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8007 PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Free Practice Exam Questions (2025 Updated)

Prepare effectively for your PRMIA 8007 Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition certification with our extensive collection of free, high-quality practice questions. Each question is designed to mirror the actual exam format and objectives, complete with comprehensive answers and detailed explanations. Our materials are regularly updated for 2025, ensuring you have the most current resources to build confidence and succeed on your first attempt.

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Total 132 questions

Over four consecutive years fund X returns 1%, 5%, -3%, 8%. What is the average growth rate of fund X over this period?

A.

2.67%

B.

2.75%

C.

2.49%

D.

None of the above

What is the 40th term in the following series: 4, 14, 30, 52, …?

A.

240

B.

4598

C.

4840

D.

4960

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)

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.

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

Which of the following is consistent with the definition of a Type I error?

A.

The probability of a Type I error is 100% minus the significance level

B.

A Type I error would have occurred if the performance of a stock was positively correlated with the performance of a hedge fund, but in a linear regression, the hypothesis of positive correlation was rejected

C.

A Type I error would have occurred if the performance of a stock was positively correlated with the performance of a hedge fund, but in a linear regression, the hypothesis of no correlation was rejected

D.

A Type I occurs whenever data series are serially correlated

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

Concerning a standard normal distribution and a Student's t distribution (with more than four degrees of freedom), which of the following is true?

A.

The distributions have the same kurtosis.

B.

The normal distribution has higher kurtosis than the t distribution.

C.

The normal distribution has lower kurtosis than the t distribution.

D.

Which has the higher kurtosis depends on the degrees of freedom of the t distribution.

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.

2/5 and 1/2

B.

2/5 and 3/5

C.

1/3 and 8/17

D.

9/25 and 12/25

When the errors in a linear regression show signs of positive autocorrelation, which of the statements below is true?

A.

The regression coefficient will be too high and the standard error of the regression coefficient will be understated

B.

The regression coefficient will be too low and the standard error of the regression coefficient will be overstated

C.

The regression coefficient will be unbiased, but the standard error of the regression coefficient will be understated

D.

The regression coefficient will be unbiased, but the standard error of the regression coefficient will be overstated

A bond has modified duration 6 and convexity 30. Find the duration-convexity approximation to the percentage change in bond price when its yield increases by 5 basis points

A.

10 basis point rise

B.

24 basis fall

C.

24 basis point rise

D.

30 basis points fall.

A quadratic form is

A.

defined as a positive definite Hessian matrix.

B.

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

C.

a specific solution of the Black-Scholes pricing formula

D.

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

Which statement regarding the matrix below is true?

A.

It is not positive definite

B.

It is positive semi-definite

C.

It is positive definite

D.

It is negative definite

A 2-step binomial tree is used to value an American put option with strike 104, given that the underlying price is currently 100. At each step the underlying price can move up by 20% or down by 20% and the risk-neutral probability of an up move is 0.55. There are no dividends paid on the underlying and the discretely compounded risk free interest rate over each time step is 2%. What is the value of the option in this model?

A.

11.82

B.

12.33

C.

12.49

D.

12.78

A linear regression gives the following output:

Figures in square brackets are estimated standard errors of the coefficient estimates.

Which of the following is an approximate 95% confidence interval for the true value of the coefficient of ?

A.

[0, 1.5]

B.

[1, 2]

C.

[0, 3]

D.

None of the above

For each of the following functions, indicate whether its graph is concave or convex:

Y = 7x2 + 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

A 2-step binomial tree is used to value an American put option with strike 105, given that the underlying price is currently 100. At each step the underlying price can move up by 10 or down by 10 and the risk-neutral probability of an up move is 0.6. There are no dividends paid on the underlying and the continuously compounded risk free interest rate over each time step is 1%. What is the value of the option in this model?

A.

7.12

B.

6.59

C.

7.44

D.

7.29

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%

The fundamental theorem of analysis establishes a relation between

A.

First and second derivative of a function

B.

The derivative of a function and the slope of its graph

C.

Integration and differentiation of functions

D.

The derivative of a function and the derivative of its inverse function

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