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程序代写案例-MN50322

时间：2021-01-02

University of Bath School of Management

MN50322 Investment Management Autumn 2020

Revision Quiz B

Final review / submit once

This quiz This mini quiz is part of of the series of quizzes that form 10% of your

overall mark in this unit. The present quiz is the type-B quiz. It has 7 questions,

with a total of 50 marks. All quizzes together will have a total of 100 marks.

For this type-B quiz, you are asked to work on your own. The Forum is open

for general queries and for queries on the type-A quizzes, but the Forum is not open

for the present type-B quiz.

Submission is via Moodle. You can make your submission at any time between

publication of the quiz and the final deadline. (There is no re-submission.) The

final deadline is the 3rd of January, at 12:00 noon UK time.

The two questions in Part I carry a larger weight of 10 marks each. The five questions

in Part II are not necessarily any easier but they carry a lower weight of 6 marks each.

1

Part I: Investment Cases

Q1 Style Investment [10 Marks] You have access to two well-diversified portfolios L

and M , with factor loadings bL1 = 4 and bL2 = 0.25 for L and bM1 = .75 and bM2 = 2

for M . Mean returns are rL = 9 (per cent) for L and rL = 4 (per cent) for M . The

risk-free bond G has a rate of return rg of 2 per cent. Your client requests a portfolio

S that has the style

bS2

bS1

=

1

5

and a mean rate of return of rS = 4 (per cent). Find this portfolio. What is the weight

of L in S? (Rounding to 4 decimal points.)

(A) -0.2292

(B) 0.2292

(C) 0.2633

(D) 0.7708

(E) None of the above.

Q2 Active Investment [10 Marks] You are an active investor as in the Treynor-Black

model. The market portfolio has a mean rate of rM = 0.10 and a standard deviation

of σm = 0.14. The bond has a riskfree rate of rg = 0.03. You have special information

about stock A, which in your view has a mean rate of rA = 0.20. The beta of the

stock is βA = 1.2, the standard deviation is σa = 0.4. In your optimal mix of A and

M , how much of the the stock should you hold? (Rounded to 4 decimal places.)

(A) 0.1277

(B) 0.1422

(C) 0.3663

(D) 0.4595

(E) None of the above.

2

Part II: Elements of Portfolio Construction

Q3 Three assets in a 1-factor model [6 Marks] Suppose the market is governed by

a one-factor APT model, with factor-load equations

rj = aj + bjf + j .

Consider three well-diversified portfolios, L, M and N , each with zero residuals. There

is a riskfree bond with rate rg. The three portfolios have different factor exposures,

all positive. All assets are traded at no-arbitrage prices. The correct factor price is λ,

and we assume that lambda is positive. In a diagram with f on the horizontal axis

and rj on the vertical axis, we can draw the factor-load equations of L, M and N as

straight lines. We ask ourselves: do these three lines ever intersect with each other?

This is the same as asking whether there is a value of f at which the random returns

of the three portfolios happen to have the same return,

rL = rM = rN .

Which of the following statements is true?

(A) There exists no value of f for which all three assets have the same return.

(B) There exists a value of f for which all three assets have the same return, and this

value may be positive or negative depending on the specific factor loadings bL, bM ,

bN .

(C) There exists a value of f for which all three assets have the same return, and this

value will be negative. The precise value of f where the three assets have the same

return will be smaller (in absolute terms, closer to zero) if λ is larger.

(D) There exists a value of f for which all three assets have the same return, and this

value will be negative. The precise value of f where the three assets have the same

return will be larger (in absolute terms, ie further away from zero) if λ is larger.

Q4 Asset replication in a single-factor model [6 Marks] In a single-factor APT,

there are two widely diversified portfolios, L and M . Factor loadings are bL > 0 and

bM > 0, both different from each other. Intercepts are aL and aM . There is a riskfree

bond with riskfree rate rg. Which of the following statements is true?

(A) We can always find a portfolio of bond G and portfolio L that has the same factor

loading as portfolio M . The portfolio weight of G may be positive or negative.

(B) We can always find a portfolio of bond G and portfolio L that has the same factor

loading as portfolio M . The portfolio weight of G will be negative.

(C) We can always find a portfolio of bond G and portfolio L that has the same factor

loading as portfolio M . The portfolio weight of G will be positive.

(D) We can never find a portfolio of bond G and portfolio L that has the same factor

loading as portfolio M .

3

Q5 Asset Correlation in a two-factor model [6 Marks] Consider two individual assets

A and B, each with nonzero residual terms, a and b. Asset returns are governed by

a 2-factor model, with the standard assumptions. Which of the following statements

is true?

(A) The returns of the two assets will have correlation less than 1.

(B) The returns of the two assets will only be correlated with each other if their residual

terms are correlated.

(C) The returns of the two assets will not be correlated with each other.

(D) The returns of the two assets will only be correlated with each other if the factors

are correlated with each other.

(E) None of the above.

Q6 Styles and Efficiency [6 Marks] Consider a 2-factor market trading in a large

number of assets. The usual APT assumptions apply. The assets considered in this

question may be individual stocks or large portfolios. Which of the following statements

is correct?

(A) If the returns of asset A have a larger variance than the returns of asset B, and if

both returns have the same mean, then A must have more residual risk than B.

(B) If two assets have returns of equal mean and equal variance, they must have the

same factor exposures.

(C) In a market that satisfies the APT assumptions, if you wish to reduce portfolio

variance without reducing mean returns, the only way to do that is by increase the

number of assets in your portfolio.

(D) If the lambda equations predict that two portfolios A and B should both have the

same mean rate of return, then the APT investor will be indifferent between holding

portfolio A or portfolio B, regardless of their variance.

(E) None of the above.

4

Q7 Treynor-Black procedure [6 Marks] The Treynor-Black model is based on the

distinction between an “active stock”, about which the fund manager has special

knowledge, and the market portfolio that represents the consensus. Which of the

following statements about the Treynor-Black model is correct?

(A) If the fund manager chooses just one active stock, then the stock with the high-

est “performance index” (Qa = αa/IR

2

a) will lead to the highest increase of the

performance of the overall portfolio.

(B) If the fund manager chooses just one active stock, then the stock with the highest

“appraisal ratio” will lead to the highest increase of the performance of the overall

portfolio.

(C) If the fund manager chooses just one active stock, then the stock with the highest

“Treynor ratio” will lead to the highest increase of the performance of the overall

portfolio.

(D) In the Treynor-Black model, the fund manager includes larger holdings of the active

stock with the aim to maximise the Treynor ratio of her overall portfolio.

(E) The Treynor-Black model balances the active stock’s alpha against the active stock’s

idiosyncratic risk, and if the idiosincratic risk of the active stock is too large, the

fund manager will hold only the market portfolio.

END

5

MN50322 Investment Management Autumn 2020

Revision Quiz B

Final review / submit once

This quiz This mini quiz is part of of the series of quizzes that form 10% of your

overall mark in this unit. The present quiz is the type-B quiz. It has 7 questions,

with a total of 50 marks. All quizzes together will have a total of 100 marks.

For this type-B quiz, you are asked to work on your own. The Forum is open

for general queries and for queries on the type-A quizzes, but the Forum is not open

for the present type-B quiz.

Submission is via Moodle. You can make your submission at any time between

publication of the quiz and the final deadline. (There is no re-submission.) The

final deadline is the 3rd of January, at 12:00 noon UK time.

The two questions in Part I carry a larger weight of 10 marks each. The five questions

in Part II are not necessarily any easier but they carry a lower weight of 6 marks each.

1

Part I: Investment Cases

Q1 Style Investment [10 Marks] You have access to two well-diversified portfolios L

and M , with factor loadings bL1 = 4 and bL2 = 0.25 for L and bM1 = .75 and bM2 = 2

for M . Mean returns are rL = 9 (per cent) for L and rL = 4 (per cent) for M . The

risk-free bond G has a rate of return rg of 2 per cent. Your client requests a portfolio

S that has the style

bS2

bS1

=

1

5

and a mean rate of return of rS = 4 (per cent). Find this portfolio. What is the weight

of L in S? (Rounding to 4 decimal points.)

(A) -0.2292

(B) 0.2292

(C) 0.2633

(D) 0.7708

(E) None of the above.

Q2 Active Investment [10 Marks] You are an active investor as in the Treynor-Black

model. The market portfolio has a mean rate of rM = 0.10 and a standard deviation

of σm = 0.14. The bond has a riskfree rate of rg = 0.03. You have special information

about stock A, which in your view has a mean rate of rA = 0.20. The beta of the

stock is βA = 1.2, the standard deviation is σa = 0.4. In your optimal mix of A and

M , how much of the the stock should you hold? (Rounded to 4 decimal places.)

(A) 0.1277

(B) 0.1422

(C) 0.3663

(D) 0.4595

(E) None of the above.

2

Part II: Elements of Portfolio Construction

Q3 Three assets in a 1-factor model [6 Marks] Suppose the market is governed by

a one-factor APT model, with factor-load equations

rj = aj + bjf + j .

Consider three well-diversified portfolios, L, M and N , each with zero residuals. There

is a riskfree bond with rate rg. The three portfolios have different factor exposures,

all positive. All assets are traded at no-arbitrage prices. The correct factor price is λ,

and we assume that lambda is positive. In a diagram with f on the horizontal axis

and rj on the vertical axis, we can draw the factor-load equations of L, M and N as

straight lines. We ask ourselves: do these three lines ever intersect with each other?

This is the same as asking whether there is a value of f at which the random returns

of the three portfolios happen to have the same return,

rL = rM = rN .

Which of the following statements is true?

(A) There exists no value of f for which all three assets have the same return.

(B) There exists a value of f for which all three assets have the same return, and this

value may be positive or negative depending on the specific factor loadings bL, bM ,

bN .

(C) There exists a value of f for which all three assets have the same return, and this

value will be negative. The precise value of f where the three assets have the same

return will be smaller (in absolute terms, closer to zero) if λ is larger.

(D) There exists a value of f for which all three assets have the same return, and this

value will be negative. The precise value of f where the three assets have the same

return will be larger (in absolute terms, ie further away from zero) if λ is larger.

Q4 Asset replication in a single-factor model [6 Marks] In a single-factor APT,

there are two widely diversified portfolios, L and M . Factor loadings are bL > 0 and

bM > 0, both different from each other. Intercepts are aL and aM . There is a riskfree

bond with riskfree rate rg. Which of the following statements is true?

(A) We can always find a portfolio of bond G and portfolio L that has the same factor

loading as portfolio M . The portfolio weight of G may be positive or negative.

(B) We can always find a portfolio of bond G and portfolio L that has the same factor

loading as portfolio M . The portfolio weight of G will be negative.

(C) We can always find a portfolio of bond G and portfolio L that has the same factor

loading as portfolio M . The portfolio weight of G will be positive.

(D) We can never find a portfolio of bond G and portfolio L that has the same factor

loading as portfolio M .

3

Q5 Asset Correlation in a two-factor model [6 Marks] Consider two individual assets

A and B, each with nonzero residual terms, a and b. Asset returns are governed by

a 2-factor model, with the standard assumptions. Which of the following statements

is true?

(A) The returns of the two assets will have correlation less than 1.

(B) The returns of the two assets will only be correlated with each other if their residual

terms are correlated.

(C) The returns of the two assets will not be correlated with each other.

(D) The returns of the two assets will only be correlated with each other if the factors

are correlated with each other.

(E) None of the above.

Q6 Styles and Efficiency [6 Marks] Consider a 2-factor market trading in a large

number of assets. The usual APT assumptions apply. The assets considered in this

question may be individual stocks or large portfolios. Which of the following statements

is correct?

(A) If the returns of asset A have a larger variance than the returns of asset B, and if

both returns have the same mean, then A must have more residual risk than B.

(B) If two assets have returns of equal mean and equal variance, they must have the

same factor exposures.

(C) In a market that satisfies the APT assumptions, if you wish to reduce portfolio

variance without reducing mean returns, the only way to do that is by increase the

number of assets in your portfolio.

(D) If the lambda equations predict that two portfolios A and B should both have the

same mean rate of return, then the APT investor will be indifferent between holding

portfolio A or portfolio B, regardless of their variance.

(E) None of the above.

4

Q7 Treynor-Black procedure [6 Marks] The Treynor-Black model is based on the

distinction between an “active stock”, about which the fund manager has special

knowledge, and the market portfolio that represents the consensus. Which of the

following statements about the Treynor-Black model is correct?

(A) If the fund manager chooses just one active stock, then the stock with the high-

est “performance index” (Qa = αa/IR

2

a) will lead to the highest increase of the

performance of the overall portfolio.

(B) If the fund manager chooses just one active stock, then the stock with the highest

“appraisal ratio” will lead to the highest increase of the performance of the overall

portfolio.

(C) If the fund manager chooses just one active stock, then the stock with the highest

“Treynor ratio” will lead to the highest increase of the performance of the overall

portfolio.

(D) In the Treynor-Black model, the fund manager includes larger holdings of the active

stock with the aim to maximise the Treynor ratio of her overall portfolio.

(E) The Treynor-Black model balances the active stock’s alpha against the active stock’s

idiosyncratic risk, and if the idiosincratic risk of the active stock is too large, the

fund manager will hold only the market portfolio.

END

5