8002 Practice Exam Questions with Answers PRM Certification - Exam II: Mathematical Foundations of Risk Measurement Certification

What is a Hessian?

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:

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

Let E(X ) = 1, E(Y ) = 3, Corr(X, Y ) = -0.2, E(X2 ) = 10 and E(Y2 ) = 13. Find the covariance between X and Y

An indefinite integral of a polynomial function is

Which of the following statements is not correct?

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

Which of the following can be used to evaluate a regression model?

(i) Magnitude of R2

(ii) Magnitude of TSS (total sum of squares)

(iii) Tests for statistical significance

(iv) Sign and magnitude of each regression parameter

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]?

Which of the following statements is true for symmetric positive definite matrices?

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?

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

If a random variable X has a normal distribution with mean zero and variance 4, approximately what proportion of realizations of X should lie between -4 and +4?

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