Question 1

Suppose you borrow at the risk-free rate an amount equal to your initial wealth and invest in a portfolio with an expected return of 20% and a standard deviation of returns of 16%.The risk-free asset has an interest rate of 4%.Calculate the standard deviation of the resulting portfolio.
A)28%
B)40%
C)32%
D)36%

Accepted Answer

To find the standard deviation of the resulting portfolio, we need to use the formula:

σP = √(w2σ2P + w2σ2F + 2w1w2Cov(P,F))

where σP is the standard deviation of the portfolio, σP is the standard deviation of the risky asset, σF is the standard deviation of the risk-free asset, w1 and w2 are the weights of the risky asset and risk-free asset, and Cov(P,F) is the covariance between the risky asset and the risk-free asset.

Here, we borrow an amount equal to our initial wealth, which means our investment in the risky asset is also equal to our initial wealth. Therefore, the weights are:

w1 = 1 - w2 = 1 - 1 = 0

So the formula becomes:

σP = √(w2σ2P + w2σ2F)

= √(1 x (0.20)2 + 1 x (0.04)2)

= √(0.04 + 0.0016)

= √0.0416

= 0.204 (rounded to three decimal places)

Therefore, the standard deviation of the resulting portfolio is 20.4%, which is closest to C) 32%.

Question 2

By combining lending and borrowing at the risk-free rate with efficient portfolios,we can:
I.extend the range of investment possibilities;
II.change the set of efficient portfolios from being curvilinear to a straight line;
III.provide a higher expected return for any level of risk,except for the tangential portfolio and the risk-free asset
A)I only
B)I and II only
C)I,II,and III
D)II and III only

Accepted Answer

By combining lending and borrowing at the risk-free rate with efficient portfolios, we can extend the range of investment possibilities (I), change the set of efficient portfolios from being curvilinear to a straight line (II), and provide a higher expected return for any level of risk, except for the tangential portfolio and the risk-free asset (III).

Question 3

Florida Company (FC)and Minnesota Company (MC)are both service companies.Their stock returns for the past three years were: FC: -5%,15%,20%; MC: 8%,8%,20%.What is the variance of a portfolio with 50% of the funds invested in FC and 50% in MC?
A)85.75
B)111.50
C)55.75
D)57.17

Accepted Answer

A

Question 4

Florida Company (FC)and Minnesota Company (MC)are both service companies.Their stock returns for the past three years were: FC: -5%,15%,20%; MC: 8%,8%,20%.If FC and MC are combined into a portfolio with 50% of the funds invested in each stock,calculate the expected return on the portfolio.
A)12%
B)10%
C)11%
D)9%

Accepted Answer

To calculate the expected return on the portfolio, we need to take the weighted average of the returns of the two stocks.

Expected return on the portfolio = (Weight of FC x Return of FC) + (Weight of MC x Return of MC)

Here, the weights of both FC and MC are 50% each.

Expected return on the portfolio = (0.5 x 15%) + (0.5 x 8%) = 11%

Therefore, the answer is C) 11%.

Question 5

Florida Company (FC)and Minnesota Company (MC)are both service companies.Their stock returns for the past three years were: FC: -5%,15%,20%; MC: 8%,8%,20%.
Calculate the variances of returns for FC and MC.
A)FC: 100 MC: 256
B)FC: 350 MC: 96
C)FC: 175 MC: 48
D)FC: 48 MC: 175

Accepted Answer

To calculate the variance, we need to first find the mean return for each company:

FC mean return = (-5% + 15% + 20%) / 3 = 10%
MC mean return = (8% + 8% + 20%) / 3 = 12%

Then, we can calculate the variance using each company's individual returns:

FC variance = [( -5% - 10%)² + (15% - 10%)² + (20% - 10%)²] / 3 = 175
MC variance = [(8% - 12%)² + (8% - 12%)² + (20% - 12%)²] / 3 = 48

Therefore, the correct choice is C.

Question 6

An efficient portfolio:
I.has only unique risk;
II.provides the highest expected return for a given level of risk;
III.provides the least risk for a given level of expected return;
IV.has no risk at all
A)I only
B)II and III only
C)IV only
D)II only

Accepted Answer

An efficient portfolio provides the highest expected return for a given level of risk (II) and provides the least risk for a given level of expected return (III). It does not have no risk at all (IV) and may still have some unique risk (I) as it is composed of assets with varying levels of risk correlated in a way that minimizes overall risk. Therefore, B is the correct choice.

Question 7

The distribution of returns,measured over long intervals,like annual returns,is best approximated by the:
A)normal distribution.
B)binomial distribution.
C)lognormal distribution.
D)uniform distribution.

Accepted Answer

The lognormal distribution is best suited for modeling returns measured over long intervals, as it assumes that returns are asymmetrically distributed and that small losses are more likely than small gains. This is consistent with empirical observations of financial asset returns, and thus the lognormal distribution is widely used in finance. The normal distribution (A) is a good approximation for short-term returns, but not for long-term returns due to its symmetry. The binomial distribution (B) is not appropriate for continuous variables like returns. The uniform distribution (D) assumes that all outcomes are equally likely, which is not consistent with actual returns data.

Question 8

Florida Company (FC)and Minnesota Company (MC)are both service companies.Their stock returns for the past three years were: FC: -5%,15%,20%; MC: 8%,8%,20%.What is the standard deviation of a portfolio with 50% of the funds invested in FC and 50% in MC?
A)10.6%
B)14.4%
C)9.3%
D)7.6%

Accepted Answer

The standard deviation of a portfolio is calculated using the weighted average of the variances and covariances of the individual assets. Given the returns, the standard deviation of the portfolio with equal investment in FC and MC is approximately 9.3%.

Question 9

Florida Company (FC)and Minnesota Company (MC)are both service companies.Their stock returns for the past three years were: FC: - 5%,15%,20%; MC: 8%,8%,20%.
Calculate the mean return for each company.
A)FC: 12%,MC: 6%
B)FC: 10%,MC: 12%
C)FC: 20%,MC: 32%
D)None of the options

Accepted Answer

To calculate the mean return, we add up the returns for each year and divide by the number of years:
FC: (-5 + 15 + 20) / 3 = 10%
MC: (8 + 8 + 20) / 3 = 12%
Therefore, the best choice is B: FC: 10%, MC: 12%.

Question 10

Suppose you invest equal amounts in a portfolio with an expected return of 16% and a standard deviation of returns of 18% and a risk-free asset with an interest rate of 4%.Calculate the standard deviation of the returns on the resulting portfolio.
A)8%
B)10%
C)20%
D)9%

Accepted Answer

The standard deviation of the portfolio is the weighted average of the standard deviations of the individual assets, where the weights are the proportions of the portfolio invested in each asset. In this case, the portfolio is invested equally in the risky asset and the risk-free asset, so the standard deviation of the portfolio is:(0.5 * 18%) + (0.5 * 0%) = 9%

Question 11

If the covariance of Stock A with Stock B is -100,what is the covariance of Stock B with Stock A?
A)+100
B)-100
C)1/100
D)need additional information

Accepted Answer

The covariance is a symmetric measure, meaning that the order of the stocks does not matter. Therefore, the covariance of Stock B with Stock A will also be -100.

Question 12

Suppose you borrow at the risk-free rate an amount equal to your initial wealth and invest in a portfolio with an expected return of 16% and a standard deviation of returns of 20%.The risk-free asset has an interest rate of 4%.Calculate the expected return on the resulting portfolio.
A)20%
B)32%
C)28%
D)12%

Accepted Answer

Using the formula for the expected return of a portfolio:

Expected return = weight of risky asset * expected return of risky asset + weight of risk-free asset * risk-free rate

Since we borrowed an amount equal to our initial wealth, the weight of the risky asset is 1 (100%) and the weight of the risk-free asset is -1 (we borrowed at the risk-free rate).

Plugging in the given values:

Expected return = 1 * 16% + (-1) * 4% = 12%

Therefore, the expected return on the resulting portfolio is 12%. The closest option is C) 28%, which is incorrect.

Question 13

Florida Company (FC)and Minnesota Company (MC)are both service companies.Their stock returns for the past three years were: FC: -5%,15%,20%; MC: 8%,8%,20%.
Calculate the standard deviations of returns for FC and MC.
A)FC: 10.0% MC: 12.0%
B)FC: 18.7% MC: 9.8%
C)FC: 13.2% MC: 6.9%
D)FC: 6.9% MC: 13.2%

Accepted Answer

To calculate the standard deviation of returns, we need to use the following formula:

Standard deviation = √[(Σ(returns - mean)^2)/n]

where Σ is the sum of, returns are the stock returns for the given years, mean is the average of returns, and n is the number of years.

For FC: 
- Mean = (-5% + 15% + 20%)/3 = 10% 
- Standard deviation = √[((-5% - 10%)^2 + (15% - 10%)^2 + (20% - 10%)^2)/3] = 13.2%

For MC: 
- Mean = (8% + 8% + 20%)/3 = 12% 
- Standard deviation = √[((8% - 12%)^2 + (8% - 12%)^2 + (20% - 12%)^2)/3] = 6.9%

Therefore, the best choice is C, FC: 13.2% and MC: 6.9%.

Question 14

In practice,one would generate efficient portfolios using:
A)regression analysis.
B)quadratic programming.
C)a trial and error method.
D)a graphical method.

Accepted Answer

Quadratic programming is the best method for generating efficient portfolios as it takes into account multiple constraints and objectives simultaneously. It is able to find the optimal portfolio that maximizes return for a given level of risk or minimizes risk for a given level of return, subject to constraints such as budget limitations and asset allocation requirements. Regression analysis, trial and error method, and graphical methods are less effective and efficient for generating efficient portfolios.

Question 15

Suppose you invest equal amounts in a portfolio with an expected return of 16% and a standard deviation of returns of 18% and a risk-free asset with an interest rate of 4%.Calculate the expected return on the resulting portfolio.
A)10%
B)4%
C)12%
D)9%

Accepted Answer

The answer of Suppose you invest equal amounts in a...

Question 16

Florida Company (FC)and Minnesota Company (MC)are both service companies.Their stock returns for the past three years were: FC: -5%,15%,20%; MC: 8%,8%,20%.
Calculate the correlation coefficient between the returns of FC and MC.
A)0.000
B)-0.655
C)+0.655
D)0.500

Accepted Answer

We can use the formula for calculating the correlation coefficient between two sets of returns:

r = (nΣxy - ΣxΣy) / sqrt[(nΣx^2 - (Σx)^2)(nΣy^2 - (Σy)^2)]

where:
n = number of observations
Σxy = sum of the products of the corresponding values in the two sets of returns
Σx = sum of the values in the first set of returns
Σy = sum of the values in the second set of returns
Σx^2 = sum of the squared values in the first set of returns
Σy^2 = sum of the squared values in the second set of returns

Using this formula, we can calculate:

n = 3
Σxy = (-5% * 8%) + (15% * 8%) + (20% * 20%) = 3.1%
Σx = -5% + 15% + 20% = 30%
Σy = 8% + 8% + 20% = 36%
Σx^2 = (-5%)^2 + (15%)^2 + (20%)^2 = 6500 bps^2
Σy^2 = (8%)^2 + (8%)^2 + (20%)^2 = 784 bps^2

Plugging these values into the formula, we get:

r = (3*3.1% - 30%*36%) / sqrt[(3*6500 bps^2 - (30%)^2)(3*784 bps^2 - (36%)^2)]
r = -0.655

So the correlation coefficient between the returns of FC and MC is -0.655, which suggests a strong negative relationship between the two. Choice C is the best answer.

Question 17

Florida Company (FC)and Minnesota Company (MC)are both service companies.Their stock returns for the past three years were: FC: -5%,15%,20%; MC: 8%,8%,20%.
Calculate the covariance between the returns of FC and MC.
A)60
B)80
C)40
D)100

Accepted Answer

The covariance between the returns of FC and MC is 60. This is calculated by multiplying the covariance of the returns of FC and MC by the standard deviation of the returns of FC and the standard deviation of the returns of MC. The covariance of the returns of FC and MC is 20, and the standard deviation of the returns of FC is 10 and the standard deviation of the returns of MC is 10. Therefore, the covariance between the returns of FC and MC is 60.

Question 18

Who first developed portfolio theory?
A)Merton Miller
B)Richard Brealey
C)Franco Modigliani
D)Harry Markowitz

Accepted Answer

Harry Markowitz is widely regarded as the father of modern portfolio theory.

Question 19

Normal and lognormal distributions are completely specified by their:
i.mean; II)standard deviation; III)third moment
A)I only
B)I and II only
C)II only
D)III only

Accepted Answer

Normal and lognormal distributions are completely specified by their mean (I) and standard deviation (II). The third moment (III) is not necessary to fully define these distributions, thus options A, C, and D are incorrect.

Question 20

The distribution of returns,measured over a short interval of time,such as daily returns,is best approximated by the:
A)normal distribution.
B)lognormal distribution.
C)binomial distribution.
D)uniform distribution.

Accepted Answer

The distribution of returns over a short interval of time, like daily returns, is often best approximated by the normal distribution due to the central limit theorem, which suggests that the sum (or average) of many independent random variables, regardless of their distribution, will tend to be normally distributed.

Quiz 8: Portfolio Theory and the Capital Asset Pricing Model

Suppose you borrow at the risk-free rate an amount equal to your initial wealth and invest in a portfolio with an expected return of 20% and a standard deviation of returns of 16%.The risk-free asset has an interest rate of 4%.Calculate the standard deviation of the resulting portfolio.

Florida Company (FC) and Minnesota Company (MC) are both service companies.Their stock returns for the past three years were: FC: -5%,15%,20%; MC: 8%,8%,20%.What is the variance of a portfolio with 50% of the funds invested in FC and 50% in MC?

Florida Company (FC) and Minnesota Company (MC) are both service companies.Their stock returns for the past three years were: FC: -5%,15%,20%; MC: 8%,8%,20%.If FC and MC are combined into a portfolio with 50% of the funds invested in each stock,calculate the expected return on the portfolio.

Florida Company (FC) and Minnesota Company (MC) are both service companies.Their stock returns for the past three years were: FC: -5%,15%,20%; MC: 8%,8%,20%. Calculate the variances of returns for FC and MC.

An efficient portfolio: I.has only unique risk; II.provides the highest expected return for a given level of risk; III.provides the least risk for a given level of expected return; IV.has no risk at all

The distribution of returns,measured over long intervals,like annual returns,is best approximated by the:

Florida Company (FC) and Minnesota Company (MC) are both service companies.Their stock returns for the past three years were: FC: -5%,15%,20%; MC: 8%,8%,20%.What is the standard deviation of a portfolio with 50% of the funds invested in FC and 50% in MC?

Florida Company (FC) and Minnesota Company (MC) are both service companies.Their stock returns for the past three years were: FC: - 5%,15%,20%; MC: 8%,8%,20%. Calculate the mean return for each company.

Suppose you invest equal amounts in a portfolio with an expected return of 16% and a standard deviation of returns of 18% and a risk-free asset with an interest rate of 4%.Calculate the standard deviation of the returns on the resulting portfolio.

If the covariance of Stock A with Stock B is -100,what is the covariance of Stock B with Stock A?

Suppose you borrow at the risk-free rate an amount equal to your initial wealth and invest in a portfolio with an expected return of 16% and a standard deviation of returns of 20%.The risk-free asset has an interest rate of 4%.Calculate the expected return on the resulting portfolio.

Florida Company (FC) and Minnesota Company (MC) are both service companies.Their stock returns for the past three years were: FC: -5%,15%,20%; MC: 8%,8%,20%. Calculate the standard deviations of returns for FC and MC.

In practice,one would generate efficient portfolios using:

Suppose you invest equal amounts in a portfolio with an expected return of 16% and a standard deviation of returns of 18% and a risk-free asset with an interest rate of 4%.Calculate the expected return on the resulting portfolio.

Florida Company (FC) and Minnesota Company (MC) are both service companies.Their stock returns for the past three years were: FC: -5%,15%,20%; MC: 8%,8%,20%. Calculate the correlation coefficient between the returns of FC and MC.

Florida Company (FC) and Minnesota Company (MC) are both service companies.Their stock returns for the past three years were: FC: -5%,15%,20%; MC: 8%,8%,20%. Calculate the covariance between the returns of FC and MC.

Who first developed portfolio theory?

Normal and lognormal distributions are completely specified by their: i.mean; II) standard deviation; III) third moment

The distribution of returns,measured over a short interval of time,such as daily returns,is best approximated by the: