In a quadratic Taylor approximation, a function is approximated by:
In a portfolio there are 7 bonds: 2 AAA Corporate bonds, 2 AAA Agency bonds, 1 AA Corporate and 2 AA Agency bonds. By an unexplained characteristic the probability of any specific AAA bond outperforming the others is twice the probability of any specific AA bond outperforming the others. What is the probability that an AA bond or a Corporate bond outperforms all of the others?
There are two portfolios with no overlapping of stocks or bonds. Portfolio 1 has 6 stocks and 6 bonds. Portfolio 2 has 4 stocks and 8 bonds. If we randomly select one stock, what is the probability that it came from Portfolio1?
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.
Which of the following statements about skewness of an empirical probability distribution are correct?
1. When sampling returns from a time series of asset prices, discretely compounded returns exhibit higher skewness than continuously compounded returns
2. When the mean is significantly less than the median, this is an indication of negative skewness
3. Skewness is a sign of asymmetry in the dispersion of the data
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?
What is the simplest form of this expression: log2(165/2)
Calculate the determinant of the following matrix:
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:
Suppose 60% of capital is invested in asset 1, with volatility 40% and the rest is invested in asset 2, with volatility 30%. If the two asset returns have a correlation of -0.5, what is the volatility of the portfolio?
If a random variable X has a normal distribution with mean zero and variance 4, approximately what proportion of realizations of X should lie between -4 and +4?
Let A be a square matrix and denote its determinant by x. Then the determinant of A transposed is:
What is the indefinite integral of the function f(x) = ln(x), where ln(x) denotes the natural logarithmic function?
Concerning a standard normal distribution and a Student's t distribution (with more than four degrees of freedom), which of the following is true?
Maximum likelihood estimation is a method for:
Which of the provided answers solves this system of equations?
2y – 3x = 3y +x
y2 + x2 = 68
Let X be a random variable distributed normally with mean 0 and standard deviation 1. What is the expected value of exp(X)?
For a quadratic equation, which of the following is FALSE?
Let f(x) = c for x in [0,4] and 0 for other values of x.
What is the value of the constant c that makes f(x) a probability density function; and what if f(x) = cx for x in [0,4]?