PRMIA 8007 Exam Practice Test Instant Access

Question 1

Let f(x) = c for x in [0,4] and 0 for other values of x.

What is the value of the constant c that makes f(x) a probability density function; and what if f(x) = cx for x in [0,4]?

A1/4 and 1/7

B1/7 and 1/9

C1/4 and 1/6

DNone of the above

Answer : D

Question 2

Let X be a random variable distributed normally with mean 0 and standard deviation 1. What is the expected value of exp(X)?

AE(exp(X)) = 1.6487

BE(exp(X)) = 1

CE(exp(X)) = 2.7183

DE(exp(X)) = 0.6065

Answer : A

Question 3

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

ASome portfolios could have a negative variance

BIt could not be used to simulate correlated asset paths

CThe associated correlation matrix would not be positive semi-definite

DAll the above statements are true

Answer : D

Question 4

When a number is written with a fraction as an exponent, such as , which of the following is the correct computation?

ATake the square-root of 75 and raise it to the 5th power

BDivide 75 by 2, then raise it to the 5th power

CMultiply 75 by 2.5

DSquare 75, then take the fifth root of it

Answer : A

Question 5

I have a portfolio of two stocks. The weights are 60% and 40% respectively, the volatilities are both 20%, while the correlation of returns is 50%. The volatility of my portfolio is

A16%

B17.4%

C20%

D24.4%

Answer : B

Question 6

The fundamental theorem of analysis establishes a relation between

AFirst and second derivative of a function

BThe derivative of a function and the slope of its graph

CIntegration and differentiation of functions

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

Answer : C

Question 7

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

ASome portfolios could have a negative variance

BOne or more of its eigenvalues would be negative

CThere would be no Cholesky decomposition matrix

DAll the above statements are true

Answer : D

PRMIA Mathematical Foundations of Risk Measurement – 2015 Edition 8007 Exam Practice Test