PRMIA 8007 Exam II: Mathematical Foundations of Risk Measurement – 2015 Edition Online Training
PRMIA 8007 Online Training
The questions for 8007 were last updated at Apr 23,2025.
- Exam Code: 8007
- Exam Name: Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition
- Certification Provider: PRMIA
- Latest update: Apr 23,2025
You are given the following regressions of the first difference of the log of a commodity price on the lagged price and of the first difference of the log return on the lagged log return. Each regression is based on 100 data points and figures in square brackets denote the estimated standard errors of the coefficient estimates:
Which of the following hypotheses can be accepted based on these regressions at the 5% confidence level (corresponding to a critical value of the Dickey Fuller test statistic of C 2.89)?
- A . The commodity prices are stationary
- B . The commodity returns are stationary
- C . The commodity returns are integrated of order 1
- D . None of the above
In a multiple linear regression, the significance of R2 can be tested using which distribution?
- A . Normal distribution
- B . Student’s t distribution
- C . F-distribution
- D . Binomial distribution
If A and B are two events with P(A) = 1/4, P(B) = 1/3 and P(A intersection B) =1/5, what is P(Bc | Ac) i.e. the probability of the complement of B when the complement of A is given?
- A . 12/29
- B . 37/45
- C . 3/4
- D . None of these
What is the maximum value of the function F(x, y)=x2+y2 in the domain defined by inequalities x 1, y -2, y-x 3 ?
- A . 29
- B . -25
- C . 1
- D . 17
Which of the following statements are true about Maximum Likelihood Estimation?
(i) MLE can be applied even if the error terms are not i.i.d. normal.
(ii) MLE involves integrating a likelihood function or a log-likelihood function.
(iii) MLE yields parameter estimates that are consistent.
- A . (i) and (ii)
- B . (i) only
- C . (i) and (iii)
- D . (i), (ii), and (iii)
An option has value 10 when the underlying price is 99 and value 9.5 when the underlying price is 101. Approximate the value of the option delta using a first order central finite difference.
- A . -4
- B . 0.25
- C . -0.5
- D . -0.25
Every covariance matrix must be positive semi-definite. If it were not then:
- A . Some portfolios could have a negative variance
- B . One or more of its eigenvalues would be negative
- C . There would be no Cholesky decomposition matrix
- D . All the above statements are true
Which of the following can be used to evaluate a regression model?
(i) Magnitude of R2
(ii) Magnitude of TSS (total sum of squares)
(iii) Tests for statistical significance
(iv) Sign and magnitude of each regression parameter
- A . (i) and (iv)
- B . (i), (ii), and (iii)
- C . (i), (iii), and (iv)
- D . (i), (ii), (iii), and (iv)
Which of the following properties is exhibited by multiplication, but not by addition?
- A . associativity
- B . commutativity
- C . distributivity
- D . invertibility
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