8007 Practice Questions

A quadratic form is

For the function f(x) =3x-x3 which of the following is true?

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

Consider two functions f(x) and g(x) with indefinite integrals F(x) and G(x), respectively. The indefinite integral of the product f(x)g(x) is given by

Which of the following statements concerning class intervals used for grouping of data is correct?

When grouping data, attention must be paid to the following with regards to class intervals:

1. Class intervals should not overlap

2. Class intervals should be of equal size unless there is a specific need to highlight data within a specific subgroup

3. The class intervals should be large enough so that they not obscure interesting variation within the group

Let X be a random variable distributed normally with mean 0 and standard deviation 1. What is the expected value of exp(X)?

In a binomial tree lattice, at each step the underlying price can move up by a factor of u = 1.1 or down by a factor of . The continuously compounded risk free interest rate over each time step is 1% and there are no dividends paid on the underlying. The risk neutral probability for an up move is:

Your stockbroker randomly recommends stocks to his clients from a tip sheet he is given each day. Today, his tip sheet has 3 common stocks and 5 preferred stocks from Asian companies and 3 common stocks and 5 preferred stocks from European companies. What is the probability that he will recommend a common stock AND/OR a European stock to you when you call and ask for one stock to buy today?

A bond has modified duration 6 and convexity 30. Find the duration-convexity approximation to the percentage change in bond price when its yield increases by 5 basis points

An asset price S is lognormally distributed if: