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

What is the maximum value for f(x)= 8-(x+3)(x-3)?

Suppose I trade an option and I wish to hedge that option for delta and vega. Another option is available to trade. To complete the hedge I would

Exploring a regression model for values of the independent variable that have not been observed is most accurately described as…

Suppose we perform a principle component analysis of the correlation matrix of the returns of 13 yields along the yield curve. The largest eigenvalue of the correlation matrix is 9.8. What percentage of return volatility is explained by the first component? (You may use the fact that the sum of the diagonal elements of a square matrix is always equal to the sum of its eigenvalues.)

The Lagrangian of a constrained optimisation problem is given by L(x,y,λ) = 16x+8x2+4y-λ(4x+y-20), where λ is the Lagrange multiplier. What is the solution for x and y?

Let N(.) denote the cumulative distribution function and suppose that X and Y are standard normally distributed and uncorrelated. Using the fact that N(1.96)=0.975, the probability that X ≤ 0 and Y ≤ 1.96 is approximately

In a 2-step binomial tree, at each step the underlying price can move up by a factor of u = 1.1 or down by a factor of d = 1/u. The continuously compounded risk free interest rate over each time step is 1% and there are no dividends paid on the underlying. Use the Cox, Ross, Rubinstein parameterization to find the risk neutral probability and hence find the value of a European put option with strike 102, given that the underlying price is currently 100.

Which statement regarding the matrix below is true?

What is the indefinite integral of the function f(x) = ln(x), where ln(x) denotes the natural logarithmic function?

Evaluate the derivative of exp(x2 + 2x + 1) at the point x = -1

The quarterly compounded rate of return is 6% per annum. What is the corresponding effective annual return?

Over four consecutive years fund X returns 1%, 5%, -3%, 8%. What is the average growth rate of fund X over this period?

Consider an investment fund with the following annual return rates over 8 years: +6%, -6%, +12%, -12%, +3%, -3%, +9%, -9% .

What can you say about the annual geometric and arithmetic mean returns of this investment fund?

The gradient of a smooth function is

Which of the following is not a sequence?

The determinant of a matrix X is equal 2. Which of the following statements is true?