PRM Certification - Exam II: Mathematical Foundations of Risk Measurement (8002) Practice Test

Questions # 31:

The fundamental theorem of analysis establishes a relation between

Options:

First and second derivative of a function

The derivative of a function and the slope of its graph

Integration and differentiation of functions

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

Questions # 32:

A quadratic form is

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defined as a positive definite Hessian matrix.

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

a specific solution of the Black-Scholes pricing formula

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

Questions # 33:

Let X be a random variable normally distributed with zero mean and let . Then the correlation between X and Y is:

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negative

zero

not defined

positive

Questions # 34:

Which statement regarding the matrix below is true?

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It is not positive definite

It is positive semi-definite

It is positive definite

It is negative definite

Questions # 35:

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

Options:

1.95

1.86

1.75

Questions # 36:

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

Options:

0.5

None of the above

Questions # 37:

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

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-1

None of these

Questions # 38:

An indefinite integral of a polynomial function is

Options:

always positive

always increasing

always less than the function itself

none of the above

Questions # 39:

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 ?

Options:

[0, 1.5]

[1, 2]

[0, 3]

None of the above

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