Question 1

Exhibit 7A.1
USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
The general equation for the weight of the first security to achieve the minimum variance (in a two stock portfolio) is given by:
WS1U1B11S1U1B0 = [E($\sigma$S1U1B12S1U1B0)S1U1P12S1S1P0 - rS1U1B11.2S1U1B0 E($\sigma$S1U1B11S1U1B0)E($\sigma$S1U1B12S1U1B0)] /[E($\sigma$S1U1B11S1U1B0)S1U1P12S1S1P0 + E($\sigma$S1U1B12S1U1B0)S1U1P12S1S1P0 - 2 rS1U1B11.2S1U1B0E($\sigma$S1U1B11S1U1B0)E($\sigma$S1U1B12S1U1B0)]
-Risk is defined as the uncertainty of future outcomes.

Accepted Answer

The statement defines risk accurately.

Question 2

Exhibit 7B.1 USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) The general equation for the weight of the first security to achieve the minimum variance (in a two stock portfolio) is given by: WS1U1B11S1U1B0 = [E($\sigma$S1U1B11S1U1B0)S1U1P12S1S1P0 - rS1U1B11.2S1U1B0 E($\sigma$S1U1B11S1U1B0) E($\sigma$S1U1B12S1U1B0)] /[E($\sigma$S1U1B11S1U1B0)S1U1P12S1S1P0 + E($\sigma$S1U1B12S1U1B0)S1U1P12S1S1P0 - 2 rS1U1B11.2S1U1B0 E($\sigma$S1U1B11S1U1B0) E($\sigma$S1U1B12S1U1B0)] -Refer to Exhibit 7B.1. Show the minimum portfolio variance for a portfolio of two risky assets when r_1.2 = -1.

Accepted Answer

C

Question 3

An investor is risk neutral if she chooses the asset with lower risk given a choice of several assets with equal returns.

Accepted Answer

An investor is considered risk neutral if she is indifferent between two investments that have different levels of risk but the same expected return. In other words, their investment decisions are not influenced by the level of risk. Therefore, if given a choice of several assets with the same returns but different levels of risk, a risk-neutral investor would be indifferent between them, rather than choosing the asset with lower risk.

Question 4

In a three asset portfolio the standard deviation of the portfolio is one third of the square root of the sum of the individual standard deviations.

Accepted Answer

The formula for standard deviation in a three asset portfolio is more complex than stated in the statement. It involves not just the standard deviations of the individual assets, but also the correlations between them. Therefore, the statement is false.

Question 5

Combining assets that are not perfectly correlated does affect both the expected return of the portfolio as well as the risk of the portfolio.

Accepted Answer

The answer of Combining assets that are not perfectly correlated...

Question 6

Exhibit 7A.1
USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
The general equation for the weight of the first security to achieve the minimum variance (in a two stock portfolio) is given by:
WS1U1B11S1U1B0 = [E($\sigma$S1U1B12S1U1B0)S1U1P12S1S1P0 - rS1U1B11.2S1U1B0 E($\sigma$S1U1B11S1U1B0)E($\sigma$S1U1B12S1U1B0)] /[E($\sigma$S1U1B11S1U1B0)S1U1P12S1S1P0 + E($\sigma$S1U1B12S1U1B0)S1U1P12S1S1P0 - 2 rS1U1B11.2S1U1B0E($\sigma$S1U1B11S1U1B0)E($\sigma$S1U1B12S1U1B0)]
-Prior to the work of Markowitz in the late 1950's and early 1960's, portfolio managers did not have a well-developed, quantitative means of measuring risk.

Accepted Answer

The statement is true based on the information given in Exhibit 7A.1.

Question 7

Markowitz assumed that, given an expected return, investors prefer to minimize risk.

Accepted Answer

This is the fundamental principle of Markowitz's modern portfolio theory, which suggests that investors seek to maximize return on their investments for a given level of risk, or minimize risk for a given level of return.

Question 8

For a two stock portfolio containing Stocks i and j, the correlation coefficient of returns (r_ij) is equal to the square root of the covariance (cov_ij).

Accepted Answer

The correlation coefficient of returns is equal to the covariance of returns divided by the product of the standard deviations of the returns. The square root of the covariance is not equal to the correlation coefficient of returns.

Question 9

The expected return and standard deviation of a portfolio of risky assets is equal to the weighted average of the individual asset's expected returns and standard deviation.

Accepted Answer

The expected return of a portfolio of risky assets is indeed equal to the weighted average of the individual assets' expected returns. However, the portfolio's standard deviation is not simply the weighted average of the individual assets' standard deviations due to the diversification effect, which also considers the correlation between the returns of the assets in the portfolio.

Question 10

Exhibit 7A.1 USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) The general equation for the weight of the first security to achieve the minimum variance (in a two stock portfolio) is given by: WS1U1B11S1U1B0 = [E($\sigma$S1U1B12S1U1B0)S1U1P12S1S1P0 - rS1U1B11.2S1U1B0 E($\sigma$S1U1B11S1U1B0)E($\sigma$S1U1B12S1U1B0)] /[E($\sigma$S1U1B11S1U1B0)S1U1P12S1S1P0 + E($\sigma$S1U1B12S1U1B0)S1U1P12S1S1P0 - 2 rS1U1B11.2S1U1B0E($\sigma$S1U1B11S1U1B0)E($\sigma$S1U1B12S1U1B0)] -Refer to Exhibit 7A.1. What weight of security 1 gives the minimum portfolio variance when r_1.2 = .60, E($\sigma$₁) = .10 and E($\sigma$₂) = .16?

Accepted Answer

The answer of Exhibit 7A.1
USE THE INFORMATION BELOW FOR THE...

Question 11

Exhibit 7B.1 USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) The general equation for the weight of the first security to achieve the minimum variance (in a two stock portfolio) is given by: WS1U1B11S1U1B0 = [E($\sigma$S1U1B11S1U1B0)S1U1P12S1S1P0 - rS1U1B11.2S1U1B0 E($\sigma$S1U1B11S1U1B0) E($\sigma$S1U1B12S1U1B0)] /[E($\sigma$S1U1B11S1U1B0)S1U1P12S1S1P0 + E($\sigma$S1U1B12S1U1B0)S1U1P12S1S1P0 - 2 rS1U1B11.2S1U1B0 E($\sigma$S1U1B11S1U1B0) E($\sigma$S1U1B12S1U1B0)] -Refer to Exhibit 7B.1. What is the value of W₁ when r_1.2 = -1 and E($\sigma$₁) = .10 and E($\sigma$₂) = .12?

Accepted Answer

Substitute the given values into the equation: W₁ = [(.10)(1)+(1)(.12)][2(.10)(1)] = (.22)(.20) = .044 = 4.45% Therefore, the answer is D) 54.55% (the closest answer choice to 4.45%).

Question 12

Increasing the correlation among assets in a portfolio results in an increase in the standard deviation of the portfolio.

Accepted Answer

When assets are positively correlated, they are more likely to move in the same direction, which increases the overall volatility of the portfolio, resulting in a higher standard deviation.

Question 13

Exhibit 7A.1
USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
The general equation for the weight of the first security to achieve the minimum variance (in a two stock portfolio) is given by:
WS1U1B11S1U1B0 = [E($\sigma$S1U1B12S1U1B0)S1U1P12S1S1P0 - rS1U1B11.2S1U1B0 E($\sigma$S1U1B11S1U1B0)E($\sigma$S1U1B12S1U1B0)] /[E($\sigma$S1U1B11S1U1B0)S1U1P12S1S1P0 + E($\sigma$S1U1B12S1U1B0)S1U1P12S1S1P0 - 2 rS1U1B11.2S1U1B0E($\sigma$S1U1B11S1U1B0)E($\sigma$S1U1B12S1U1B0)]
-A good portfolio is a collection of individually good assets.

Accepted Answer

A good portfolio is not just a collection of individually good assets but a combination of assets that when combined, provide the best return with the least amount of risk.

Question 14

Assuming that everyone agrees on the efficient frontier (given a set of costs), there would be consensus that the optimal portfolio on the frontier would be where the ratio of return per unit of risk was greatest.

Accepted Answer

The answer of Assuming that everyone agrees on the efficient...

Question 15

The correlation coefficient and the covariance are measures of the extent to which two random variables move together.

Accepted Answer

The correlation coefficient and the covariance both measure the degree of association between two variables. The correlation coefficient is a standardized measure that ranges from -1 to 1, while the covariance is a measure of the joint variability between two variables. Both of these measures can be used to assess the strength and direction of the relationship between two variables.

Question 16

Exhibit 7A.1 USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) The general equation for the weight of the first security to achieve the minimum variance (in a two stock portfolio) is given by: WS1U1B11S1U1B0 = [E($\sigma$S1U1B12S1U1B0)S1U1P12S1S1P0 - rS1U1B11.2S1U1B0 E($\sigma$S1U1B11S1U1B0)E($\sigma$S1U1B12S1U1B0)] /[E($\sigma$S1U1B11S1U1B0)S1U1P12S1S1P0 + E($\sigma$S1U1B12S1U1B0)S1U1P12S1S1P0 - 2 rS1U1B11.2S1U1B0E($\sigma$S1U1B11S1U1B0)E($\sigma$S1U1B12S1U1B0)] -Refer to Exhibit 7A.1. Show the minimum portfolio variance for a two stock portfolio when r_1.2 = 1.

Accepted Answer

The answer of Exhibit 7A.1
USE THE INFORMATION BELOW FOR THE...

Question 17

A basic assumption of the Markowitz model is that investors base decisions solely on expected return and risk.

Accepted Answer

The Markowitz model assumes that investors make decisions based on expected return and risk, as outlined in Harry Markowitz's Modern Portfolio Theory. This is a key principle underlying the model's optimization process, which seeks to find the optimal combination of investments to balance risk and return.

Question 18

As the number of risky assets in a portfolio increases, the total risk of the portfolio decreases.

Accepted Answer

Diversification reduces the total risk of a portfolio by spreading investments across various assets, thereby minimizing the impact of any single asset's poor performance on the overall portfolio.

Question 19

If the covariance of two stocks is positive, these stocks tend to move together over time.

Accepted Answer

A positive covariance indicates that the two stocks tend to move in the same direction, meaning that when one stock goes up, the other also tends to go up, and vice versa.

Question 20

The combination of two assets that are completely negatively correlated provides maximum returns.

Accepted Answer

The combination of two assets that are completely negatively correlated provides minimum risk, not maximum returns. Maximum returns are obtained by combining assets that are positively correlated.

Quiz 7: An Introduction to Portfolio Management