# Value-at-Risk (VaR) of a portfolio. Financial Risk Management Paper

**Financial Risk Management **

**Max word count 2000 words, not including mathematics**

**Answer ALL FIVE parts. Each part carries the same number of marks.**

**Your paper AND the Excel spreadsheet used to compute the answers to parts 3, 4 and 5**

**should be emailed to**

- What is the Value-at-Risk (VaR) of a portfolio? Describe the roles of the two model parameters, holding period h and significance level a and the effect they have on VaR. Also define expected shortfall (ES). What is the relationship between VaR and ES?

[20 Marks]

- Define how VaR and ES can be estimated in (a) the normal linear model and (b) the historical simulation model. Explain this in detail, using properly defined mathematical notation.

[20 Marks]

- Using the daily price data on the S&P500 index provided in the Excel spreadsheet
**N1569 RESIT DATA**compute the daily returns and hence calculate the a% h-day VaR and a% h-day ES using the normal linear model. Report your answers as a percentage of the portfolio value and for a selection of appropriate choices for h and a.

[20 Marks]

- Using the same data as for part 3, calculate the hence calculate the a% h-day VaR and a% h-day ES using the historical simulation model. Report your answers as a percentage of the portfolio value and for a selection of appropriate choices for h and a.

[20 Marks]

- Compare and contrast the advantages and limitations of the normal linear and historical simulation models by discussing their general properties. Illustrate your arguments by referring to your numerical answers in parts 3, 4.

[20 Marks]

**Notes to students:**

You may use any information available on the canvas site or elsewhere to help you with your answers to the written and numerical questions. However, be careful NOT to copy and paste from any public sources because there can be penalties for Turnitin scores.

A good answer will:

- Define VaR and its parameters
- Outline the steps to building the two different VaR models
- Explain how the models differ, and use mathematical notation (and diagrams, where appropriate) to describe how VaR is calculated in each model
- Define ES and describe how it is calculated in each model
- Describe the data by plotting prices and daily returns
- Report the results for each VaR model for different parameters
- Discuss these results, and explain why they are different

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