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PRMIA
PRM Certification
8007
Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Questions and Answers

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Questions # 1:

There are two portfolios with no overlapping of stocks or bonds. Portfolio 1 has 6 stocks and 6 bonds. Portfolio 2 has 4 stocks and 8 bonds. If we randomly select one stock, what is the probability that it came from Portfolio1?

Options:

0.3

0.5

0.6

None of these

Answer

Questions # 2:

Bond convexity is closely related to …

Options:

The derivative of the bond's present value with respect to yield

The second derivative of the bond's present value with respect to yield

The integral of the bond's present value with respect to yield

The sensitivity of the bond's present value with respect to yield

Answer

Questions # 3:

Identify the type and common element (that is, common ratio or common difference) of the following sequence: 6, 12, 24

Options:

arithmetic sequence, common difference 2

arithmetic sequence, common ratio 2

geometric sequence, common ratio 2

geometric sequence, common ratio 3

Answer

Questions # 4:

Consider a binomial lattice where a security price S moves up by a factor u with probability p, or down by a factor d with probability 1 - p. If we set d > 1/u then which of the following will be TRUE?

Options:

The lattice will not recombine

The probability of an up move will not be constant

There will always be a downward drift in the lattice

None of the above

Answer

Questions # 5:

Which of the following can induce a 'multicollinearity' problem in a regression model?

Options:

A large negative correlation between the dependent variable and one of the explanatory variables

A high positive correlation between the dependent variable and one of the explanatory variables

A high positive correlation between two explanatory variables

The omission of a relevant explanatory variable

Answer

Questions # 6:

You are given the following values of a quadratic function f(x): f(0)=0, f(1)=-2, f(2)=-5. On the basis of these data, the derivative f'(0) is …

Options:

in the interval ]-2.5,-2[

equal to -2

in the interval ]-2,+∞[

in the interval ]-∞,-2.5]

Answer

Questions # 7:

Which of the following statements is not correct?

Options:

Every linear function is also a quadratic function.

A function is defined by its domain together with its action.

For finite and small domains, the action of a function may be specified by a list.

A function is a rule that assigns to every value x at least one value of y.

Answer

Questions # 8:

For each of the following functions, indicate whether its graph is concave or convex:

Y = 7x2 + 3x + 9

Y = 6 ln(3x)

Y = exp(-4x)

Options:

concave, concave, concave

concave, convex, convex

convex, concave, concave

convex, convex, concave

Answer

Questions # 9:

A 2-step binomial tree is used to value an American put option with strike 104, given that the underlying price is currently 100. At each step the underlying price can move up by 20% or down by 20% and the risk-neutral probability of an up move is 0.55. There are no dividends paid on the underlying and the discretely compounded risk free interest rate over each time step is 2%. What is the value of the option in this model?