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PRM Certification - Exam II: Mathematical Foundations of Risk Measurement

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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
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