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The objective of the coursework is to allow you a first hand appreciation of some of
the key issues in measuring risk. There are two parts, one involving analysis of a
portfolio having a single risk factor, the other involving analysis of a portfolio having
two risk factors.

  1. Select, and acquire historical data for, a traded financial asset. This might, for
    instance, be a commodity, a security, or a stock market index. Suppose that
    you had invested 1 million pounds in this asset at the date given by the earliest
    date in your data.
    (a) Explain your choice of sample size.
    (b) Using the data up to, but not including, 15th July 2021, calculate the simple
    daily returns for your asset [use simple returns throughout this coursework].
    Examine and describe the key statistical features of your sample of returns.
    (c) Calculate VaR and ES for 15th July 2021 using a one day holding period, and
    a confidence level of 90%, using the following methods:
    i. Basic Historical Simulation
    ii. Age-weighted Historical Simulation
    iii. Hull-White
    iv. Parametric, using the Normal distribution, without volatility adjustment
    v. Parametric, using the Normal distribution, with volatility adjustment
    vi. Parametric, using what you believe to be an appropriate distribution,
    without volatility adjustment
    vii. Parametric, using what you believe to be an appropriate distribution,
    with volatility adjustment
    You should present your results in a single table, and briefly provide a commentary
    on the similarities and differences.
    (d) Explain why it would be problematic to have used log returns to calculate
    VaR and ES for any of the parametric methods in the previous question.
  2. Acquire data for another asset and suppose that at at the start of the time series
    you invested 1 million pounds in this asset as well. You now have a portfolio
    which at the start of the data series was worth 2 million pounds. Suppose initially
    that your portfolio is not actively managed, so that your holdings of each asset
    remain unchanged.
    (a) Using the data up to, but not including, 15th July 2021, calculate the simple
    daily returns for each of the individual assets which constitute your portfolio.
    Examine and describe the key statistical features of your sample of returns.
    (b) Calculate VaR and ES for 15th July 2021 using a one day holding period, and
    a confidence level of 95%, using each of the following methods
    i. Basic Historical Simulation
    ii. Age-weighted Historical Simulation
    iii. Hull-White
    iv. Parametric, using the Normal distribution, without volatility adjustment
    v. Parametric, using the Normal distribution, with volatility adjustment
    vi. Parametric, using what you believe to be an appropriate distribution,
    without volatility adjustment
    vii. Parametric, using what you believe to be an appropriate distribution,
    with volatility adjustment
    (c) Explain how you might have been able to reduce your risk exposure for 15th
    July 2021 had you been able to adjust your portfolio on the 14th July 2021.
    Use the Basic Historical Simulation method for this part.
    The deadline for submission is as notified in the module outline. Please see Moodle
    for further discussion of useful approaches to this topic, and hints about R code.

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……未完待续

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