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

1. I have $5m to invest in two stocks: 75% of my capital is invested in stock 1 which has price 100 and the rest is invested in stock 2, which has price 125. If the price of stock 1 falls to 90 and the price of stock 2 rises to 150, what is the return on my portfolio?

A) 2.50%
B) -2.50%
C) -5%
D) 5%

2. The first derivative of a function f(x) is zero at some point, the second derivative is also zero at this point. This means that:

A) f has necessarily a maximum at this point
B) f might have either a minimum or a maximum or neither of them at this point
C) f has necessarily neither a minimum nor a maximum at this point
D) f has necessarily a minimum at this point

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

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

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

A) Some portfolios could have a negative variance
B) There would be no Cholesky decomposition matrix
C) One or more of its eigenvalues would be negative
D) All the above statements are true

5. A quadratic form is

A) an algebraic expression in two variables, x and y, involving , , and terms.
B) a specific solution of the Black-Scholes pricing formula
C) defined as a positive definite Hessian matrix.
D) an algebraic expression in two variables, x and y, involving , and terms.

Solutions: