finance

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FN625: Financial Risk Analysis

Assignment 1

(Please read all instructions and notes very carefully)

Portfolio Choice and Performance Attribution

Feb 05, 2023

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

following:

http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

2. Then, select data from January 1963 to December 2023 on the 17 industry portfolios

(value-weighted) 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.

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 frontiers you constructed. 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. How would

you explain their differences?

4. Select data for the appropriate sample period on the risk-free rate (included among the so-

called “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 risk-

free 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 (2x3)” 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:

http://money.usnews.com/investing/articles/2016-06-07/why-investors-should-consider-

small-cap-stocks

Do so at least for “practical proxies” for the “Fama/French 3 Factors” and, ideally, also for

the “Fama/French 5 Factors (2x3)” 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

5 Factors (2x3)” mimicking portfolios over two contiguous time periods of equal length,

one ending in December 1993 and the other one ending in December 2023,

including the risk-free asset in the investment opportunity set. Pick at least one portfolio

1 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?

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

three 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 Finance.

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 submitted report should be

attached to the appropriate submission form, which should closely adhere to the template

provided in Moodle and clearly provide all information required therein, including the

assignment number, name and student number.

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, M a t l a b , R code and data should be a d d e d

t o M o o d l e p a g e e-mailed to e-mail address: [email protected]. Although grades are

solely based on your report, the workings are required to verify all calculations. In the email title,

you should indicate FN625: Assignment 1.2

The weighting on the overall module grade of this assignment are as specified in the course

outline.

2 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.

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Notes:

• 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 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 Moodle). 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:

https://www.researchaffiliates.com/en_us/publications/articles/442_how_can_smart_beta_go_horribl

y_wrong.html

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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

student.

• 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.

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

Data”.