PRM Certification - Exam II: Mathematical Foundations of Risk Measurement

Question 1

Suppose that f(x) and g(x,y) are functions. What is the partial derivative of f(g(x,y)) with respect to y?

A. f'(g(x,y)) dg/dy

B. f'(g(x,y))

C. f(dg/dy)

D. f(g(x,y)) dg/dy

Correct Answer: A

Question 2

What is the maximum value for f(x)= 8-(x+3)(x-3)?

A. None of these

B. -1

C. 17

D. 8

Correct Answer: C

Question 3

I have a portfolio of two stocks. The weights are 60% and 40% respectively, the volatilities are both 20%, while the correlation of returns is 100%. The volatility of my portfolio is

A. 4%

B. 20%

C. 14.4%

D. 24%

Correct Answer: B

Question 4

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) + f(x)G(x)

C. F(x)G(x)

D. F(x)g(x) - F(x)g'(x)dx

Correct Answer: D

Question 5

A quadratic form is

A. an algebraic expression in two variables, x and y,involving , and terms.

B. a specific solution of the Black-Scholes pricing formula

C. defined as a positive definite Hessian matrix.

D. an algebraic expression in two variables, x and y, involving , , and terms.

Correct Answer: A

Question 6

Which of the following statements concerning class intervals used for grouping of data is correct?
When grouping data, attention must be paid to the following with regards to class intervals:
1.Class intervals should not overlap
2.Class intervals should be of equal size unless there is a specific need to highlight data within a specific subgroup
3.The class intervals should be large enough so that they not obscure interesting variation within the group

A. All three statements are correct

B. Statements 1 and 3 are correct

C. Statements 2 and 3 are correct

D. Statements 1 and 2 are correct

Correct Answer: D

Question 7

Which of the following statements is true?

A. Continuous compounding is the better method because it results in higher present values compared to discrete compounding.

B. Discrete and continuous compounding produce the same results if the discount rate is positive.

C. Continuous compounding can be thought as making the compounding period infinitesimally small.

D. The constant plays an important role in the mathematical description of continuous compounding.

Correct Answer: C

Question 8

What is the total derivative of the function f(x,y) = ln(x+y), where ln() denotes the natural logarithmic function?

A. (x + y) / (x+y)

B. 1 / (x+y)

C. ln(x+y) x + ln(x+y) y

D. -x/(x+y) - y/(x+y)

Correct Answer: A

Question 9

An indefinite integral of a polynomial function is

A. always positive

B. always less than the function itself

C. none of the above

D. always increasing

Correct Answer: C

Question 10

You want to test the hypothesis that a population parameter of a regression model is zero. Your alternative hypothesis is that 0. Denote by SD() the estimated standard deviation of , and by MEAN() the estimated mean of . Which test statistic is appropriate, and what is its distribution?

A. test statistic = MEAN()/SD(), normal distribution

B. test statistic = SD()/MEAN(), t distribution

C. test statistic = SD()/MEAN(), normal distribution

D. test statistic = MEAN()/SD(), t distribution

Correct Answer: D

PRMIA PRM Certification - Exam II: Mathematical Foundations of Risk Measurement - 8002 Exam Practice Test

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