London School of EconomicsFM321

Risk Management and Modelling Autumn 2024

1 Assessment criteria

The marking frame that applies to this course is

70+:First

60-69:Upper Second

50-59:Lower Second

40-49:Third

0-39:Fail

Assessment for this course has the following four parts:

1. Homework 1, 10 marks

2. Homework 2, 10 marks

3. Project, 30 marks

4. Exam, 50 marks

2 Administrative details

Administrative contacts: Ella Lucas, [email protected]

Office MAR 7.39. Office hours Tuesdays 15:00 - 16:30. Zoom meetingson

demand.

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3 Syllabus

Main textbook:Financial Risk Forecasting:, Jon Danielsson, 2011.

Other readings are listed in the slides.

Slides: will be on Moodle, but also book website,www.financialriskforecasting.com.

The sample code is on the book website.

Book chapters covered:

1. Financial Markets, Prices and Risk

2. Univariate Volatility Modelling

3. Multivariate Volatility Models

4. Risk Measures

5. Implementing Risk Forecasts

6. Analytical Value-at-Risk for Options and Bonds

7. Simulation Methods for VaR for Options and Bonds

8. Backtesting and Stress Testing

9. Endogenous Risk

10. Market risk regulations (only slides)

11. Artificial intelligence (only slides)

4 Learning resources

More information in lecture slides.

You can find detailed information on R specific to the course on the book web-

sitewww.financialriskforecasting.comand the LSE Digital Skills Lab.

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5 Data sources

For this course, it is essential to register for a WRDS (Wharton Research

Data Services) account. This is done by going to

https://wrds-www.wharton.upenn.edu/register/

and completing the requested details. In the department field,enter the

module code to ensure easy authorisation by the Library, which is usually

done within 2 working days. Do NOT write Department of Finance in the

department field as this will delay the account authorisationdue to proce-

dures that have to be followed as part of LSE’s contracts with suppliers.

Once authorised by the Library, your WRDS account will expireon 20 June

2025.

See www.financialriskforecasting.com/notebook/Background/FinancialData.html

for a list of data sources.

6 Assessed homeworks and project

There are two assessed homework assignments and one project.

They should be uploaded to Moodle in PDF format (Word does not ensure

pictures and equations look the same when opened with different versions of

Word).

You should hand in three files: one with the code, one with the data, and a

PDF file with the solution. The PDF solution should have a 12-point font

size and a regular margin size.

We normally expect you to program in R, but you can also use Python,

Matlab, or Julia. If you want to use any of these alternative languages, do

check with us first.

You can use any software you choose to make the PDFs. Most will use

Microsoft Word or Quarto (the language of RStudio).

The homeworks and project are summative assignments and are marked

anonymously. Therefore,you MUST NOT use your name anywhere

on any materials you submit. This applies to your PDF file with your

write-up, the comments included in your programs, your file names, or any-

thing else in your submissions. Instead, use your exam candidate number to

identify yourself.

These assignments are meant to allow students to apply the knowledge ac-

quired in the course in a realistic setting. Your goal is to use thetools you

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have learned to analyse data and provide interesting and relevant conclu-

sions. You can imagine that you are working in the finance industry as a

quantitative analyst, and your supervisor has asked you to carryout a project

(analyse data, implement a model, and so on) that will be useful for your

firm.

It is up to you to choose how you present your solution, data, plots, statistics

and data transformation. It is just like if your superior in an organisation

asks you for such a document. You will have to decide how to best execute

it, and that choice is part of the assessment.

6.1 Assessment

Please note that if you fail to submit the assignments on time, a penalty will

apply. One mark out of 100 will be deducted for any piece of coursework

submitted within 24 hours of the deadline, and a further one mark will be

deducted for each subsequent 24-hour period until the coursework is submit-

ted. After five days, work will not be accepted, and you will receive a mark

of zero.

The assessment will be based on two elements:the effectiveness of your

presentation and the quality of your quantitative work.Your ability

to describe your work, interpret your results, provide meaningful conclusions

and answer questions all matter.

Naturally, the correctness of your work matters, and you should convince

your supervisors that what you’ve done makes sense. Thus, the accuracy of

your code and the methodological choices you make are important. However,

they are not everything: your ability to draw relevant practical conclusions

from your work and answer questions matters as well.

We will also run your code to ensure that it is correct and produces the

results you present. These elements are part of the assessment.

On the other hand, your coding style won’t be assessed. Nevertheless,we

strongly suggest that you follow good programming practice by indenting

your code appropriately, providing helpful comments, and choosing mean-

ingful variable names.

Thehomeworks and projectare strictly individual and independent work.

The choice of topic, data collection, empirical analysis, andthe writing of

the project are entirely the responsibility of the student.

Besides the quality of the analysis you do, presentation is also important for

assessment. It is important to use the correct font size and standardpage

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margins, as well as ensure the documents follow the prescribed number of

pages for the homework and the word count for the project is not exceeded.

We expect the visual aspect of the documents to be of business quality. We

suggest you follow the guidelines in the R notebook on how to incorporate

images into your document. In particular, screenshots are of low quality and

don’t meet the expected standard.

7 Assessed homework

7.1 Assessed homework 1

The main solution PDF document should be two pages.

Due date 11 November 2024 at 9:00 am.

Download two daily stock prices from WRDS (or some other data source),

where the stocks are traded on the same exchange. Describe where you

got the stocks from and what companies they are. Plot the prices, convert

them into returns, and plot those. Present the relevant sample statistics and

describe them. Point out major events as reflected in the plots you show.

Show how volatility and correlations have evolved throughout your sample

period. Make a recommendation to your employer based on your results.

7.2 Assessed homework 2

The main solution PDF document should be five pages.

Due date 17 December 2024 at 9:00 am.

Pick one of the questions from Appendix A at the end of this document.

Find the appropriate data, transform the data, present summary statistics,

and execute the analysis in the question.

8 Project

Due date 22 January 2025 at 9:00 am.

Number of words not to exceed 3,000.

The project consists of a written document that analyses a research ques-

tion related to the course material and demonstrates that you have correctly

acquired the content and skills developed throughout the course.

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The research question analysed in the project needs to be answered em-

pirically. This means that the project is an applied projectthat involves

collecting data, analysing the data using statistical techniques discussed in

the course and interpreting the results of the analysis in the context of the

research question posed in the project.

The project also involves placing the research question and empirical results

in the context of the existing literature on the same topic. It should be the

student’s original contribution; it cannot be a replicationof an existing study.

The project should be submitted in PDF format. It needs to be self-contained,

including references and tables. The number of words includes tables, foot-

notes, code in the document, figures, and references. It does notinclude the

code provided in the separate file or the data. Note that it is possible to do

excellent work that is much shorter than that.

Separately, and not counting towards the word length, you should submit

two files, one with the data used and the second with the computer code.

You need to ensure that the reader can replicate all the analysis in the paper

by simply running the computer code.

All project materials will be submitted using the appropriate links in Moodle.

The following materials must all be submitted by the deadline:

1. A PDF file with your project write-up. Do not submit a Word file,as

pictures and equations may not look right in different versions of Word

2. Any code files used to produce the results in the presentation

3. Any input data files needed for the code to run in either Excel (.xlsx)

or Comma-Separated Values (.csv) format

8.1 Structure

The structure should be similar to the structure of empirical research papers,

whether produced in academia, central banks or other government agencies,

or financial institutions. In particular, it should have the following sections.

1. Introduction. This section contains the motivation of theresearch ques-

tion. Why is it interesting? Why is it important? Is it new? What is

the contribution of the project with respect to what we already know

about the topic? The introduction should also have a short discussion

of other work on a similar topic; the objective is to demonstrate to

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the reader that the student is aware of other related work on the same

topic.

2. Data. This section describes the data used in the empirical analysis.

Sources, criteria for selecting it, processing prior to analysis,sample

frequencies, distribution and the sample period. It also contains de-

scriptive statistics in table and or graphical formats and relates the

data to the fundamental concepts of returns and financial assets as dis-

cussed in the course. Furthermore, the data should be related to key

events in the time-series history of the chosen data, like big price move-

ments or big shocks. It is up to you to find the appropriate data source;

WRDS, Finance Yahoo, End of Day Historical Data, Bloomberg, and

Wind are all excellent sources.

3. Empirical analysis. This section describes the empirical methodology

used in analysing the data. Statistical techniques, models, why these

techniques and models were chosen and other related factors. It should

furthermore contain a description of the computer program used for

analysis, the libraries used, the particular functions, and howthey were

parameterised. The students should discuss why they chose that par-

ticular way of doing the analysis.

4. Results. This section describes the results obtained from the empiri-

cal analysis, perhaps as tables of estimated coefficients and or graphs

displaying key output. A key component of this analysis is the in-

terpretation of the results, such as magnitude and significance,in the

context of the research question asked in the project. Are the results

as expected? What do they imply? When comparing different models,

data periods or assets, compare and contrast the results in the context

of the overall research question.

5. Analysis. Discuss how the research question, data, empirical analysis

and results can be interpreted in the broader context of particular ap-

plications, perhaps trading for risk management, investment fund risk

management or financial regulations.

6. Conclusion. A summary of the project and the lessons learned.

7. Bibliography.

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8.2 Research question

The research question should relate to a topic studied in the course but

should not be a mere replication of existing work. It can be basedon the

questions in Appendix A, but these are fairly simple, and you wouldneed to

go beyond those questions. However, there is no need to follow them. The

choice of topic is up to you. Provided your research question is within the

confines of the topics discussed in the course, it is likely to be acceptable. If

in doubt, contact the course instructor.

An important part of the assignment is how you choose to execute the project.

Therefore, project design and implementation are all important. We will not

tell you what you should do, but we are happy to discuss any ideas you may

have.

Originality and creativity are rewarded. A project that replicates an existing

paper using different data is valued less than a project that adds original

analysis.

Clarity, language and structure are especially valued.

Since this is a course on quantitative methods, a central focusshould be

on how the methods you have chosen address the issues you are studying.

Accordingly, your implementation of those methods is of central interest to

the project. Your submissions must include any data you use and code you

write to produce the results you present in your write-up. You must include

anything that is needed to reproduce your results in your submissions.

It is generally best to focus your efforts on only one of these three dimensions.

1. Mathematical modelling, that is, using particularly complicated math-

ematical models for the problem you choose, ensuring that yourunder-

standing and contribution of the mathematics is emphasised.

2. Programming, that is, you use sophisticated programming and ensure

that your contribution to the programming is emphasised.

3. Application, that is, you are solving a particular practicalproblem, and

you emphasise how your project provides the best solution.

8.3 Marking criteria

For passing projects to receive marks in a certain range, projects must fulfil

all of the criteria below:

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• 80 or above: Unique and rare projects with exceptional quality. Concise

and relevant presentation of facts. Exceptionally insightful analysis.

Truly original insights. Demonstrates full proficiency in collecting and

analysing data. Choice of topics that are at the heart of the course.

Uses multiple ideas discussed in class and introduces new ones. Flawless

writing.

• 70-79: Outstanding projects with no visible weaknesses. Conciseand

relevant presentation of facts. Insightful analysis. Somewhat original

insights. Demonstrates full proficiency in collecting and analysing data.

Choice of topics that are at the heart of the course. Uses multiple ideas

discussed in class. Well written.

• 60-69: Very good projects, with very few weaknesses. The analysis is

mostly correct and insightful, perhaps with a few questionableconclu-

sions. Demonstrates full proficiency in collecting and analysing data.

Choice of topics that are mostly related to the course. Uses multiple

ideas discussed in class. Well written.

• 50-59: Good projects with few weaknesses. The analysis is mostly

correct but with a few questionable conclusions. Uses at least one

important idea discussed in class.

• 40-49: Projects with at least one of the following fundamental flaws

–Very poor analysis; mostly incorrect conclusions.

–No relation whatsoever with topics discussed in class.

–Demonstrates poor command of finance concepts related to the

course.

–Little evidence of background research; poor presentation offacts

and data.

–Extremely hard/difficult to read/understand.

–Lacks a minimum of originality; there is evidence of plagiarism or

insufficient attribution.

• Fail: Projects that fail to receive a passing mark (39 or less) have at

least two of the following fundamental flaws:

–Very poor analysis; mostly incorrect conclusions.

–No relation whatsoever with topics discussed in class.

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–Demonstrates poor command of finance concepts related to the

course.

–Little evidence of background research; poor presentation offacts

and data.

–Extremely hard/difficult to read/understand.

–Lacks a minimum of originality; there is evidence of plagiarism or

insufficient attribution.

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A Topics

Below, we list a number of suggested topics. This list is meant to beillus-

trative rather than exhaustive and covers various topics andtechniques that

we see in the course.

Please note that the description of the individual items is not meant to

constrain your work. If your analysis raises interesting questions that require

additional data or further research to answer, feel free to extend the scope

of your work.

The first are easiest.

Some of the topics are very straightforward from a technical point of view.

If you choose one of those, it is imperative that you pick interesting assets

and provide economic intuition for your findings.

1.Backtesting VaR.Select three assets and backtest EWMA and HS

VaR for a portfolio of the assets. Demonstrate the results statistically

and graphically, and provide analysis.

2.Backtesting VaR.Select 3 assets and backtest EWMA, GARCH

and HS VaR for a portfolio of the assets. Demonstrate the results

statistically and graphically, and provide analysis.

3.GARCH models.Select one return series with at least 4,000 observa-

tions. Use all available univariate GARCH-type models to forecastthe

volatility in-sample. Explain the difference between the models. Test

for the differences between the models (e.g. parameter significance, LR

tests and residual tests), and look at how their volatility forecasts and

residuals differ. Discuss the small sample properties, e.g. what happens

if you use smaller estimation windows.

4.Time-Varying Correlation. Use three returns series. Calculate a

moving window volatility and correlations for various window lengths.

Discuss the sensitivity of window length for volatility/correlation esti-

mation. Try to explain the time varying-correlation economically.

5.Backtesting EWMA.Select three assets with a long history (at least

4,000 days) and backtest EWMA with all the methods discussed in

the lecture notes, violation rations, VaR volatility, coverage test and

independence test. Do sub-period analysis, that is, focus on model

performance in particular sub-periods of the sample, perhapsvery quiet

and dramatic periods.

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6.Backtesting VaR.Select three assets and backtest normal GARCH,

Student-t GARCH, and HS for each asset individually. For one of

the asset plots, the parameter estimates of the GARCH and Student-

t GARCH models, e.g. the time series of the estimatedω, α, β, ν.

Demonstrate the results statistically and graphically, and provide anal-

ysis.

7.Risk Management during a period of heightened stress. Eval-

uate the performance of various risk measures during some period of

heightened stress, perhaps 2008, Covid, the Ukraine war or any other

episode. Identify which methods performed well before, during and af-

ter the event. Explain why they did perform in this way, and provide

practical recommendations to an organisation wishing to risk manage

a future period of heightened stress.

8.Multivariate GARCH. Select two return series. Estimate a univari-

ate GARCH model of each return and a multivariate GARCH model

of both returns and analyse the results. Focus on the statistical signifi-

cance between the univariate and multivariate models, the difference in

the univariate and multivariate volatility forecasts and residuals, and

the behaviour of the covariance over time.

9.Simulate Portfolio Option VaR. Choose two return series with at

least 3,000 observations. Decide on an estimation and testing window.

Calculate VaR for a portfolio of 2 return series and two options over a

testing window. Apply several risk forecast methods. Investigate the

importance of simulation size.

10.Price and Volatility Forecasting(only for students with a solid

knowledge of time series analysis). Select three price series, load them

into R, and convert them to returns. Briefly describe the data statisti-

cally. Create a forecasting model for returns and volatility.

11.Risk Forecasting With Machine Learning (ML)(only for stu-

dents with a solid knowledge of ML). Select three price series, load

them into R, and convert them to returns. Briefly describe the data

statistically. Create a ML forecasting model for risk.This question

must be executed in R.

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