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 14,2025.
- Exam Code: 8007
- Exam Name: Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition
- Certification Provider: PRMIA
- Latest update: Apr 14,2025
The determinant of a matrix X is equal 2 .
Which of the following statements is true?
- A . det(2X) =
- B . det(2X) = 2 det(X)
- C . det(2X) = det(X)2
- D . det(2X) = 4 det(X)
For the function f(x) =3x-x3 which of the following is true?
- A . x = 0 is a minimum
- B . x = -3 is a maximum
- C . x = 2 is a maximum
- D . None of these
You intend to invest $100 000 for five years. Four different interest payment options are available. Choose the interest option that yields the highest return over the five year period.
- A . a lump-sum payment of $22 500 on maturity (in five years)
- B . an annually compounded rate of 4.15%
- C . a quarterly-compounded rate of 4.1%
- D . a continuously-compounded rate of 4%
Suppose we perform a principle component analysis of the correlation matrix of the returns of 13 yields along the yield curve. The largest eigenvalue of the correlation matrix is 9.8 .
What percentage of return volatility is explained by the first component? (You may use the fact that the sum of the diagonal elements of a square matrix is always equal to the sum of its eigenvalues.)
- A . 64%
- B . 75%
- C . 98%
- D . Cannot be determined without estimates of the volatilities of the individual returns
Let N(.) denote the cumulative distribution function of the standard normal probability distribution, and N’ its derivative .
Which of the following is false?
- A . N(0) = 0.5
- B . N'(0) 0
- C . N(x) 0 as x
- D . N'(x) 0 as x
A 2-year bond has a yield of 5% and an annual coupon of 5% .
What is the Modified Duration of the bond?
- A . 2
- B . 1.95
- C . 1.86
- D . 1.75
Simple linear regression involves one dependent variable, one independent variable and one error variable. In contrast, multiple linear regression uses…
- A . One dependent variable, many independent variables, one error variable
- B . Many dependent variables, one independent variable, one error variable
- C . One dependent variable, one independent variable, many error variables
- D . Many dependent variables, many independent variables, many error variables
Which of the following is a false statement concerning the probability density function and the cumulative distribution function of a random variable?
- A . the PDF is non-negative.
- B . the definite integral of the CDF from minus infinity to plus infinity is undefined.
- C . the CDF approaches 1 as its argument approaches infinity.
- D . the definite integral of the PDF from minus infinity to plus infinity is zero.
Which of the provided answers solves this system of equations?
2y C 3x = 3y +x
y2 + x2 = 68
- A . x = 1; y = square root of 67
- B . x = 2; y = 8
- C . x = 2; y = -8
- D . x = -2; y = -8
In a binomial tree lattice, at each step the underlying price can move up by a factor of u = 1.1 or down by a factor of . The continuously compounded risk free interest rate over each time step is 1% and there are no dividends paid on the underlying.
The risk neutral probability for an up move is:
- A . 0.5290
- B . 0.5292
- C . 0.5286
- D . 0.5288
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