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LSE ST2020/ST436 Page 1 of 4
Summer Assessment 2020
Assessment paper and instructions to
candidates: ST436 – FINANCIAL STATISTICS
Suitable for all candidates
Instructions to candidates
This paper contains 3 questions.
Answer 3 questions. Question 1 is worth 34%. Questions 2 and 3 are worth 33%
each.
Answers should be justified by showing work.
Time Allowed: until 12pm on 27th May
Upper word limit: 4000-5000 (this is an approximate limit and there are no
penalties for exceeding it)
You may use: any sources that are available to you; please reference all
sources in a bibliography.
• Specify the question numbers that you answered in the boxes provided at the
end of the paper.
• You will need to include a bibliography or a list of references at the end of
your submission. Whenever you use the words or thoughts of another, you
need to reference it in (Name, Year) format in the text of your answer, and the
corresponding full reference needs to appear in the bibliography at the end.
When inserting a section of text (of any size) from someone else's work in to
your own, you must use quotation marks and a reference to the source in
(Name, Year: Page) format to make clear that you are citing verbatim. Failure
to do so may result in allegations of plagiarism.
• This online assessment has an approximate upper word limit of 1500 words
per question (so that is 4000-5000 words overall). This is in addition to any
LSE ST2020/ST436 Page 2 of 4
tables, figures, bibliography, computer code. There is no penalty for
exceeding this upper limit; however, please fit your entire assessment
(including everything) on 25 pages A4 maximum. Anything from page 26
onwards will not be read or assessed. If you use MS Word, please use font
Roboto size 11. If you use Latex, please use double spacing and a font of size
11. Please use margins of about one inch (2.54cm) on all four sides of the
page.
• Any code included in your report must be in R, and must be executable on a
clean install of R. Please keep your code listings to an absolute minimum as
they take up precious writing space, and are usually very hard to read. Any
code submitted without thorough and detailed comments will not be read or
assessed.
• We expect you to spend approximately up to a day per question to prepare
and revise, and another day per question to write up. Organise your time
well, and avoid working all night. Sleep and a social life are good for the
quality of your thinking.
Assessment questions
1. Read the paper by Catalin Starica entitled “Is GARCH(1,1) as good a model as the
Nobel Prize accolades would imply?” The paper is available on the Moodle page for
ST436, or please download it from
https://pdfs.semanticscholar.org/d5f7/b07d931274e7c9fbae10c647021696971731.pd
f. If neither of these methods of obtaining the paper work, please email
p.fryzlewicz@lse.ac.uk for a copy. Having read the paper, please perform the
following tasks.
(a) In your own words, say what the paper is about. What is its main message? What
is the paper trying to argue?
(b) Describe in detail the two methods for volatility forecasting presented in the
paper: (i) based on the GARCH(1,1) model and (ii) based on the time-varying
unconditional variance approach. Your description must be detailed enough for
someone who has completed ST436 but has no prior knowledge of Starica’s article
to be able to re-code both predictors in a computer programming language based on
your description. However, please answer this part in your own words and using
mathematical notation only; do not include any code.
(c) In your experience, which approach is better in what circumstances? To answer
this question, implement both approaches in R. Design and carry out a numerical
study to compare the empirical performance of both approaches in forecasting
volatility. In executing this task, please bear in mind the following points.
- You may wish to base your argument on a diverse selection of financial time series
(e.g. foreign exchange, individual share prices, stock indices from various regions of
the world). For each dataset you use, please say precisely how you have obtained it;
your reference must be precise enough for your reader to be able to obtain exactly
the same dataset. For this project, it is enough to focus on daily data.
- As of April 2020, many financial markets are experiencing huge fluctuations; it
LSE ST2020/ST436 Page 3 of 4
would be of great interest how the two approaches compare in particular during this
extraordinary period. You may want to include the period January-April 2020 in your
test sets.
- Please remember to base your findings on a variety of forecasting horizons; not
only “one day ahead”. What error measure are you going to use? How are you going
to measure the “true” volatility to be forecast?
- Please include your R code in the appendix; it must be commented and executable
on a clean install of R. With the help of the code, your reader must be able to
reproduce exactly any tables and/or figures included in your answer to this question.
- Important: your answer to this question must be in prose that is easy to understand
for your peers. (You can imagine, for example, that you are writing a blog post for a
specialised “financial statistics” blog started recently by your former classmates from
your undergraduate university.)
2. In the recent weeks, markets in several western countries experienced very high
levels of volatility. Several popular press articles commented that the recent market
swings were “the biggest since . . .”, with different articles making different versions
of this argument: “the biggest since 1929”, “the biggest since 1987”, or “the biggest
since 2008”, amongst others.
Use your knowledge and skills gained in ST436 to develop and convey your own
understanding of how the magnitude of the recent market movements compares to
the biggest moves seen in the 20th and 21st centuries, listed above. Have the recent
market movements really been “the biggest since. . .”? If so, since when? In your
analysis, you may want to pay attention to the points below.
(a) What markets are you going to use to draw your argument on? It is a good idea to
look at a diverse selection of markets from different continents, including Asia,
Europe and the Americas.
(b) How are you going to measure the magnitude of market movements? Examine
the lecture notes to look for ideas. In particular, you may want to review the content
of the following chapters: “Exploratory analysis of financial data”, “ARCH-type models
for low-frequency asset returns”, “Value at Risk”.
As in question 1,
- For each dataset you use, please say precisely how you have obtained it; your
reference must be precise enough for your reader to be able to obtain exactly the
same dataset. For this project, it is enough to focus on daily data.
- Please include your R code in the appendix; it must be commented and executable
on a clean install of R. With the help of the code, your reader must be able to
reproduce exactly any tables and/or figures included in your answer to this question.
- Important: your answer to this question must be in prose that is easy to understand
for your peers. (You can imagine, for example, that you are writing a blog post for a
specialised “financial statistics” blog started recently by your former classmates from
your undergraduate university.)
LSE ST2020/ST436 Page 4 of 4
3. In this project, you will re-visit the case study of Chapter 4 of the lecture notes.
Instead of basing it on linear regression as was done in the lectures, you will base it
on two other classification and prediction technologies discussed in the course:
nearest neighbours, and CART. Here is a possible workflow to guide you.
(a) Code, in R, your own implementation of nearest neighbours in a form that will
make it convenient for you to use it in the case study. This should be done from first
principles, i.e. you should not be using any specialised R packages (see item (b)
below).
(b) Locate any existing R packages that implement nearest neighbours classification.
Write alternative code for nearest-neighbour classification that uses one of these
packages.
(c) Code, in R, your own implementation of CART in a form that will make it
convenient for you to use it in the case study. This should be done from first
principles, i.e. you should not be using any specialised R packages (see item (d)
below).
(b) Locate any existing R packages that implement CART. Write alternative code for
CART that uses one of these packages.
(e) Re-do the case study, i.e. re-do Exercises 7 from the lecture course, but replacing
the linear regression method of prediction with your code from parts (a), (b), (c) and
(d).
(f) In addition to the questions contained in Exercises 7, answer one additional
question: if your Sharpe ratios obtained on the test set are positive, are they
“significantly” positive? For a hint on how to answer this question, please see the
very final part of Chapter 6 of the lecture notes. If your Sharpe ratios are not positive,
are you able to idenfity what causes this performance?
As in the two previous questions,
- Please include your R code in the appendix; it must be commented and executable
on a clean install of R. With the help of the code, your reader must be able to
reproduce exactly any tables and/or figures included in your answer to this question.
- It would be a good idea to include the period January-April 2020 in your test set.
- Important: your answer to this question must be in prose that is easy to understand
for your peers. (You can imagine, for example, that you are writing a blog post for a
specialised “financial statistics” blog started recently by your former classmates from
your undergraduate university.)

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