# Financial Risk Management

#### Financial Risk Management

1. There is a 24 hour period set aside for this examination. Once started you have 2 hours to complete the paper and 60 minutes to prepare and upload your submission. Students with reasonable adjustments have 25% extra time.

2. Your submission for each Section A question should consist of a PDF document and an Excel workbook. Your submission for the Section B essay is a typed and illustrated Word document converted to PDF document. Do not leave it too late to prepare and upload your submission. In case of technical problems please email your submission to the exam coordinator within 2 hours of the start of the 24 hour period.

3. You may use any Excel spreadsheets of your own making or from this module’s canvas site, as appropriate to the question asked. If you use pre-prepared module materials please start a new Excel file and paste any relevant course Excel materials there. Ensure your own name is in File -> Properties -> Summary -> Author.

4. The answers to each Section A question in the PDF must be written in your own handwriting. Take photos of your written solutions to embed in a Word doc along with any screenshots named by the question number and candidate number, e.g. Q3-123456.

5. For Section B, type your answers in word, but include screenshots from any Excel workbooks or equations to illustrate your answers. Convert the final Word into PDF.

6. Marks for the PDF will be awarded for presentation, defining notation and showing workings and not only for obtaining the correct answers. You may use any resources from the N1569 canvas site. You may use external web resources if you add the direct URL to any such material used. This includes text, figures, tables and equations. Any text used verbatim must be enclosed in quotation marks. Your work will be checked and so students should be sure to understand the penalties that apply for plagiarism.

**Financial Risk Management SECTION A**

Attempt BOTH questions in this section. Each question is worth 25 marks. 10 marks are awarded for the quality of the Excel file. 15 marks are awards for the quality of your descriptive solution in the PDF file.

1. You hold 50 shares of Tesla, 30 shares of Amazon and 20 shares of Google.

(a) Suppose the share prices are: $1,015 for Tesla; $3,390 for Amazon; and $2,850 for Google. Calculate the portfolio value and the vector of portfolio weights, reporting results to 3 decimal places;

(b) Suppose the volatilities are: 75% for Tesla; 32% for Amazon; and 32% for Google, and the correlations are: 0.42 for Tesla-Amazon; 0.40 for Tesla-Google; and 0.65 for Google-Amazon. Calculate the covariance matrix;

(c) Calculate the portfolio volatility using the formula either based on summation or on the quadratic form. Report your result as a percentage to 1 decimal place;

(d) Use the prices given in the Excel spreadsheet Mock-CEX-Stocks-data.xls to calculate the ordinary returns (percentage price changes) per share, from 1 Jan 2020 to 3 Dec 2021, then apply the portfolio weights vector from part (a) to obtain another time series of portfolio returns, assuming these weights are constant;

(e) Find the portfolio volatility based on this time series. Report your result as a percentage to 1 decimal place.

**Financial Risk Management SECTION B**

This essay is worth 50 marks. Equal marks are awarded to each of the parts (a) – (d). Provide between 700 and 800 of your own words. Take screenshots of equations and/or illustrations to enhance your written response. Excessively short or long answers will be penalised. You may take your own screenshots of any Excel file you make for yourself. Or of any Excel file or equation that you use from any part of the Canvas site.

2. (a) Define, in words, Value-at-Risk (VaR) and Expected Shortfall (ES) and describe the role of their parameters. Give numerical examples to illustrate your answers;

(b) Describe, using properly defined notation, how VaR and ES are calculated, for different significance levels and holding period, when a portfolio’s returns are assumed to be i.i.d. and normally distributed;

(c) Use a time series of at least 5 years of daily stock or index prices of your own choice to calculate the 1% 1-day normal VaR and ES based on a rolling window of 100 returns, where the volatility is derived from the standard deviation over each rolling window. Plot the results as time series on the same graph and take a screenshot of this plot;

(d) Use the result of part (d) to backtest the VaR time series, using the unconditional and conditional coverage tests. Describe the tests using in mathematical notation and discuss what they a testing for, report the results you obtain and and discuss why the model passes or fails these backtests. Illustrate your answers to (b) using equations, which can be screenshot from your lecture notes, but you must name each variable in the mathematical notation displayed. The data for part (c) are best downloaded from the internet so they are clearly your own choice, but you may also use any data from the Excel files on Canvas. You do not need to upload an Excel file for this essay. Instead, you may illustrate your answers using screenshots of time series plots and tables of outputs from Excel, based on any data of your choice.

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