three principal components
- A. III and IV
- B. I and III
- C. I, II and IV
- D. III
Answer: D
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.
NEW QUESTION # 94
There are two bonds in a portfolio, each with a market value of $50m. The probability of default of the two bonds over a one year horizon are 0.03 and 0.08 respectively. If the default correlation is zero, what is the one year expected loss on this portfolio?
- A. $5.5m
- B. $1.38m
- C. $11m
- D. $5.26m
Answer: A
Explanation:
The probabilities of default of the two bonds are independent (as indicated by a zero default correlation). The various possible states of the portfolio are as follows:
First bond defaults, and the second does not: Probability * Loss = 0.03*0.92 * $50m = $1.38m Second bond defaults, and the first does not: Probability * Loss = 0.97*0.08 * $50m = $3.88m Both bonds default: Probability * Loss = 0.03*0.08 * $100m = $0.24m Thus total expected loss on this portfolio = $5.5m. Since recovery rates are not provided, those should be assumed to be zero.
There is an easier way to solve this as well: default correlation does not affect expected losses, but their volatility. You can calculate the expected losses of the two bonds and add them up, ie, $50m*0.03 + $50m *0.
08 = $5.5m
NEW QUESTION # 95
If the loss given default is denoted by L, and the recovery rate by R, then which of the following represents the relationship between loss given default and the recovery rate?
- A. L = 1 + R
- B. R = 1 / L
- C. R = 1 + L
- D. R = 1 - L
Answer: D
Explanation:
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.
NEW QUESTION # 96
The frequency distribution for operational risk loss events can be modeled by which of the following distributions:
I. The binomial distribution
II. The Poisson distribution
III. The negative binomial distribution
IV. The omega distribution
- A. I, III and IV
- B. I, II, III and IV
- C. I and III
- D. I, II and III
Answer: D
Explanation:
The binomial, Poisson and the negative binomial distributions can all be used to model the loss event frequency distribution. The omega distribution is not used for this purpose, therefore Choice 'a' is the correct answer.
Also note that the negative binomial distribution provides the best model fit because it has more parameters than the binomial or the Poisson. However, in practice the Poisson distribution is most often used due to reasons of practicality and the fact that the key model risk in such situations does not arise from the choice of an incorrect underlying distribution.
NEW QUESTION # 97
Which of the following cannot be used to address the issue of heavy tails when modeling market returns
- A. EWMA
- B. EVT
- C. Normal mixtures
- D. Student's t-distribution
Answer: A
Explanation:
Normal mixtures, EVT and the t-distribution are all possible solutions addressing the issue of heavy tails in financial returns.
EWMA and GARCH address volatility clustering, which is the other problem when doing risk calculations.
Therefore Choice 'b' is the correct answer as EWMA is not used to address heavy tails but volatility clustering.
NEW QUESTION # 98
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