Question 1

You intend to invest $100 000 for five years. Four different interest payment options are available. Choose the interest option that yields the highest return over the five year period.

Question 2

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

Question 3

The bisection method can be used for solving f(x)=0 for a unique solution of x, when

Question 4

The correlation between two asset returns is 1. What is the smallest eigenvalue of their correlation matrix?

Question 5

A quadratic form is

Question 6

Consider the following distribution data for a random variable X: What is the mean and variance of X?

Question 7

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)?

Question 8

For a quadratic equation, which of the following is FALSE?

Question 9

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

Question 10

Let E(X ) = 1, E(Y ) = 3, Corr(X, Y ) = -0.2, E(X2 ) = 10 and E(Y2 ) = 13. Find the covariance between X and Y

Question 11

Which of the provided answers solves this system of equations?

2y – 3x = 3y +x

y2 + x2 = 68

Question 12

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?

Question 13

Which of the following is a false statement concerning the probability density function and the cumulative distribution function of a random variable?

Question 14

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?

Question 15

You are investigating the relationship between weather and stock market performance. To do this, you pick 100 stock market locations all over the world. For each location, you collect yesterday's mean temperature and humidity and yesterday's local index return. Performing a regression analysis on this data is an example of…

Question 16

Let A be a square matrix and denote its determinant by x. Then the determinant of A transposed is:

Question 17

Newton-Raphson iteration is used to find a solution of x5 - x3 + x = 1. If xn = 2, what is xn+1?

Question 18

In a multiple linear regression, the significance of R2 can be tested using which distribution?

Question 19

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