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Maximum likelihood estimation is a method for:

A.

Finding parameter estimates of a given density function

B.

Estimating the solution of a partial differential equation

C.

Solving a portfolio optimization problem

D.

Estimating the implied volatility of a simple European option

A quadratic form is

A.

defined as a positive definite Hessian matrix.

B.

an algebraic expression in two variables, x and y,involving , and terms.

C.

a specific solution of the Black-Scholes pricing formula

D.

an algebraic expression in two variables, x and y, involving , , and terms.

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

A.

Statements 2 and 3 are correct

B.

Statements 1 and 2 are correct

C.

All three statements are correct

D.

Statements 1 and 3 are correct

Suppose we perform a principle component analysis of the correlation matrix of the returns of 13 yields along the yield curve. The largest eigenvalue of the correlation matrix is 9.8. What percentage of return volatility is explained by the first component? (You may use the fact that the sum of the diagonal elements of a square matrix is always equal to the sum of its eigenvalues.)

A.

64%

B.

75%

C.

98%

D.

Cannot be determined without estimates of the volatilities of the individual returns

The bisection method can be used for solving f(x)=0 for a unique solution of x, when

A.

The function f(x) is continuous and monotonic

B.

The function f(x) is differentiable

C.

The function f(x) is differentiable and we have an explicit expression for the derivative

D.

The function f(x) is continuous

Which of the following can induce a 'multicollinearity' problem in a regression model?

A.

A large negative correlation between the dependent variable and one of the explanatory variables

B.

A high positive correlation between the dependent variable and one of the explanatory variables

C.

A high positive correlation between two explanatory variables

D.

The omission of a relevant explanatory variable

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?

A.

0.3

B.

0.5

C.

0.6

D.

None of these

Two vectors are orthogonal when:

A.

one is a scalar multiple of the other

B.

their components are linearly dependent

C.

their determinant is zero

D.

their scalar product (sum product) is zero

Exploring a regression model for values of the independent variable that have not been observed is most accurately described as…

A.

Estimation

B.

Regression

C.

Hypothesis testing

D.

Prediction

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 less than 1?

A.

0.32

B.

0.64

C.

0.96

D.

1.92