Date Due: 11pm 31 March, with electronic submission via the course website.

1. In this question we will conduct a backtesting exercise for the 1997 year. For each trading day in 1997 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 sim- ulation of daily changes in prices.  Finally, one should interpret the findings from both of these graphical displays,  (noting presentation quality is important).

For these exercises,  assume that we hold  a portfolio of  12  assets, namely aan1,  aan2,  aan6,  aan7,  aan8,  aan9,  aan10,  aan11,  aan12, aan13, aan17, aan18 where $1,000,000 dollars was the value of our holdings in each of the stocks ten trading days before the first trading day in 1997.  i.e.  On 17 December 1996, the value of our portfolio is $12,000,000. 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 850 changes in prices. The data is located on the fins5542 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 (for each method, 2 marks for coding, 4 marks for graph- ing, 4 marks for write-up) ]

2. In this question we will conduct a backtesting exercise for a portfolio of 6 stocks for the 2020 year.  For each trading day in 2020 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 sim- ulation of daily changes in prices.  Finally, one should interpret the findings from both of these graphical displays,  (noting presentation quality is important).

For these exercises, assume that $1,000,000 dollars was the value of our holdings in each of 6 U.S. travel related companies (sourced from the CRSP database), ten trading days before the first trading day in 2020.  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 850 changes in prices.

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

[30 marks (for each method, 3 marks for coding, 3 marks for data description, 4 marks for graphing, 5 marks for write-up) ]

3.   Discuss, in less than  1200 words, the limitations of VaR  (both mathematical and statistical limitations), relating these to the results you obtained above in question 2.

Please include appropriate references, with a reference section.  Both content and writing quality are key criteria of equal importance.

[30 marks]