8002 Sample Questions Answers

The gradient of a function f(x, y, z) = x + y2 - x y z at the point x = y = z = 1 is

Let a, b and c be real numbers. Which of the following statements is true?

Stress testing portfolios requires changing the asset volatilities and correlations to extreme values. Which of the following would lead to a non positive definite covariance matrix?

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 biased coin has a probability of getting heads equal to 0.3. If the coin is tossed 4 times, what is the probability of getting heads at least two times?

A 2-step binomial tree is used to value an American put option with strike 105, given that the underlying price is currently 100. At each step the underlying price can move up by 10 or down by 10 and the risk-neutral probability of an up move is 0.6. There are no dividends paid on the underlying and the continuously compounded risk free interest rate over each time step is 1%. What is the value of the option in this model?

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

Two vectors are orthogonal when:

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

Kurtosis(X) is defined as the fourth centred moment of X, divided by the square of the variance of X. Assuming X is a normally distributed variable, what is Kurtosis(X)?

In a quadratic Taylor approximation, a function is approximated by:

You are given the following regressions of the first difference of the log of a commodity price on the lagged price and of the first difference of the log return on the lagged log return. Each regression is based on 100 data points and figures in square brackets denote the estimated standard errors of the coefficient estimates:

Which of the following hypotheses can be accepted based on these regressions at the 5% confidence level (corresponding to a critical value of the Dickey Fuller test statistic of – 2.89)?

Calculate the determinant of the following matrix:

Which of the following statements is true?

Which of the following is consistent with the definition of a Type I error?

Consider two securities X and Y with the following 5 annual returns:

X: +10%, +3%, -2%, +3%, +5%

Y: +7%, -2%, +3%, -5%, +10%

In this case the sample covariance between the two time series can be calculated as: