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Choose any three of the financial assets (e.g., indices, stocks, bonds, options, bitcoin
(or any cryptocurrency), credit default swaps…). Consider diversifying your selection.
Please ensure your selected sample spanning entirely from 1
st January 2019 to
31st December 2023. Please see the appendix for more details about data collection
and cleaning.

1. Risk Factor Analysis:
   Explain how the selected assets contribute to diversification of your portfolio.
   Discuss the risk factors that your portfolio may exposed to.
   [5 marks]
2. Summary statistics:
   For each asset, calculate the daily log returns, and the following statistics
   using the daily log returns: mean, volatility (standard deviation), skewness,
   kurtosis and correlations among the three assets.
   1
   Organize your findings into a table with each row representing an asset and
   columns for each of the summary statistics (Mean, Volatility, Skewness,
   Kurtosis).
   Analyse the results for each asset, focusing on the risk and return profile
   indicated by the mean and volatility. Discuss the implications of skewness and
   kurtosis on the risk assessment of each asset.
   [5 marks]
3. Historical VaR/ES estimation:
   Assume you manage a portfolio of £1 million, allocated across three assets.
   You are flexible with the weight allocations. Generate a series of your
   portfolio returns. Use the daily log return data,
   (1) Calculate 1% Historical VaR and ES for individual assets in monetary
   terms;
   (2) Calculate 1% Historical VaR and ES for the portfolio in monetary terms;
   (3) Compare the weighted sum of 1% Historical VaR and ES of three individual
   assets and the 1% Historical VaR and ES of the portfolio;
   (4) Discuss whether you would have a possible result that the weighted sum of
   1% Historical VaR and ES of three individual assets is less than the 1%
   Historical VaR and ES of the portfolio.
   [15 marks]
   1 You could use Excel or Matlab to conduct such calculations.
   3
4. Normal linear VaR/ES estimation:
   (1) Calculate 1% Normal linear VaR and ES for individual assets in monetary
   terms;
   (2) Calculate 1% Normal linear VaR and ES for the portfolio (by using a
   covariance matrix) in monetary terms;
   (3) Compare the weighted sum of 1% Normal linear VaR and ES of three
   individual assets and the 1% Normal linear VaR and ES of the portfolio;
   (4) Discuss whether you would have a possible result that the weighted sum of
   1% Normal linear VaR and ES of three individual assets is less than the 1%
   Normal linear VaR and ES of the portfolio.
   [15 marks]
5. Monte Carlo VaR:
   Calculate the 1-year 10% Monte Carlo VaR of the portfolio in monetary terms
   by using the covariance matrix and Cholesky decomposition.2 You are flexible
   with any software to calculate Monte Carlo VaR and with the number of
   simulation times. Discuss the sensitivity of the estimates to the selection of
   simulation times.
   [10 marks]
6. Forecasting VaR:
   For the portfolio level series, compute the log-returns and build the following
   forecasting volatility series, starting with January 20233
   :
   (a) historical volatility using a 4-year rolling window (move one day forward);
   (b) EWMA volatility for λ = 0.94;
   (c) GARCH volatility (see how to estimate the GARCH parameters on
   Moodle).
   For the above volatilities build the standardized returns series. For the original
   returns series compute the 1-day ahead 1% VaR (assuming a normal
   distribution) in return. Comparing the actual number of VaR exceptions, which
   model performs best?
   [20 marks]
7. Backtesting and analysis:
   For each forecasting VaR series, count how often the returns exceed the
   negative of the VaR and compute the VaR LR test statistics. Discuss which
   model performs best and whether these models pass the unconditional test.
   [10 marks]
   2 The Matlab code for Cholesky decomposition is available on Moddle. You also could use any other online
   resources to calculate the Cholesky matrix.
   3 Using the sample from January 2019 to December 2022 to estimate the GARCH parameters.
   4
8. Model improvement:
   Discuss potential improvements to risk models, focusing on strategies to better
   capture characteristics such as heavy-tailedness and negative skewness.
   Additionally, consider the types of information that could be integrated into
   these models to improve their predictive accuracy and reliability.
   [5 marks]
9. Big Data and Machine learning:
   In the context of the big data landscape, explore the improvement of risk
   modelling and forecasting through the application of machine learning or deep
   learning techniques. Provide specific examples to illustrate your discussion.
   [15 marks]
   10.Prepare a report:
   Please write a report containing all the results and analysis that answer the
   questions above (max. words: 1,200).
   Notes:
10. You are encouraged to use the relevant references provided in the unit to
    develop your analysis. All references in addition to the lecture material must
    be detailed in a reference list.
11. Please make sure you submit your answers as an PDF file and an Excel
    file. If you completed the coursework in Python or Matlab, please also attach
    your code in .txt. A single PDF file will NOT be marked. Save your
    answer in PDF format using the following name:
    CandidateNumberUnitCode.pdf.
12. Please write your candidate number and unit details on the top your COVER
    PAGE.
13. Format: Font: 12-point Arial font;
    Line spacing: 1.5 lines;
    Page numbers: required, Pages are numbered and sequentially ordered.
    Cover page: required;
14. Excel file: please answer Questions 3, 4, 5, 6, 7 in separated spreadsheets
    in ONE Excel file. Please rename the spreadsheets as “Q4”, “Q5”, … If you
    use Matlab or Python to do the calculation, please provide a comment for
    each question.
    5
    Appendix:
15. Data collection:
    You may use any data sources to download historical price data: Bloomberg
    Terminal, DataStream, Yahoo Finance, other reputable financial data sources
    (Ensure you cite the data sources appropriately in your report).
    a. Bloomberg/DataStream: Access through your institution’s finance lab if
    available. Use the platform’s data export function to download the daily
    closing prices of your selected assets from January 1, 2019, to December
    31, 2023.4
    b. Yahoo Finance:
    Go to the Yahoo Finance website.
    Search for your selected asset using the search bar.
    Navigate to the “Historical Data” tab.
    Select the time period (start date: January 1, 2019, end date: December 31,
    2023) and the frequency (daily).
    Click on “Download” to save the data in a CSV file.
16. Data Preparation:
    (1) Import the downloaded CSV files into a spreadsheet or statistical software
    of your choice (e.g., Excel, Matlab, or Python).
    (2) Ensure each dataset includes the date and the closing price of the asset.
    (3) Creating Balanced Panel Data:
    Since your analysis requires balanced panel data, select a common period
    where data for all three assets are available. You might need to exclude
    dates where any of the assets lack data.
    Ensure the final dataset represents a balanced panel with an equal
    number of observations for each asset across the same time points.
    See the example below: we just need to remove the cells “21/01/2019
    27.5863” to get a balanced a dataset.

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