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PRM Certification - Exam II: Mathematical Foundations of Risk Measurement

Last Update 5 days ago
Total Questions : 132

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Question # 1

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

Options:

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

Discussion 0
Question # 2

Which of the following properties is exhibited by multiplication, but not by addition?

Options:

A.  

associativity

B.  

commutativity

C.  

distributivity

D.  

invertibility

Discussion 0
Question # 3

I have a portfolio of two stocks. The weights are equal. The one volatility is 30% while the other is 40%. The minimum and maximum possible values of the volatility of my portfolio are:

Options:

A.  

30% and 40%

B.  

5% and 35%

C.  

10% and 40%

D.  

10% and 70%

Discussion 0
Question # 4

The quarterly compounded rate of return is 6% per annum. What is the corresponding effective annual return?

Options:

A.  

1.50%

B.  

6%

C.  

6.14%

D.  

None of the above

Discussion 0
Question # 5

The gradient of a smooth function is

Options:

A.  

a vector that shows the direction of fastest change of a function

B.  

matrix of second partial derivatives of a function

C.  

infinite at a maximum point

D.  

a matrix containing the function's second partial derivatives

Discussion 0
Question # 6

Which of the following is not a direct cause of autocorrelation or heteroskedasticity in the residuals of a regression model?

Options:

A.  

A structural break in the dependent variable

B.  

A high positive correlation between two explanatory variables

C.  

The omission of a relevant explanatory variable

D.  

Using an inappropriate functional form in the model

Discussion 0
Question # 7

The gradient of a function f(x, y, z) = x + y2 - x y z at the point x = y = z = 1 is

Options:

A.  

(0, 2, 1)

B.  

(0, 0, 0)

C.  

(1, 1, 1)

D.  

(0, 1, -1)

Discussion 0
Question # 8

A 2-year bond has a yield of 5% and an annual coupon of 5%. What is the Modified Duration of the bond?

Options:

A.  

2

B.  

1.95

C.  

1.86

D.  

1.75

Discussion 0
Question # 9

You are to perform a simple linear regression using the dependent variable Y and the independent variable X (Y = a + bX). Suppose that cov(X,Y)=10, var(X)= 5, and that the mean of X is 1 and the mean of Y is 2. What are the values for the regression parameters a and b?

Options:

A.  

b=0.5, a=2.5

B.  

b=0.5, a=1.5

C.  

b=2, a=4

D.  

b=2, a=0

Discussion 0
Question # 10

A linear regression gives the following output:

Figures in square brackets are estimated standard errors of the coefficient estimates. What is the value of the test statistic for the hypothesis that the coefficient of is zero against the alternative that is less than zero?

Options:

A.  

0.125

B.  

2.5

C.  

-1.25

D.  

-2.5

Discussion 0
Question # 11

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

Options:

A.  

1 / (x+y)

B.  

(∆x + ∆y) / (x+y)

C.  

-∆x/(x+y) - ∆y/(x+y)

D.  

ln(x+y) ∆x + ln(x+y) ∆y

Discussion 0
Question # 12

Maximum likelihood estimation is a method for:

Options:

A.  

Finding parameter estimates of a given density function

B.  

Estimating the solution of a partial differential equation

C.  

Solving a portfolio optimization problem

D.  

Estimating the implied volatility of a simple European option

Discussion 0
Question # 13

An asset price S is lognormally distributed if:

Options:

A.  

the change in price (dS) is normally distributed

B.  

1/S is normally distributed

C.  

ln(dS/S) is normally distributed

D.  

ln(1+dS/S) is normally distributed

Discussion 0
Question # 14

Simple linear regression involves one dependent variable, one independent variable and one error variable. In contrast, multiple linear regression uses…

Options:

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

Discussion 0
Question # 15

An operational risk analyst models the occurrence of computer failures as a Poisson process with an arrival rate of 2 events per year. According to this model, what is the probability of zero failures in one year?

Options:

A.  

0.02

B.  

0.14

C.  

0.25

D.  

0.50

Discussion 0
Question # 16

Variance reduction is:

Options:

A.  

A technique that is applied in regression models to improve the accuracy of the coefficient estimates

B.  

A numerical method for finding portfolio weights to minimize the variance of a portfolio that has a given expected return

C.  

A numerical method for finding the variance of the underlying that is implicit in a market price of an option

D.  

A method for reducing the number of simulations required in a Monte Carlo simulation

Discussion 0
Question # 17

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

Options:

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

Discussion 0
Question # 18

What is the angle between the following two three dimensional vectors: a=(1,2,3), b=(-4,2,0)?

Options:

A.  

90 degrees

B.  

180 degrees

C.  

57 degrees

D.  

45 degrees

Discussion 0
Question # 19

A typical leptokurtotic distribution can be described as a distribution that is relative to a normal distribution

Options:

A.  

peaked and thin at the center and with heavy (fat) tails

B.  

peaked and thin at the center and with thin tails

C.  

flat and thick at the center and with heavy (fat) tails

D.  

flat and thick at the center and with thin tails

Discussion 0
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