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

A linear regression gives the following output:

Figures in square brackets are estimated standard errors of the coefficient estimates. What is the value of the test statistic for the hypothesis that the coefficient of is zero against the alternative that is less than zero?

In statistical hypothesis tests, 'Type I error' refers to the situation in which…

Let X be a random variable normally distributed with zero mean and let . Then the correlation between X and Y is:

Find the roots, if they exist in the real numbers, of the quadratic equation

An underlying asset price is at 100, its annual volatility is 25% and the risk free interest rate is 5%. A European put option has a strike of 105 and a maturity of 90 days. Its Black-Scholes price is 7.11. The options sensitivities are: delta = -0.59; gamma = 0.03; vega = 19.29. Find the delta-gamma approximation to the new option price when the underlying asset price changes to 105

A 2-year bond has a yield of 5% and an annual coupon of 5%. What is the Modified Duration of the bond?

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

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?

A typical leptokurtotic distribution can be described as a distribution that is relative to a normal distribution

What is the simplest form of this expression: log2(165/2)

Simple linear regression involves one dependent variable, one independent variable and one error variable. In contrast, multiple linear regression uses…

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?

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.)

Bond convexity is closely related to …

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

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?