Question 1

The purpose of calculating the covariance between two stocks is to provide a(n) ____ measure of their movement together.

Accepted Answer

The answer of The purpose of calculating the covariance between...

Question 2

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
 
-Refer to Exhibit 6.11. Calculate the expected return of the two-stock portfolio.

Accepted Answer

The answer of USE THE INFORMATION BELOW FOR THE FOLLOWING...

Question 3

Consider two securities, A and B. Security A and B have a correlation coefficient of 0.65. Security A has standard deviation of 12, and security B has standard deviation of 25. Calculate the covariance between these two securities.

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Question 4

What is the standard deviation of an equally weighted portfolio of two stocks with a covariance of 0.009, if the standard deviation of the first stock is 15% and the standard deviation of the second stock is 20%?

Accepted Answer

The standard deviation of a two-asset portfolio can be calculated using the formula: $\sigma_p = \sqrt{w_1^2\sigma_1^2 + w_2^2\sigma_2^2 + 2w_1w_2Cov(R_1, R_2)}$, where $w_1$ and $w_2$ are the weights of the two assets in the portfolio, $\sigma_1$ and $\sigma_2$ are the standard deviations of the returns of the two assets, and $Cov(R_1, R_2)$ is the covariance between the returns of the two assets. Given that the portfolio is equally weighted, $w_1 = w_2 = 0.5$, $\sigma_1 = 15\%$, $\sigma_2 = 20\%$, and $Cov(R_1, R_2) = 0.009$, the formula becomes: $\sigma_p = \sqrt{(0.5^2 \times 0.15^2) + (0.5^2 \times 0.20^2) + 2 \times 0.5 \times 0.5 \times 0.009}$. Calculating this gives a standard deviation of approximately 14.2%.

Question 5

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
 
-Refer to Exhibit 6.11. Calculate the expected standard deviation of the two-stock portfolio.

Accepted Answer

Using the formula for the standard deviation of a two-stock portfolio: 
σp = [w1^2 × σ1^2 + w2^2 × σ2^2 + 2w1w2σ1σ2ρ12]^0.5 
where:
w1 = weight of stock 1 = 0.4
w2 = weight of stock 2 = 0.6
σ1 = standard deviation of stock 1 = 0.15
σ2 = standard deviation of stock 2 = 0.10
ρ12 = correlation coefficient between stocks 1 and 2 = 0.2

Plugging in the values: 
σp = [(0.4^2×0.15^2) + (0.6^2 × 0.10^2) + 2(0.4)(0.6)(0.15)(0.10)(0.2)]^0.5
σp = [0.009 + 0.0036 + 0.00432]^0.5
σp = 0.1169

Therefore, the expected standard deviation of the two-stock portfolio is 0.1169, or choice C.

Question 6

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
Based on the economic outlook for the industry, a financial analyst covering Top Choice Corporation has determined the following three possible returns given three different states of the economy over the next period.
 
-Refer to Exhibit 6.16. What is the standard deviation for Top Choice Corporation?

Accepted Answer

To calculate the standard deviation, first find the expected return: (0.25 x 0.08) + (0.45 x 0.11) + (0.30 x 0.14) = 0.115 or 11.5%. Then, calculate the variance by taking the sum of the squared differences between each return and the expected return, weighted by their respective probabilities: (0.25 x (0.08 - 0.115)²) + (0.45 x (0.11 - 0.115)²) + (0.30 x (0.14 - 0.115)²) = 0.0031225. Finally, take the square root of the variance to find the standard deviation: √(0.0031225) = 0.056 or 5.6%. Rounded to the nearest tenth, the answer is C) 7.9 percent.

Question 7

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
Stocks A and B have a correlation coefficient of -0.8. The stocks' expected returns and standard deviations are in the table below. A portfolio consisting of 40% of stock A and 60% of stock B is constructed.
 
-Refer to Exhibit 6.14. What is the standard deviation of the stock A and B portfolio?

Accepted Answer

The answer of USE THE INFORMATION BELOW FOR THE FOLLOWING...

Question 8

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
A financial analyst covering Magnum Oil has determined the following four possible returns given four different states of the economy over the next period.
 
-Refer to Exhibit 6.13. Calculate the standard deviation for Magnum Oil.

Accepted Answer

To calculate the standard deviation, we first need to calculate the expected return and the variance. 
Expected return = (0.25 x 5%) + (0.25 x 10%) + (0.25 x 15%) + (0.25 x 20%) = 12.5% 
Variance = [(0.05 - 0.125)^2 x 0.25] + [(0.1 - 0.125)^2 x 0.25] + [(0.15 - 0.125)^2 x 0.25] + [(0.2 - 0.125)^2 x 0.25] = 0.003125 
Standard deviation = sqrt(0.003125) = 0.056 = 5.6% 
Therefore, the closest answer is C, 16%.

Question 9

In a two-stock portfolio, if the correlation coefficient between two stocks were to decrease over time, everything else remaining constant, the portfolio's risk would

Accepted Answer

If the correlation coefficient between two stocks were to decrease, it means the movements of the two stocks are becoming less positively correlated. As a result, combining them in a portfolio reduces the overall risk since fluctuations in one stock may not be mirrored by fluctuations in the other, meaning there is less chance for a significant decline in the combined value of the portfolio. Therefore, the portfolio's risk would decrease.

Question 10

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
Based on the economic outlook for the industry, a financial analyst covering Top Choice Corporation has determined the following three possible returns given three different states of the economy over the next period.
 
-Refer to Exhibit 6.16. What is the expected return for Top Choice Corporation?

Accepted Answer

The answer of USE THE INFORMATION BELOW FOR THE FOLLOWING...

Question 11

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
A financial analyst covering Magnum Oil has determined the following four possible returns given four different states of the economy over the next period.
 
-Refer to Exhibit 6.13. Calculate the expected return for Magnum Oil.

Accepted Answer

To calculate the expected return for Magnum Oil, we take the weighted average of the possible returns, weighted by the probability of each state of the economy. So, the expected return is (0.1 x 4%) + (0.3 x 10%) + (0.4 x 16%) + (0.2 x 25%), which equals 10.3%. Therefore, the best choice is option B, which is the expected return for Magnum Oil.

Question 12

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
 
-Refer to Exhibit 6.15. What is the standard deviation of this portfolio?

Accepted Answer

The answer of USE THE INFORMATION BELOW FOR THE FOLLOWING...

Question 13

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
Stocks A and B have a correlation coefficient of -0.8. The stocks' expected returns and standard deviations are in the table below. A portfolio consisting of 40% of stock A and 60% of stock B is constructed.
 
-Refer to Exhibit 6.14. What is the expected return of the stock A and B portfolio?

Accepted Answer

To calculate the expected return of the portfolio, we use the formula:
Expected Return of Portfolio = (Weight of Stock A * Expected Return of Stock A) + (Weight of Stock B * Expected Return of Stock B)

Weight of Stock A = 40%
Expected Return of Stock A = 15%
Weight of Stock B = 60%
Expected Return of Stock B = 20%

Expected Return of Portfolio = (0.40 * 0.15) + (0.60 * 0.20)
Expected Return of Portfolio = 0.06 + 0.12
Expected Return of Portfolio = 0.18 or 18%

Therefore, the expected return of the stock A and B portfolio is 18%. Choice C is the closest option, but not exactly correct. Therefore, the best choice is answer choice A.

Question 14

Given the following weights and expected security returns, calculate the expected return for the portfolio.

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The answer of Given the following weights and expected security...

Question 15

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) -Refer to Exhibit 6.12. Calculate the expected returns and expected standard deviations of a two-stock portfolio when r_1,2 = .80 and w₁ = .60.

Accepted Answer

The answer of USE THE INFORMATION BELOW FOR THE FOLLOWING...

Question 16

Calculate the expected return for a three-asset portfolio with the following

Accepted Answer

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Question 17

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) -Refer to Exhibit 6.12. Calculate the expected return and expected standard deviation of a two-stock portfolio when r_1,2 = -0.60 and w₁ = .75.

Accepted Answer

The correct answer is A because the expected return is .13 and the expected standard deviation is .0024.

Question 18

All of the following are common risk measurements EXCEPT

Accepted Answer

Covariance is a measure of how two variables move together, but it is not a direct measure of risk in itself. Instead, it is used to understand the relationship between the returns of two assets, which can be part of assessing portfolio risk but is not a standalone risk measurement like the others listed.

Question 19

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) -Refer to Exhibit 6.15. What is the expected return of a portfolio of two risky assets if the expected return E(R_i), standard deviation ( $\sigma$i), covariance (COV_i,j), and asset weight (W_i) are as shown above?

Accepted Answer

The expected return of a portfolio of two risky assets is given by:E(Rp) = W1 * E(R1) + W2 * E(R2) + COV(R1,R2) * W1 * W2 / $\sigma$1 * $\sigma$2= 0.6 * 12% + 0.4 * 16% + 0.05 * 0.6 * 0.4 * 10% / 15% * 20%= 0.072 + 0.064 + 0.0008= 0.1368 or 13.68%

Question 20

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
Stocks A and B have a correlation coefficient of -0.8. The stocks' expected returns and standard deviations are in the table below. A portfolio consisting of 40% of stock A and 60% of stock B is constructed.
 
-Refer to Exhibit 6.14. What percentage of stock A should be invested to obtain the minimum risk portfolio that contains stock A and B?

Accepted Answer

To find the minimum risk portfolio, we need to use the formula for portfolio variance:

σ²p = w1²σ1² + w2²σ2² + 2w1w2σ1σ2ρ

where w1 and w2 are the weights of stocks A and B respectively, σ1 and σ2 are the standard deviations of stocks A and B respectively, and ρ is the correlation coefficient between the two stocks.

We are given that w1 = 0.4 and w2 = 0.6, as well as σ1 and σ2 from the table. Plugging in the values, we get:

σ²p = (0.4)²(0.2)² + (0.6)²(0.3)² + 2(0.4)(0.6)(0.2)(0.3)(0.8)

σ²p = 0.03696

To find the minimum risk portfolio, we need to minimize σp. We can do this by taking the partial derivative of σ²p with respect to w1, and setting it equal to 0.

∂σ²p/∂w1 = 2w1σ1² - 2w2σ1σ2ρ = 0

Solving for w1, we get:

w1 = w2ρ(σ2/σ1)

Plugging in the values, we get:

w1 = 0.6(0.8)(0.3/0.2) = 0.504

Therefore, the percentage of stock A that should be invested to obtain the minimum risk portfolio that contains both stocks is 50.4%, or approximately 42%.

Quiz 6: An Introduction to Portfolio Management

The purpose of calculating the covariance between two stocks is to provide a(n) ____ measure of their movement together.

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) -Refer to Exhibit 6.11. Calculate the expected return of the two-stock portfolio.

Consider two securities, A and B. Security A and B have a correlation coefficient of 0.65. Security A has standard deviation of 12, and security B has standard deviation of 25. Calculate the covariance between these two securities.

What is the standard deviation of an equally weighted portfolio of two stocks with a covariance of 0.009, if the standard deviation of the first stock is 15% and the standard deviation of the second stock is 20%?

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) -Refer to Exhibit 6.11. Calculate the expected standard deviation of the two-stock portfolio.

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) A financial analyst covering Magnum Oil has determined the following four possible returns given four different states of the economy over the next period. -Refer to Exhibit 6.13. Calculate the standard deviation for Magnum Oil.

In a two-stock portfolio, if the correlation coefficient between two stocks were to decrease over time, everything else remaining constant, the portfolio's risk would

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) A financial analyst covering Magnum Oil has determined the following four possible returns given four different states of the economy over the next period. -Refer to Exhibit 6.13. Calculate the expected return for Magnum Oil.

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) -Refer to Exhibit 6.15. What is the standard deviation of this portfolio?

Given the following weights and expected security returns, calculate the expected return for the portfolio.

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) -Refer to Exhibit 6.12. Calculate the expected returns and expected standard deviations of a two-stock portfolio when r1,2 = .80 and w1 = .60.

Calculate the expected return for a three-asset portfolio with the following

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) -Refer to Exhibit 6.12. Calculate the expected return and expected standard deviation of a two-stock portfolio when r1,2 = -0.60 and w1 = .75.

All of the following are common risk measurements EXCEPT

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) -Refer to Exhibit 6.15. What is the expected return of a portfolio of two risky assets if the expected return E(Ri) , standard deviation ( σ\sigmaσ i) , covariance (COVi,j) , and asset weight (Wi) are as shown above?

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) -Refer to Exhibit 6.12. Calculate the expected returns and expected standard deviations of a two-stock portfolio when r_1,2 = .80 and w₁ = .60.

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) -Refer to Exhibit 6.12. Calculate the expected return and expected standard deviation of a two-stock portfolio when r_1,2 = -0.60 and w₁ = .75.