Which of the following properties is exhibited by multiplication, but not by addition?
Every covariance matrix must be positive semi-definite. If it were not then:
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:
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?
Evaluate the derivative of ln(1+ x2) at the point x = 1
You invest $100 000 for 3 years at a continuously compounded rate of 3%. At the end of 3 years, you redeem the investment. Taxes of 22% are applied at the time of redemption. What is your approximate after-tax profit from the investment, rounded to $10?
If the annual volatility of returns is 25% what is the variance of the quarterly returns?
Which of the following statements is true for symmetric positive definite matrices?
For a quadratic equation, which of the following is FALSE?
Exploring a regression model for values of the independent variable that have not been observed is most accurately described as…
The bisection method can be used for solving f(x)=0 for a unique solution of x, when
Calculate the determinant of the following matrix:
Consider the linear regression model for the returns of stock A and the returns of stock B. Stock A is 50% more volatile than stock B. Which of the following statements is TRUE?
Which of the following is not a direct cause of autocorrelation or heteroskedasticity in the residuals of a regression model?
The gradient of a smooth function is
If a time series has to be differenced twice in order to be transformed into a stationary series, the original series is said to be:
An indefinite integral of a polynomial function is
Two vectors are orthogonal when:
A 2-step binomial tree is used to value an American put option with strike 104, given that the underlying price is currently 100. At each step the underlying price can move up by 20% or down by 20% and the risk-neutral probability of an up move is 0.55. There are no dividends paid on the underlying and the discretely compounded risk free interest rate over each time step is 2%. What is the value of the option in this model?