**Topic: Financial Modelling **

**Estimating Value-at-Risk using Internal Risk Management Models and Backtesting their Performances.**

**Estimating Value-at-Risk using Internal Risk Management Models and Backtesting their Performances**

** **

The data (for this project) have been emailed to you individually.

The data consist of the following 3 assets – a share that is a constituent of the FTSE100, the S&P500 index, the Nikkei 225 index, and 2 exchange rates – the US dollar/British pound and the Japanese yen/British pound. The sample spans the period 01/01/03 – 30/11/07. This data set has 1283 daily observations.

You should assume that you are aUKinvestor who has long positions in aUKstock (picked from the FTSE100), in the S&P500 index, and in the Nikkei 225 index. This, of course, means that you will not only be affected by changes in the prices on those 3 particular markets (market risk), but you will also be affected by changes in the value of the pound (exchange rate risk) since you have made two investments abroad.

You are required to estimate the VaR of your portfolio using the following 3 approaches: Variance-Covariance, Historical Simulation and Monte-Carlo Simulation1 as at 15/12/06 (inclusive). The calculation of VaR should be based on both the 95% and 99% confidence levels. The rest of the data (18/12/06 – 30/11/07) i.e. 250 observations, should be used for “backtesting” the models. And backtesting should also be conducted based on both the 95% and the 99% confidence levels.

You have the following positions in your portfolio:

** ** **Positions (£m)** Share in the FTSE100

5.000

S&P500

2.000

Nikkei 225

3.000

US (FX)

2.000

Japan(FX)

3.000

Which models performs the best – based on

1) Your project’s results above, and

2) The VaR literature that you might have come across?

**Submission**:

(1) An Excel file with each of the models, as well as the backtesting, on separate worksheets. This file should be emailed to g.persand@icmacentre.ac.uk (Deadline: 20/08/12, 5:00 pm).

(2) Your explanation/description of the approaches (and the answer to the above question – “which models perform …”) should be in the form of a hard copy. (Maximum 2000 words). This hard copy should be submitted to the Reception at the ICMA Centre – deadline: 20/08/12 by 5:00 pm.

[1] No. of replications to be used should be 5,000. For simulation purposes, assume that the returns of all the assets (i.e. both stocks and FX) are standard normally distributed.