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.
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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.
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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 .
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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.
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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
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