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PRMIA 8007 Exam Syllabus Topics:

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

1. What is the maximum value of the function F(x, y)=x2+y2 in the domain defined by inequalities x 1, y -2, y-x 3 ?

A) 29
B) -25
C) 17
D) 1

2. In a portfolio there are 7 bonds: 2 AAA Corporate bonds, 2 AAA Agency bonds, 1 AA Corporate and 2 AA Agency bonds. By an unexplained characteristic the probability of any specific AAA bond outperforming the others is twice the probability of any specific AA bond outperforming the others. What is the probability that an AA bond or a Corporate bond outperforms all of the others?

A) None of these
B) 8/11
C) 6/11
D) 5/7

3. 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) 26.33%
B) 20.78%
C) 36%
D) 36.33%

4. What is the sum of the first 20 terms of this sequence: 3, 5, 9, 17, 33, 65,...?

A) 2 097 172
B) 1 048 595
C) 1 048 574
D) 2 097 170

5. What is the total derivative of the function f(x,y) = ln(x+y), where ln() denotes the natural logarithmic function?

A) 1 / (x+y)
B) ln(x+y) x + ln(x+y) y
C) (x + y) / (x+y)
D) -x/(x+y) - y/(x+y)

Solutions: