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

Demo: 19 questions
Total 132 questions

## PRM Certification - Exam II: Mathematical Foundations of Risk Measurement Questions and Answers

Question 1

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.

#### Options:

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%

Question 2

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

#### Options:

A.

Some portfolios could have a negative variance

B.

It could not be used to simulate correlated asset paths

C.

The associated correlation matrix would not be positive semi-definite

D.

All the above statements are true

Question 3

The bisection method can be used for solving f(x)=0 for a unique solution of x, when

#### Options:

A.

The function f(x) is continuous and monotonic

B.

The function f(x) is differentiable

C.

The function f(x) is differentiable and we have an explicit expression for the derivative

D.

The function f(x) is continuous

Question 4

The correlation between two asset returns is 1. What is the smallest eigenvalue of their correlation matrix?

#### Options:

A.

1

B.

0.5

C.

0

D.

None of the above

Question 5

#### Options:

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.

Question 6

Consider the following distribution data for a random variable X: What is the mean and variance of X?

#### Options:

A.

3.6 and 7.15

B.

3.4 and 3.84

C.

3.5 and 3.45

D.

None of these

Question 7

You are given the following regressions of the first difference of the log of a commodity price on the lagged price and of the first difference of the log return on the lagged log return. Each regression is based on 100 data points and figures in square brackets denote the estimated standard errors of the coefficient estimates:

Which of the following hypotheses can be accepted based on these regressions at the 5% confidence level (corresponding to a critical value of the Dickey Fuller test statistic of – 2.89)?

#### Options:

A.

The commodity prices are stationary

B.

The commodity returns are stationary

C.

The commodity returns are integrated of order 1

D.

None of the above

Question 8

For a quadratic equation, which of the following is FALSE?

#### Options:

A.

If the discriminant is negative, there are no real solutions

B.

If the discriminant is zero, there is only one solution

C.

If the discriminant is negative there are two different real solutions

D.

If the discriminant is positive there are two different real solutions

Question 9

Find the roots, if they exist in the real numbers, of the quadratic equation

#### Options:

A.

4 and -2

B.

-4 and 2

C.

1 and 0

D.

No real roots

Question 10

Let E(X ) = 1, E(Y ) = 3, Corr(X, Y ) = -0.2, E(X2 ) = 10 and E(Y2 ) = 13. Find the covariance between X and Y

#### Options:

A.

-2.8

B.

1.3

C.

-1.2

D.

None of the above

Question 11

Which of the provided answers solves this system of equations?

2y – 3x = 3y +x

y2 + x2 = 68

#### Options:

A.

x = 1; y = square root of 67

B.

x = 2; y = 8

C.

x = 2; y = -8

D.

x = -2; y = -8

Question 12

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?

#### Options:

A.

7.12

B.

6.59

C.

7.44

D.

7.29

Question 13

Which of the following is a false statement concerning the probability density function and the cumulative distribution function of a random variable?

#### Options:

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.

Question 14

I have \$5m to invest in two stocks: 75% of my capital is invested in stock 1 which has price 100 and the rest is invested in stock 2, which has price 125. If the price of stock 1 falls to 90 and the price of stock 2 rises to 150, what is the return on my portfolio?

#### Options:

A.

-2.50%

B.

-5%

C.

2.50%

D.

5%

Question 15

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…

#### Options:

A.

Simple time-series regression

B.

Multiple time-series regression

C.

Simple cross-section regression

D.

Multiple cross-section regression

Question 16

Let A be a square matrix and denote its determinant by x. Then the determinant of A transposed is:

#### Options:

A.

x -1

B.

x

C.

ln(x)

D.

-x

Question 17

Newton-Raphson iteration is used to find a solution of x5 - x3 + x = 1. If xn = 2, what is xn+1?

#### Options:

A.

2.362

B.

1.623

C.

1.638

D.

0.377

Question 18

In a multiple linear regression, the significance of R2 can be tested using which distribution?

#### Options:

A.

Normal distribution

B.

Student's t distribution

C.

F-distribution

D.

Binomial distribution

Question 19

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

#### Options:

A.

8

B.

-1

C.

17

D.

None of these

Demo: 19 questions
Total 132 questions