Question 1

The point where the capital market line is tangential to the efficient frontier is

Accepted Answer

A)  The point where the portfolio returns are minimised 
B)  The point where the portfolio returns are maximised 
C)  The point where the portfolio's Sharpe ratio is minimised 
D)  The point where the portfolio's Sharpe ratio is maximised 
A)  The point where the portfolio returns are minimised 
B)  The point where the portfolio returns are maximised 
C)  The point where the portfolio's Sharpe ratio is minimised 
D)  The point where the portfolio's Sharpe ratio is maximised D

Question 2

Log(1) is:

Accepted Answer

A)  1 
B)  0 
C)  2.71828… 
D)  Undefined 
A)  1 
B)  0 
C)  2.71828… 
D)  Undefined B

Question 3

The derivative of log(5x) is:

Accepted Answer

A)  5/x 
B)  1/x 
C)  5log(x) 
D)  5/log(x) 
A)  5/x 
B)  1/x 
C)  5log(x) 
D)  5/log(x) B

Question 4

For two conformable matrices A and B, expanding the parentheses of (AB)-1 gives:

Accepted Answer

A)  A-1B-1 
B)  B-1A-1 
C)  BA 
D)  AB 
A)  A-1B-1 
B)  B-1A-1 
C)  BA 
D)  AB

Question 5

The rank of matrices A and B from the previous question are:

Accepted Answer

A)  1 and 2, respectively 
B)  2 and 1, respectively 
C)  1 and 3, respectively 
D)  3 and 1, respectively 
A)  1 and 2, respectively 
B)  2 and 1, respectively 
C)  1 and 3, respectively 
D)  3 and 1, respectively

Question 6

The simplest possible way of writing 3x5 * 7x3 is:

Accepted Answer

A)  21 x5 * x3 
B)  21 x15 
C)  21x8 
D)  21x53 
A)  21 x5 * x3 
B)  21 x15 
C)  21x8 
D)  21x53

Question 7

Consider the following graphs. 
A.  B.  
Which of the following statements is true?

Accepted Answer

A)  A is depicts a non-linear relationship between y and x 
B)  B is depicts a linear relationship between y and x 
C)  A and B depict linear and non-linear relationships between y and x respectively 
D)  A and B depict non-linear and linear relationships between y and x respectively 
A)  A is depicts a non-linear relationship between y and x 
B)  B is depicts a linear relationship between y and x 
C)  A and B depict linear and non-linear relationships between y and x respectively 
D)  A and B depict non-linear and linear relationships between y and x respectively

Question 8

What is the inverse of matrix ?

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 9

Consider the following data series: 11, 10, 6, 8, 4, 3, 7. What is its semi-interquartile range of this series?

Accepted Answer

A)  6 
B)  5 
C)  4 
D)  3 
A)  6 
B)  5 
C)  4 
D)  3

Question 10

Assume that the relationship between a company's stock price (y) and dividends paid per share (x) is linear. If the slope of the equation is 0.50 and the intercept is 30, what would be the expected stock price if the dividend paid was 3?

Accepted Answer

A)  33 
B)  30.50 
C)  31.5 
D)  30 
A)  33 
B)  30.50 
C)  31.5 
D)  30

Question 11

What are the roots of the equation y = 2x2 + 2x - 4?

Accepted Answer

A)  -2 and 1 
B)  -1 and 2 
C)  -2 and 2 
D)  -2 (repeated) 
A)  -2 and 1 
B)  -1 and 2 
C)  -2 and 2 
D)  -2 (repeated)

Question 12

Consider the following two graphs: 
A.  B.  Which of the following statements is true if A represents a normal distribution?
(I) The skewness of the distribution plot A is 0 and its kurtosis is 3
(II) The skewness of the distribution plot B is 0 and its kurtosis is 3
(III) The excess kurtosis of the distribution plot A is 3
(IV) The excess kurtosis of the distribution plot B is 0

Accepted Answer

A)  Both (I) and (III) are true 
B)  Only (III) is true 
C)  Only (I) is true 
D)  Both (I) and (IV) are true 
A)  Both (I) and (III) are true 
B)  Only (III) is true 
C)  Only (I) is true 
D)  Both (I) and (IV) are true

Question 13

Which of the following values are closes to the roots of the following quadratic equation: ?

Accepted Answer

A)  0 and 4 
B)  1 and 4 
C)  0.5 and 3 
D)  0.3 and 3.7 
A)  0 and 4 
B)  1 and 4 
C)  0.5 and 3 
D)  0.3 and 3.7

Question 14

What are the roots of the equation y = x2 + 2x - 6 closest to?

Accepted Answer

A)  -4 and 2 
B)  -3.65 and 1.65 
C)  -7.3 and 3.3 
D)  Both complex 
A)  -4 and 2 
B)  -3.65 and 1.65 
C)  -7.3 and 3.3 
D)  Both complex

Question 15

If A is of dimension 1 * 4 and B is of dimension 4 * 1, what is the most accurate term to describe the result of the matrix multiplication AB?

Accepted Answer

A)  A scalar 
B)  A column vector 
C)  A row vector 
D)  A matrix 
A)  A scalar 
B)  A column vector 
C)  A row vector 
D)  A matrix

Question 16

What is the (first order) derivative of the function ?

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 17

The derivative of e4x-2 is:

Accepted Answer

A)  4/(4x-2) 
B)  (4x-2)e4 
C)  (4x-2)e4x-2 
D)  4e4x-2 
A)  4/(4x-2) 
B)  (4x-2)e4 
C)  (4x-2)e4x-2 
D)  4e4x-2

Question 18

"x to the power 3" could be written:

Accepted Answer

A)  3x 
B)  3x3 
C)  x3 
D)  3x * 3x * 3x 
A)  3x 
B)  3x3 
C)  x3 
D)  3x * 3x * 3x

Question 19

The trace of matrix C is

Accepted Answer

A)  9 
B)  8 
C)  7 
D)  6 
A)  9 
B)  8 
C)  7 
D)  6

Question 20

The rank of a square matrix is also:

Accepted Answer

A)  The product of the eigenvalues 
B)  The sum of the eigenvalues 
C)  The number of non-zero eigenvalues 
D)  The number of correlated rows or columns 
A)  The product of the eigenvalues 
B)  The sum of the eigenvalues 
C)  The number of non-zero eigenvalues 
D)  The number of correlated rows or columns

The point where the capital market line is tangential to the efficient frontier is

Log(1) is:

The derivative of log(5x) is:

For two conformable matrices A and B, expanding the parentheses of (AB)^-1 gives:

The rank of matrices A and B from the previous question are:

The simplest possible way of writing 3x⁵ * 7x³ is:

Consider the following graphs. A. B. Which of the following statements is true?

What is the inverse of matrix ?

Consider the following data series: 11, 10, 6, 8, 4, 3, 7. What is its semi-interquartile range of this series?

Assume that the relationship between a company's stock price (y) and dividends paid per share (x) is linear. If the slope of the equation is 0.50 and the intercept is 30, what would be the expected stock price if the dividend paid was 3?

What are the roots of the equation y = 2x² + 2x - 4?

Which of the following values are closes to the roots of the following quadratic equation: ?

What are the roots of the equation y = x² + 2x - 6 closest to?

If A is of dimension 1 * 4 and B is of dimension 4 * 1, what is the most accurate term to describe the result of the matrix multiplication AB?

What is the (first order) derivative of the function ?

The derivative of e⁴^x^-2 is:

"x to the power 3" could be written:

The trace of matrix C is

The rank of a square matrix is also:

Introduction

Mathematical and Statistical Foundations

Further Development and Analysis of the Classical Linear Regression Model

Classical Linear Regression Model Assumptions and Diagnostic Tests

Univariate Time Series Modelling and Forecasting

Multivariate Models

Modelling Long-Run Relationships in Finance

Modelling Volatility and Correlation

Switching Models

Panel Data and Limited Dependent Variable Models

Filters

Exam 3: A Brief Overview of the Classical Linear Regression Model

The point where the capital market line is tangential to the efficient frontier is

Log(1) is:

The derivative of log(5x) is:

For two conformable matrices A and B, expanding the parentheses of (AB)-1 gives:

The rank of matrices A and B from the previous question are:

The simplest possible way of writing 3x5 * 7x3 is:

Consider the following graphs. A. B. Which of the following statements is true?

What is the inverse of matrix ?

Consider the following data series: 11, 10, 6, 8, 4, 3, 7. What is its semi-interquartile range of this series?

Assume that the relationship between a company's stock price (y) and dividends paid per share (x) is linear. If the slope of the equation is 0.50 and the intercept is 30, what would be the expected stock price if the dividend paid was 3?

What are the roots of the equation y = 2x2 + 2x - 4?

Which of the following values are closes to the roots of the following quadratic equation: ?

What are the roots of the equation y = x2 + 2x - 6 closest to?

If A is of dimension 1 * 4 and B is of dimension 4 * 1, what is the most accurate term to describe the result of the matrix multiplication AB?

What is the (first order) derivative of the function ?

The derivative of e4x-2 is:

"x to the power 3" could be written:

The trace of matrix C is

The rank of a square matrix is also:

Introduction

Mathematical and Statistical Foundations

Further Development and Analysis of the Classical Linear Regression Model

Classical Linear Regression Model Assumptions and Diagnostic Tests

Univariate Time Series Modelling and Forecasting

Multivariate Models

Modelling Long-Run Relationships in Finance

Modelling Volatility and Correlation

Switching Models

Panel Data and Limited Dependent Variable Models

Filters

For two conformable matrices A and B, expanding the parentheses of (AB)^-1 gives:

The simplest possible way of writing 3x⁵ * 7x³ is:

What are the roots of the equation y = 2x² + 2x - 4?

What are the roots of the equation y = x² + 2x - 6 closest to?

The derivative of e⁴^x^-2 is: