Question 1

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. A)E($\sigma$₁) /[E($\sigma$₁) + E($\sigma$₂)] B)E($\sigma$₁) / [E($\sigma$₁) - E($\sigma$₂)] C)E($\sigma$₂) -[E($\sigma$₁) + E($\sigma$₂)] D)E($\sigma$₂) /[E($\sigma$₁)- E($\sigma$₂)] E)None of the above

Accepted Answer

C

Question 2

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 3

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? A).0244 B).3679 C).5697 D).6309 E).9756

Accepted Answer

E

Question 4

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 5

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 are rational and base their decisions solely on expected return and risk, without considering other factors like liquidity or personal preferences.

Question 6

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 risk neutral if she is indifferent between assets with equal expected returns but different levels of risk. In other words, the investor does not consider risk when making investment decisions. Choosing the asset with lower risk given a choice of several assets with equal returns would make the investor risk-averse, not risk-neutral.

Question 7

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

Prior to the work of Markowitz, portfolio managers mainly used qualitative means to measure risk. Markowitz's development of modern portfolio theory introduced a quantitative approach to measuring risk and revolutionized the field of portfolio management.

Question 8

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 rather a mix of assets that work well together to balance risk and return, taking into consideration correlation and diversification.

Question 9

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 the standard deviation of a three-asset portfolio is not simply one-third of the square root of the sum of the individual standard deviations. It is a more complex formula that takes into account the individual asset weights and correlations between the assets.

Question 10

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

Question 11

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 12

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

Accepted Answer

The correlation coefficient and covariance both measure the relationship between two variables, whether they are positively or negatively correlated. A positive covariance indicates that both variables increase or decrease together, while a negative covariance indicates an inverse relationship. The correlation coefficient measures the strength and direction of the relationship between the variables, while the covariance measures the magnitude of the relationship.

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)] -Refer to Exhibit 7A.1. Show the minimum portfolio variance for a two stock portfolio when r_1.2 = 1. A)E($\sigma$₂) -[E($\sigma$₁) -E($\sigma$₂)] B)E($\sigma$₂) -[E($\sigma$₁) + E($\sigma$₂)] C)E($\sigma$₁) - [E($\sigma$₁) -E($\sigma$₂)] D)E($\sigma$₁) /[E($\sigma$₁) + E($\sigma$₂)] E)None of the above

Accepted Answer

The correct answer is A because the minimum portfolio variance for a two stock portfolio when r_1.2 = 1 is given by E($\sigma$₂) -[E($\sigma$₁) -E($\sigma$₂)].

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

Accepted Answer

The combination of two assets that are completely negatively correlated minimizes risk, not necessarily maximizes returns.

Question 16

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

Accepted Answer

This is one of the key assumptions of Markowitz's modern portfolio theory, which states that investors are risk-averse and prefer portfolios with lower risk for the same expected return.

Question 17

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 move in the same direction. Therefore, if one stock goes up, the other is likely to go up as well, and vice versa.

Question 18

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

Accepted Answer

Increasing the correlation among assets in a portfolio results in a higher level of systematic risk, which increases the standard deviation of the portfolio.

Question 19

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? A)45.46% B)50.00% C)59.45% D)54.55% E)74.55%

Accepted Answer

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

Question 20

Risk is defined as the uncertainty of future outcomes.

Accepted Answer

This is a commonly accepted definition of risk, which acknowledges that there is a level of uncertainty about what may happen in the future.

Quiz 7: An Introduction to Portfolio Management