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PRM Certification - Exam II: Mathematical Foundations of Risk Measurement

Last Update 8 hours ago Total Questions : 132

The PRM Certification - Exam II: Mathematical Foundations of Risk Measurement content is now fully updated, with all current exam questions added 8 hours ago. Deciding to include 8002 practice exam questions in your study plan goes far beyond basic test preparation.

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Question # 11

Variance reduction is:

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

Question # 12

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

A.

(0, 2, 1)

B.

(0, 0, 0)

C.

(1, 1, 1)

D.

(0, 1, -1)

Question # 13

When calculating the implied volatility from an option price we use the bisection method and know initially that the volatility is somewhere between 1% and 100%. How many iterations do we need in order to determine the implied volatility with accuracy of 0.1%?

A.

10

B.

100

C.

25

D.

5

Question # 14

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

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

Question # 15

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

Question # 16

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.

Question # 17

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 ( )

Question # 18

Evaluate the derivative of ln(1+ x2) at the point x = 1

A.

0.5

B.

0

C.

1

D.

2

Question # 19

Suppose 60% of capital is invested in asset 1, with volatility 40% and the rest is invested in asset 2, with volatility 30%. If the two asset returns have a correlation of -0.5, what is the volatility of the portfolio?

A.

36%

B.

36.33%

C.

26.33%

D.

20.78%

Question # 20

Find the first-order Taylor approximation p(x) for the function: at the point .

A.

-x

B.

-x+1

C.

x-1

D.

x+1

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