Question: Select, and acquire historical data for, a traded financial asset. This might, for instance, be a commodity, a security, or a stock market index.

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, 8th February 2023, calculate the simple daily returns for your asset [R2-R1R1]. Examine and describe the key statistical features of your sample of returns.

(c) Calculate VaR and ES for 8th Feb 2023 using a one day holding period, and a confidence level of 95%, 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 an appropriate distribution, without volatility adjustment

vii. Parametric, using 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, 8th Feb 2023, 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 8th Feb 2023 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 an appropriate distribution, without volatility adjustment

vii. Parametric, using an appropriate distribution, with volatility adjustment

(c) Explain how you might have been able to reduce your risk exposure for 8th Feb 2023 if you had been able to adjust your portfolio on the 7th Feb 2023.