I’m working on a risk management writing question and need an explanation to help me understand better.Please note that ANSWER HAS BEEN FINISHED, what I need is some supplement of chart or diagram of the data to QUESTION 3 ONLY, I will provide the answers and you need to provide chart or diagram of the data to explain the data.FIN41360: Portfolio and Risk Management
Assignment 1
(Please read all instructions and notes very carefully)
Portfolio Choice and Performance Attribution
January 21, 2021
Required tasks:
1. Familiarize yourself with the content of the data library on Professor Kenneth French’s
webpage by reading the online legends and help. The web address of the data library is the
2. Then, select data from January 1963 to December 2020 on the 17 industry portfolios and
carry out the following analysis:
a. Sketch the monthly MV efficient frontier of these portfolios using first the sample
estimates of the required means and variance-covariance matrix and subsequently
their Bayes-Stein counterparts, first by shrinking only the mean and then shrinking
both the mean and the variance-covariance matrix.
b. On the frontiers you constructed, highlight the points corresponding to the global
minimum variance portfolio and to the tangency portfolio, assuming a risk-free rate
equal to its average over the sample period. For these portfolios, also compute and
report the mean excess-return, volatility and Sharpe ratio.
c. Compare and contrast the three frontiers you constructed (the frontier based on
sample estimates and the two based on their Bayes-Stein counterparts). How would
you explain their differences?
3. Next, choose one stock from each of the 17 industries and repeat the analysis above.
Compare and contrast the two pairs of MV efficient frontiers you constructed, first when
using sample estimates and then when using their Bayes-Stein counterparts. How would
you explain their differences?
4. Select data for the appropriate sample period on the risk-free rate (included among the socalled “Fama and French factors”, and available for download from the same data library)
and sketch the monthly MV efficient frontier for the 17 industry portfolios and the riskfree asset, using sample estimates of the required means and variance-covariance matrix.
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Compare and contrast this frontier to the ones previously constructed, after having
explained the sample period for which you obtained data on the risk-free rate.
5. Repeat the analysis required in the item just above (i.e., in question 4) using the Fama and
French factor-mimicking portfolios, also available from the webpage of Prof Kenneth
French, in place of the industry portfolios. Do so first using the so called “Fama/French 3
Factors” and then the “Fama/French 5 Factors (2×3)” mimicking portfolios (See Fama and
French, 1993, ”Common Risk Factors in the Returns on Stocks and Bonds,” Journal of
Financial Economics, and Fama and French, 2014, “A Five-Factor Asset Pricing Model”
for a complete description of the factor returns). Compare the resulting efficient frontiers
to the ones previously obtained. How would you explain their differences?
6. Repeat the above analysis (as specified in the item just above, namely question 5) using
suitable “practical proxies” for the Fama and French factor-mimicking portfolios in place
of the Fama and French factor-mimicking portfolios themselves. These practical proxies
should be highly investable, keeping transaction and execution costs in mind. That is, they
should be investable by the average portfolio manager, not necessarily the highly
sophisticated portfolio manager capable of replicating the actual factor-mimicking
portfolios. You may look for such proxy portfolios by checking out the websites of the
main futures exchanges (e.g., look for futures on small caps, such as the Russell 2000 Index
mini futures, and value/growth stocks) or even look for suitably focused ETFs (exchange
traded funds).1 In particular, try and find ways to work around the difficulty of short-selling
or minimize the associated costs. For ideas, check out this web-article:
Do so at least for “practical proxies” for the “Fama/French 3 Factors” and, ideally, also for
the “Fama/French 5 Factors (2×3)” mimicking portfolios, for as long a sample period for
which you can find data, making sure that the last observation is for December 2019 or
later (i.e., do not work with ‘dead’ series). To work around the lack of long time series on
suitable “practical proxies” (e.g., the Russell 2000 Index mini futures), you may use the
time series on a closely correlated asset or portfolio (e.g., the stock index underlying the
Russell 2000 Index mini futures, available since 1978), possibly after showing some
evidence on the strength of the correlation.
Compare and contrast the resulting efficient frontiers for the “practical proxies” to the ones
for the corresponding factor mimicking portfolios (make sure both frontiers are estimated
using the same sample period), explaining and/or commenting as appropriate.
7. Re-estimate the monthly frontiers for the 17 industry portfolios and for the “Fama/French
3 Factors (2×3)” mimicking portfolios over two contiguous time periods of equal length,
one ending in December 1991 and the other one ending in December 2020,
including the risk-free asset in the investment opportunity set. Pick at least one portfolio
See, for example, the approach adopted by Faff (2003) [Faff, R.W., 2003, “Creating Fama and French Factors with
Style”. Financial Review 38(2), 311-322].
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from each of the frontiers estimated in the first period and, for the portfolios thus selected,
compare the performance during this period to the performance during the second period.
Do these portfolios remain on the efficient frontier out-of-sample? Conduct the comparison
using the ‘all-time classic’ Jobson and Korkie (1981) test for the equality of the Sharpe
ratios (the test statistic is defined in footnote 20, page 271 of the Jorion (1985) article) as
well as the more modern test that does not require either the i.i.d. assumption or normality
(check out the article by Ledoit and Wolf (2008) and the accompanying Matlab code
available in the Brightspace page of the course).
8. Then, for at least some of the assets previously considered, repeat the above analysis
subject to any constraint and/or by applying any method, approach or technique (e.g.,
adding assets to better exploit the benefits of diversification, relying on the global
minimum variance portfolio, resampling, etc.) that you believe might be of interest and
might offer valuable insight from an investment management point of view.
9. Use the market portfolio, the practical proxies and the tangency portfolios (as appropriate)
on the various efficient frontiers you constructed above to assess the performance of tree
mutual funds of your choice, commenting on the results. A good source of data on mutual
funds is Yahoo Finance. Please see the Appendix for help on how to access data on Yahoo
Provide a soft copy report containing your findings, which should be appropriately tabulated so
as to maximize their legibility, any required evaluation and discussion of your findings and,
when appropriate, a description of the methodology adopted. The report should be submitted
via the submission folder on Brightspace by 22nd February 2021 (midnight). The submitted
report should be attached to the appropriate submission form, which should closely
adhere to the template provided in Brightspace and clearly provide all information
required therein, including the assignment number, the team number, the name and student
number of each team member and details on their individual contribution.2
The maximum length of the report should be 3000 words, including tables and figures (and
everything else). Do not neglect to cite references as appropriate (of course, the bibliography
is included in the word count). To stay within the word count, it will be important to organize
your report appropriately (e.g., making appropriate use of tables, avoiding repetitions, etc.).
Workings by way of MS Excel spreadsheets or Matlab code and data should be e-mailed to
my e-mail address: emmanuel.eyiah-donkor@ucd.ie. Although grades are solely based on
your report, the workings are required to verify all calculations. In the email title, you should
indicate FIN41360: Assignment 1, followed by the team number in brackets.3
The due date and weighting on the overall module grade of this assignment are as specified in
the course outline.
Please note that this is a requirement and, if not fulfilled, I will not accept the submission, applying any relevant late
submission penalty until a proper submission is made.
Please note that this is a requirement and, if not fulfilled, I will not accept the submission, applying any relevant late
submission penalty until a proper submission is made.
Page 3 of 5

The required tasks in the above list are, to a large extent, in a sequential order, in the sense that
the initial ones are necessary for the subsequent ones. Hence, if you run out of time, it is better
to carry out the earlier ones to the best of your ability rather than trying to do everything to a
lesser standard.

Clarity is of paramount importance and lack thereof will be penalized heavily. Essentially, as
in real world endeavors, unclear answers and discussion will amount to not having provided
the required answer/discussion. Hence, try and privilege clarity and quality over quantity. For
example, if you are running out if time, it is better to address well a few questions than to
attempt to address them all in a poor and, hence, necessarily obscure manner.

All the relevant information for the assignment is provided in this document and the course
outline. If an aspect of the analysis is not specified in either document, it means that it is left
for students to make a choice on it, in light of the theory covered in the course.

Students are required to make and motivate any such choice relying on the insight offered by
the theory covered in the course and relevant references. The soundness of such choices,
evaluated in the light of available theory and empirical evidence, will be assessed and
contribute to the overall mark. The more advanced aspects of the assignment also require a
certain amount of autonomous research, which will play an especially important role in the
assignment of higher marks.

Submissions should contain, as appropriate, a literature review. The latter should strive to offer
a comprehensive and systematic, yet succinct, review and discussion of academic and
practitioners contributions to the body of knowledge on issues and topics examined during the
course that are relevant to address the issues at hand, with the aim to expand and offer
additional substantial insight compared to the insight and level of knowledge developed by the
course material (including lectures).

In this regard, keep in mind that the assignment is designed so that only a small fraction of the
teams will be able to address all questions well, because marking practice in serious
Universities (such as UCD, which has this enshrined in official marking rules) dictate that the
highest marks be awarded with parsimony.

In preparing the report, try and replicate as closely as possible the layout and structure (though
subject to the applicable maximum length restriction) of academic papers that evaluate the
performance of alternative portfolio construction methodologies. A good yet nice and readable
example is the article by Stevenson (2002) titled “Ex-Ante and Ex-Post Performance of
Optimal REIT Portfolios” (among the readings in Brightspace). You might also take heed from
industry reports that do something similar, which often have nice and witty ways of making
insightful points, though strive to aim at a level of clarity and rigor comparable to the academic
papers. The paper by Rob Arnott of Research Affiliates (titled “How Can Smart Beta Go
Horribly Wrong”) is a good example of clear and compelling industry report:
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Please keep in mind however that, if you lack the insight of an industry maverick (that comes
with many years of first-hand experience), the academic format might be a safer option as it is
designed to facilitate making a point in an effective way relying only on research, without
needing any special experience of the subject matter. An academic researcher gains insight
from research, not necessarily experience, so it is a situation closer to the one of a typical

Appropriate use of tables and figures, as in academic papers and rigorous industry reports, is
of crucial importance to attain the required clarity. They should be thoughtfully designed to
maximize clarity and impact. For example, annotate your tables and figures to help the reader
gain an immediate understanding of the findings reported therein. Also, try and condense your
findings in as few tables and figures as possible, to help the reader see the overall picture
emerging from your study.

Mutatis mutandis (i.e., with the appropriate adaptation) and unless otherwise specified, all the
above notes apply to subsequent assignments too.

Teams are strongly encouraged to appoint an “editor” whose job should be to coordinate the
efforts of the team and make sure that the final report is coherent and well organized.
Appendix – Accessing data in Yahoo Finance
On Yahoo Finance, find two ETFs (Exchange Traded Funds) that have been listed for at least a year and
download the time series of closing prices for the last 251 trading days (if any one of the ETFs does not
trade on a given trading day, assume that the closing price is the same as for the previous trading day).
To get this data, you need to go to https://finance.yahoo.com. Then, under the “My Screeners” tab, select
the “Mutual Fund Screener” tab and, when the “Mutual Fund Screener” dialog box opens, add or remove
filters according to your own preference. When you are done, press “Find Mutual Funds”. A selection of
Mutual Funds will be shown. Choose the ones you want by clicking on the symbol of each. In the screen
that opens when you click each Mutual Fund symbol, select the “Historical Data” tab and, in the screen that
opens next, select the “Daily” frequency (from the dedicated drop-down menu) and then click “Download
Page 5 of 5
Portfolio and Risk Management
Student’s Name:
Institutional affiliations:
Question 3:
An efficient Frontier is a set of optimal portfolios that provides the best returns in a given
level of risks or have the lowest chances in a defined group of expected returns. In industry 17,
the weighted average returns of clothes and mines are used to discuss the efficient frontiers for
sector 21.
Average weighted returns
The variance level is directly proportional to the risk level, where high variance indicates a high
level of risks and low friction shows a low-risk group.
Portfolio variance = W12Q12+W22Q22+ 2w1w2Cov1, 2
The correlation of Clothes Is 0.17, and the correlation of mines is 0.12
= (17.212 *0.172) + (11.742 *0.122) + (0.17*0.12 17.21*11.24)
= (296.18* 0.0289) =0.8559602
= (137.83* 0.0144) = 1.984752
= (0.17*0.12) = 0.0204
= (17.21*11.24) = 193.4404
(0.0204 193.4404) = 1.055
0.8559602+ 1.984752+1.055= 3.8957122
Average weighted returns
Portfolio variance = W12Q12+W22Q22+ 2w1w2Cov1, 2
(11.492 *0.112) + (10.522 *0.112) + (0.11*0.11 11.49*10.52)
= (132.0202* 0.0121) =1.59744
= 110.6704* 0.0121= 1.33911184
0.0121 120.8748 =1.001
=1.59744+ 1.33911184+1.001= 3.93755184
The two pairs are different where the first was 3.8957122, and the second one was
3.93755184. The second pair has higher efficient frontiers showing that the first has lower
chances of risks. The second production mix has a higher level of risk and lower returns.
According to Kalygin (2020), the producer may consider the first pair due to the lower risk rate.
Risk management is an important aspect to determine the product mix with lower rates of risks.
The difference in the results is also due to the differences in the average value-weighted returns.
The first pair has a higher average value-weighted return than the second one and thus the
differences in efficient frontiers.
Question 4:
The two frontiers are different due to the differences in the various aspects of the
production mix. The risk-free rate is where the investor can operate and runs the project risk-free
over a specified period. In this period, the risk management strategies are of no need, and thus
the operation runs smoothly. Kalygin (2020) affirmed that the investor expects to earn on
investments with zero risks during this period. The return rate where the returns of a
hypothetical investment meet a fixed period’s payments and all payment obligations are covered.
The free, risk-free rate results impact the optimal portfolio in the real aspects, not only the
assumption. The theory of risk-free is unrealistic, and thus it is criticized as compared to the
efficient frontier, which is considered more realistic. Risk-free trade eliminates unsystematic or
specific risk, unlike the effective frontier, which does not stop these risks (Bauder, 2019). The
disadvantage of risk-free trade is that it leads to vitality, unlike the latter and thus not considered.
It also negatively impacts the return on the market. It may also lead to the backward presentation
of the returns and, therefore, may not be preventable in the future market returns.
Question 5:
Factor mimicking portfolio is a list of assets designed to stand in place of the background
factors. It is the replication of the stock to produce the same in an equal period. It is an important
aspect used as an exchange-traded fund that serves as proxies for global factors. The firm’s size
is also a cause of the disparity between the two variables (Bauder, 2019). The other aspect is the
value premium and excess returns on the market. Profitability and investment is also a
mimicking tool. The profitability of a project and a successful investment can be used to decide
what investment to replicate. Large firms’ portfolios have a high average return than the small
firms and thus the difference in the different aspects. The significant size factor is also defined
as small minus big. The difference in size influences portfolio returns since the amount of risk is
relative to the market (Das, 2011). The differences are in a stock’s total return, the risk-free
return rate of the two projects, absolute market portfolio differences, and size and value
premium. Coefficient factors, momentum, and quality are also other differences in the two
Question 6:
Useful proxies are the art of statistical and portfolio modeling. It is a comparison of the
performance of the stock in the market and that of the market. Also, the theoretical perceptive
and presentation of the price movements of all market sectors. The larger market size and
complexity influences the practical proxies of the portfolio modeling. The pricing model strategy
ensures that the investment provides more returns and increases the project; pricing restriction is
excellent, primarily with an observable risk-free rate (Das, 2011). This mode holds all security
returns, including the proxy returns and the structural relationship between the security and
proxy returns. The model also confirms the number of replication a stock can take to make a
profit and ensure the profitability of the organization’s investment. These techniques save cost
and provide even though the project’s organization is small; it matches their target indices ad thus
a practical method to compare the index returns accounting effort the transaction costs as
affirmed by Kalygin (2020). This proxy matches the dimensions of the relevant risk, and with
accuracy, the analysis results are of perfection and thus profitability of the organization. It also
ensures systemic reduction of risks and therefore sufficiently matches the industry’s dynamics
providing credit qualities and prevents domination of non-systemic risks.
Kalygin, V. A., & Slashchinin, S. V. (2020, May). Uncertainty of Efficient Frontier in Portfolio
Optimization. In International Conference on Learning and Intelligent Optimization (pp.
371-376). Springer, Cham.
Bauder, D., Bodnar, R., Bodnar, T., & Schmid, W. (2019). Bayesian estimation of the efficient
frontier. Scandinavian Journal of Statistics, 46(3), 802-830.
Das, S., Markowitz, H., Scheid, J., & Statman, M. (2011). Portfolios for Investors Who Want to
Reach TheirGoals While Staying on the Mean-Variance Efficient Frontier. The Journal
of Wealth Management, 14(2), 25-31.
Portfolio and Risk Management Outline
1.1 Question 3
1.2 Question 4
1.3 Question 5
1.4 Question 6
1.5 References

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