PRMIA Mathematical Foundations of Risk Measurement :II 8002 P R M Exam Practice Test

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

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

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?

If the annual volatility of returns is 25% what is the variance of the quarterly returns?

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]?

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 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