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 22,2025.
- Exam Code: 8007
- Exam Name: Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition
- Certification Provider: PRMIA
- Latest update: Apr 22,2025
A simple linear regression is based on 100 data points. The total sum of squares is 1.5 and the correlation between the dependent and explanatory variables is 0.5 .
What is the explained sum of squares?
- A . 0.75
- B . 1.125
- C . 0.3333
- D . 0.375
Consider two securities X and Y with the following 5 annual returns:
X: +10%, +3%, -2%, +3%, +5%
Y: +7%, -2%, +3%, -5%, +10%
In this case the sample covariance between the two time series can be calculated as:
- A . 0.40729
- B . 0.00109
- C . 0.00087
- D . 0.32583
What is the angle between the following two three dimensional vectors: a=(1,2,3), b=(-4,2,0)?
- A . 90 degrees
- B . 180 degrees
- C . 57 degrees
- D . 45 degrees
Which of the following statements is true for symmetric positive definite matrices?
- A . Its eigenvalues are all positive
- B . One of its eigenvalues equals 0
- C . If a is its eigenvalue, then -a is also its eigenvalue
- D . If a is its eigenvalue, then is also its eigenvalue
Solve the simultaneous linear equations: x + 2y – 2 = 0 and y – 3x = 8
- A . x = 1, y = 0.5
- B . x = -2, y = 2
- C . x = 2, y = 0
- D . None of the above
At what point x does the function f(x) = x3 – 4×2 + 1 have a local minimum?
- A . -0.666666667
- B . 0
- C . 2.66667
- D . 2
A 95% confidence interval for a parameter estimate can be interpreted as follows:
- A . The probability that the real value of the parameter is within this interval is 95%.
- B . The probability that the real value of the parameter is outside this interval is 95%.
- C . The probability that the estimated value of the parameter is within this interval is 95%.
- D . The probability that the estimated value of the parameter is outside this interval is 95%.
Suppose I trade an option and I wish to hedge that option for delta and vega. Another option is available to trade.
To complete the hedge I would
- A . trade the underlying in such a way as to make the portfolio delta and vega neutral.
- B . trade the other option in such a way as to make the portfolio delta and vega neutral.
- C . trade the other option in such a way as to make the portfolio vega neutral, and then trade the underlying in such a way as to make the portfolio delta neutral.
- D . trade the underlying in such a way as to make the portfolio delta neutral, and then trade the other option in such a way as to make the portfolio vega neutral.
For each of the following functions, indicate whether its graph is concave or convex:
Y = 7×2 + 3x + 9
Y = 6 ln(3x)
Y = exp(-4x)
- A . concave, concave, concave
- B . concave, convex, convex
- C . convex, concave, concave
- D . convex, convex, concave
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