1. Discuss, in less than 1000 words, the role of backtesting of VaR models in portfolio management.

[30 marks]

A useful reference for backtesting is Lucas, A., (2001), “Evaluating the Basle Guidelines for Backtesting Banks’ Internal Risk Management Models,” Journal of Money, Credit and Banking, Vol. 33, No. 3. In particular, one should read p826-831 and the concluding remarks.

2.In this question we will conduct a backtesting exercise for the 1994 year. For each trading day in 1994 we must graph the 99% VaR that was computed 10 trading days before and we must also graph the realised loss in the portfolio that occurs over this same period.

One is required to produce two graphs. The first graph should be the backtesting of the VaR method under normality. The second graph should be the backtesting of the VaR method under historical simulation of daily changes in prices. Finally, one should interpret the findings from both of these graphical displays.

For these exercises, assume that $10,000 dollars was the value of our holdings in each of our nineteen stocks, ten trading days before the first trading day in 1994. i.e. On 17 December 1993, the value of our portfolio is $190,000. Also assume that the number of shares we hold in each of these stocks does not change over the time frame of our back-testing exercise. Finally, in computing the VaR estimates one should use the last 500 changes in prices. The data is located on the Moodle page. See last page, for variable names.

In addition to printing out the Excel graphs, one should also print out the Ox computer code.

[20 marks]

3.In this question we will conduct a backtesting exercise for a portfolio of 4 stocks for the 2007 year. For each trading day in 2007 we must graph the 99% VaR that was computed 10 trading days before and we must also graph the realised loss in the portfolio that occurs over this same period.

One is required to produce two graphs. The first graph should be the backtesting of the VaR method under normality. The second graph should be the backtesting of the VaR method under historical simulation of daily changes in prices. Finally, one should interpret the findings from both of these graphical displays.

For these exercises, assume that $100,000 dollars was the value of our holdings in each of CISCO, Microsoft, IBM and American Express ten trading days before the first trading day in 2007. Also assume that the number of shares we hold in each of these stocks does not change over the time frame of our back-testing exercise. Finally, in computing the VaR estimates one should use the last 500 changes in prices.

In addition to printing out the Excel graphs, one should also print out the Ox computer code.

[30 marks]