ST429 – Statistical Methods for Risk Management
Green finance and COVID-19
Deadline: 7th of January 2021 at 13:00 (UK time)
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• Group project. This submission will be strictly done in groups. In- dividual projects will not be graded. Only one file per group will be submitted. Each group will have a group number assigned to them. The assignment is in an excel file available to you on Moodle.
• Files to be submitted. Two files will be submitted:
1. Project as PDF file: Include your results and code.
2. Code as R file (or .Rmd): the R code also needs to be submitted as a separated file.
• Submission. A portal for submission will be open on Moodle towards the deadline. The names of the files to be uploaded should contain your group number as indicated. For example: If your group is number 3, name your PDF file: project_group3.pdf; and name your R file: projectcode_group3.R.
• Project file organisation. You are encouraged to write your project using LATEX, to produce a professional PDF file. It is recommended to structure your project as follows:
1. Cover: title, date, candidate numbers included here (no names). 2. Introduction
3. Results
4. Conclusions
5. R code
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• R file organisation. Your code, that is also attached above, should have all necessary comments to to follow the computations and results given. Comment which participants (using candidate numbers only, no names) contributed in what parts of the code.
• Length of the project: The project in PDF should have around 16 pages (without R code attached). Use font size 11pt or 12pt.
Assessment. The project will be graded over 100 marks with 15% weight in your final grade.
• Plagiarism. You are required to read the information on plagiarism on the following website:
Plagiarism
Note in particular the first paragraph on this website:
“All work for classes and seminars as well as scripts […] must be the stu- dent’s own work. Quotations must be placed properly within quotation marks or indented and must be cited fully. All paraphrased material must be acknowledged. Infringing upon this requirement, whether de- liberately or not, or passing of the work of others as the work of the student, whether deliberately or not, is plagiarism.”
Note that all reports will be submitted to Turnitin for textual similarity review and the detection of plagiarism.
• Penalty for late submission. Please be aware of the Schools penalties for late submission of coursework:
“Five marks out of 100 will be deducted for coursework submitted within the 24-hour period after the deadline and a further five marks will be deducted for each subsequent 24-hour period (working days only) until the coursework is submitted. After five working days, coursework will only be accepted with the permission of the Chair of the Sub-Board of Examiners. ”
• Final remarks. If a member did not contribute in the solutions, indi- cate it in the submitted file so I grade only students that participated. Finally, if one group has only one participant who wants to submit the project, communicate it to me until 26 November, 2020. After this date new assignments will not be possible.
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B Project
In December 2015, 195 countries signed the Paris Agreement to reduce the risk of climate change. According to this agreement, the different countries compromised to control and limit the release of greenhouse gases. However, a clear plan on how to reduce emissions was not set and couple of years later there was no proof that countries were meeting the goals of the agreement. In 2018, Greta Thunberg started the movement “School strike for climate” that gave visibility to many other environmental movements, criticising the lack of response to climate change. One year after the world would face a pandemic crisis. Right before the COVID-19 outbreak, the US officially withdrew from the Paris agreement on November 2019. Amid the first wave of the pandemic the UK officially left the EU. The pandemic stressed the importance of climate risk and the need to look for sustainable solutions in different sectors. We are currently in the second wave of the virus. The prospects of a vaccine, recent US elections and Brexit agreements – to men- tion some US/UK events – have a great economical impact.
The purpose of this project is to analyse recent data from either the US or UK market covering current events. Choose one market before you start. You will construct your own portfolio using data of one of these markets. For the data you download, make sure you include some stocks related to green investments. Here are some ideas (American companies):
Top green investing opportunities
Some of the following instructions are intentionally vague and open ended, they may not have universal correct answers. I am giving you some guidelines for each step of the project, but you may want to add more results related to the topics we covered in class.
1. Download 10 different daily stock prices (in USD or GBP currency). The data should be recent and go back in time at least 4 years (example: from January 2016 to October 2020). You can find historic data in Wharton Research Data Services or Yahoo Finance (this option will be faster). Prepare the data so that it can be analysed by R.
2. Analyse the log returns of the assets in your portfolio. Comment on what happened for these stock prices. Can you find any special events?
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3. Construct the loss random variable associated to your portfolio assum- ing that the initial investment in each stock is $1000. Study normality and other possible models for the loss rv. Calculate capital require- ments with VaR and ES at different levels and discuss the results. Compare these measures with the empirical distribution and a normal distribution. For a fixed α > 0.8, the ES at this level will offer a fair threshold for capital requirements. If you were supposed to use only the VaR as a measure, what levels should be considered for the threshold the ES0.8 gives? Comment your results.
4. Take each stock as an individual investment and analyse the depen- dence structure of the different stocks (minus log-returns). Among the copulas we learned in class, which copula fits the best to different pairs? (You may want to fit many pairs, but include Figures of pairs that you consider interesting, more results can be included in tables). Explain all the steps of your fitting, such as possible implicit copulas, comment on the choices of initial parameters for the method of moments. You can also use the sample estimator for rank correlations.
5. Previously, you fitted a copula to pairs of losses, say (L1, L2) ∼ C, then we can estimate estimate the VaRα(L1 + L2). Choose some pairs with their corresponding fitted copulas and estimate the Value-at-risk for different levels of α of the aggregated losses. Compare these values with the VaRs if the pairs (L1, L2) ∼ M would have the comonotone copula. What can you say about the ES of the sum of losses if (L1,L2) ∼ M?
⋆ Construct a Principal component analysis and choose the first compo- nent as an index. Find the dependence structure between this index to the other stocks using copulas of different types. Among the copulas we learned in class, which copula best fits the observations?
⋆ Additional: will be graded as Homework.
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