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8002 PRMIA PRM Certification - Exam II: Mathematical Foundations of Risk Measurement Free Practice Exam Questions (2025 Updated)

Prepare effectively for your PRMIA 8002 PRM Certification - Exam II: Mathematical Foundations of Risk Measurement 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

An underlying asset price is at 100, its annual volatility is 25% and the risk free interest rate is 5%. A European put option has a strike of 105 and a maturity of 90 days. Its Black-Scholes price is 7.11. The options sensitivities are: delta = -0.59; gamma = 0.03; vega = 19.29. Find the delta-gamma approximation to the new option price when the underlying asset price changes to 105

A.

6.49

B.

5.03

C.

4.59

D.

4.54

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

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

Identify the type and common element (that is, common ratio or common difference) of the following sequence: 6, 12, 24

A.

arithmetic sequence, common difference 2

B.

arithmetic sequence, common ratio 2

C.

geometric sequence, common ratio 2

D.

geometric sequence, common ratio 3

If a time series has to be differenced twice in order to be transformed into a stationary series, the original series is said to be:

A.

non-linear

B.

integrated of order 2

C.

differential

D.

non-functional

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

Consider the linear regression model for the returns of stock A and the returns of stock B. Stock A is 50% more volatile than stock B. Which of the following statements is TRUE?

A.

The stocks must be positively correlated ( )

B.

Beta must be positive ( )

C.

Beta must be greater in absolute value than the correlation of the stocks ( )

D.

Alpha must be positive ( )

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 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.

You are investigating the relationship between weather and stock market performance. To do this, you pick 100 stock market locations all over the world. For each location, you collect yesterday's mean temperature and humidity and yesterday's local index return. Performing a regression analysis on this data is an example of…

A.

Simple time-series regression

B.

Multiple time-series regression

C.

Simple cross-section regression

D.

Multiple cross-section regression

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)

B.

F(x)g(x) + f(x)G(x)

C.

F(x)g(x) - ∫F(x)g'(x)dx

D.

f(x)G(x) - ∫F(x)g'(x)dx

Every covariance matrix must be positive semi-definite. If it were not then:

A.

Some portfolios could have a negative variance

B.

One or more of its eigenvalues would be negative

C.

There would be no Cholesky decomposition matrix

D.

All the above statements are true

On average, one trade fails every 10 days. What is the probability that no trade will fail tomorrow?

A.

0.095

B.

0.905

C.

0.95

D.

0.100

What is the simplest form of this expression: log2(165/2)

A.

10

B.

32

C.

5/2 + log2(16)

D.

log2 (5/2) + log2(16)

Let a, b and c be real numbers. Which of the following statements is true?

A.

The commutativity of multiplication is defined by

B.

The existence of negatives is defined by

C.

The distributivity of multiplication is defined by

D.

The associativity of multiplication is defined by

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 2/3

B.

mean is 0, variance is 1/3

C.

mean is 0, variance is 1/2

D.

mean is 1/3, variance is 1/3

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 the volatilities to be greater than 100%

B.

Changing all the correlations to be unity

C.

Changing all the correlations to be zero

D.

All of the above

Which of the following statements is not correct?

A.

Every linear function is also a quadratic function.

B.

A function is defined by its domain together with its action.

C.

For finite and small domains, the action of a function may be specified by a list.

D.

A function is a rule that assigns to every value x at least one value of y.

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Total 132 questions
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