[Jul-2021] PRMIA 8007 Dumps – Reduce Your Chance of Failure in 8007 Exam
To help you achieve your ultimate goal, we suggest the actual PRMIA 8007 dumps for your Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition exam preparation to use as your guideline.
NEW QUESTION 43
Every covariance matrix must be positive semi-definite. If it were not then:
- A. All the above statements are true
- B. One or more of its eigenvalues would be negative
- C. Some portfolios could have a negative variance
- D. There would be no Cholesky decomposition matrix
Answer: A
NEW QUESTION 44
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. -0.5
- B. 0.25
- C. -0.25
- D. 0
Answer: C
NEW QUESTION 45
Find the roots, if they exist in the real numbers, of the quadratic equation
- A. -4 and 2
- B. No real roots
- C. 1 and 0
- D. 4 and -2
Answer: B
NEW QUESTION 46
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. 0.375
- B. 1.125
- C. 0.3333
- D. 0.75
Answer: A
NEW QUESTION 47
The correlation between two asset returns is 1. What is the smallest eigenvalue of their correlation matrix?
- A. 0
- B. 0.5
- C. 1
- D. None of the above
Answer: A
NEW QUESTION 48
In a quadratic Taylor approximation, a function is approximated by:
- A. a cubic polynomial
- B. a parabola
- C. a constant
- D. a straight line
Answer: B
NEW QUESTION 49
Consider two functions f(x) and g(x) with indefinite integrals F(x) and G(x), respectively. The indefinite integral of the product f(x)g(x) is given by
- A. F(x)g(x) - F(x)g'(x)dx
- B. F(x)G(x)
- C. F(x)g(x) + f(x)G(x)
- D. f(x)G(x) - F(x)g'(x)dx
Answer: A
NEW QUESTION 50
Stress testing portfolios requires changing the asset volatilities and correlations to extreme values. Which of the following would lead to a non positive definite covariance matrix?
- A. Changing all the correlations to be zero
- B. All of the above
- C. Changing the volatilities to be greater than 100%
- D. Changing all the correlations to be unity
Answer: D
NEW QUESTION 51
Suppose a discrete random variable can take on the values -1, 0 and 1 each with a probability of 1/3. Then the mean and variance of the variable is
- A. mean is 0, variance is 1/2
- B. mean is 0, variance is 1/3
- C. mean is 0, variance is 2/3
- D. mean is 1/3, variance is 1/3
Answer: C
NEW QUESTION 52
You are given the following values of a quadratic function f(x): f(0)=0, f(1)=-2, f(2)=-5. On the basis of these data, the derivative f'(0) is ...
- A. in the interval ]-2,+[
- B. in the interval ]-2.5,-2[
- C. equal to -2
- D. in the interval ]-,-2.5]
Answer: A
NEW QUESTION 53
Assume that 40% of all financial organizations investigated by authorities turn out to be fraudulent.
What is the probability of randomly investigating 2 different organizations and finding that neither is fraudulent; and what is the probability of finding exactly one being fraudulent?
- A. 1/3 and 8/17
- B. 9/25 and 12/25
- C. 2/5 and 1/2
- D. 2/5 and 3/5
Answer: B
NEW QUESTION 54
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), (ii), and (iii)
- B. (i), (iii), and (iv)
- C. (i) and (iv)
- D. (i), (ii), (iii), and (iv)
Answer: B
NEW QUESTION 55
Let N(.) denote the cumulative distribution function and suppose that X and Y are standard normally distributed and uncorrelated. Using the fact that N(1.96)=0.975, the probability that X 0 and Y 1.96 is approximately
- A. 0.488%
- B. 0.25%
- C. 0.495%
- D. 0.49%
Answer: A
NEW QUESTION 56
The determinant of a matrix X is equal 2. Which of the following statements is true?
- A. det(2X) =
- B. det(2X) = 4 det(X)
- C. det(2X) = 2 det(X)
- D. det(2X) = det(X)2
Answer: B
NEW QUESTION 57
Which of the following statements about skewness of an empirical probability distribution are correct?
1. When sampling returns from a time series of asset prices, discretely compounded returns exhibit higher skewness than continuously compounded returns
2. When the mean is significantly less than the median, this is an indication of negative skewness
3. Skewness is a sign of asymmetry in the dispersion of the data
- A. Statements 1 and 3 are correct
- B. All three statements are correct
- C. Statements 2 and 3 are correct
- D. Statements 1 and 2 are correct
Answer: B
NEW QUESTION 58
For a quadratic equation, which of the following is FALSE?
- A. If the discriminant is negative there are two different real solutions
- B. If the discriminant is positive there are two different real solutions
- C. If the discriminant is zero, there is only one solution
- D. If the discriminant is negative, there are no real solutions
Answer: A
NEW QUESTION 59
Newton-Raphson iteration is used to find a solution of x5 - x3 + x = 1. If xn = 2, what is xn+1?
- A. 1.623
- B. 0.377
- C. 2.362
- D. 1.638
Answer: D
NEW QUESTION 60
The fundamental theorem of analysis establishes a relation between
- A. The derivative of a function and the derivative of its inverse function
- B. First and second derivative of a function
- C. Integration and differentiation of functions
- D. The derivative of a function and the slope of its graph
Answer: C
NEW QUESTION 61
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