The correlation between two asset returns is 1. What is the smallest eigenvalue of their correlation matrix?
A linear regression gives the following output:
Figures in square brackets are estimated standard errors of the coefficient estimates. What is the value of the test statistic for the hypothesis that the coefficient of is zero against the alternative that is less than zero?
Suppose that f(x) and g(x,y) are functions. What is the partial derivative of f(g(x,y)) with respect to y?
What is the total derivative of the function f(x,y) = ln(x+y), where ln() denotes the natural logarithmic function?
Which of the following can induce a 'multicollinearity' problem in a regression model?
The gradient of a function f(x, y, z) = x + y2 - x y z at the point x = y = z = 1 is
Consider two securities X and Y with the following 5 annual returns:
X: +10%, +3%, -2%, +3%, +5%
Y: +7%, -2%, +3%, -5%, +10%
In this case the sample covariance between the two time series can be calculated as:
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?
A simple linear regression is based on 100 data points. The total sum of squares is 1.5 and the correlation between the dependent and explanatory variables is 0.5. What is the explained sum of squares?
TESTED 22 Feb 2025
