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PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:

1. Your stockbroker randomly recommends stocks to his clients from a tip sheet he is given each day. Today, his tip sheet has 3 common stocks and 5 preferred stocks from Asian companies and 3 common stocks and 5 preferred stocks from European companies. What is the probability that he will recommend a common stock AND/OR a European stock to you when you call and ask for one stock to buy today?

A) 7/8
B) None of these
C) 11/16
D) 9/16

2. Solve the simultaneous linear equations: x + 2y - 2 = 0 and y - 3x = 8

A) x = 2, y = 0
B) x = -2, y = 2
C) None of the above
D) x = 1, y = 0.5

3. 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?

A) b=2, a=4
B) b=0.5, a=2.5
C) b=0.5, a=1.5
D) b=2, a=0

4. 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) 25
B) 100
C) 5
D) 10

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

A) -x+1
B) -x
C) x+1
D) x-1

Solutions: