African Banks model involved forward sale (45 days forward) of an investment (CD) with a price that was expected to follow the uniform distribution ranging from 90 to 110. Half of these sales (20,000 units) were in Canada, which involved an exchange rate variation that was probabilistic (uniformly distributed from 0.008 to 0.004). The expected price of the CD was normally distributed with mean 0.8139, standard deviation 0.13139. Operating expenses associated with the Canadian operation were normally distributed with mean $1,925,000 and standard deviation $192,500. The other half of sales were in the US. There was risk of customer liability lawsuits (2, Poisson distribution), with expected severity per lawsuit that was lognormally distributed with mean $320,000, standard deviation $700,000. Operational risks associated with US operations were normally distributed with mean $1,275,000, standard deviation $127,500. The Excel spreadsheet model for this is given in Table 6.1. In Crystal Ball, entries in cells B2, B3, B7, B10, B21, B22 and B23 were entered as assumptions with the parameters given in column C. Prediction cells were defined for cells B17 (Canadian net income) and B29 (Total net income after tax). Results for cell B17 are given in Fig. 6.2, with a probability of 0.9 prescribed in Crystal Ball so that we can identify the VaR at the 0.05 level. Statistics are given in Table 6.2. African Bank proposed a model reflecting hedging with futures contracts, and insurance for customer liability lawsuits. Using the hedged price in cell B4, and insurance against customer suits of $640,000, the after-tax profit is shown in Fig. 6.4. Output statistics for after-tax income

Figure 6.2 Output of Canadian Investment

Table 6.2 Output statistical for operating income

Fig 6.3 Output for after tax income

Table 6.3 Output statistics for after tax-income

From a risk modelling context, analyse the performance of the Canadian Investment portfolio, using the above figures as references. Recommend if African Bank should retain the investment. Determine and interpret VaR at 0.95 confidence level, for the alternatives provided. (6 marks) and provide an interpretation of the statistics provided (24marks)

Table 6.1 Exced Model of Imvertment \begin{tabular}{|l|l|} \hline Forecast & Forecast \\ \hline Statistic & Forecast values. \\ Trials & 500 \\ Mean & 96,022.98 \\ Median & 304,091.58 \\ Mode & - \\ \hline Standard Deviation & 1,124,864.11 \\ Variance & 1,265,319,275,756.19 \\ Skewness & -7.92 \\ Kurtosis & 90.69 \\ Coefficient of variability & 11.71 \\ Minimum & 14,706,919.79 \\ Maximum & 1,265,421.71 \\ Mean standard error & 50,305.45 \\ \hline \end{tabular} Table 6.2 Output statistics for operating income \begin{tabular}{|l|l|} \hline Forecast & Operating Income \\ \hline Statistic & Forecast values. \\ \hline Trials & 500 \\ Mean & 78,413.99 \\ Median & 67.861 .89 \\ Mode & - \\ \hline Standard Deviation & 385,962.44 \\ Variance & 148,967,005,823.21 \\ \hline Skewness & -0.0627 \\ \hline Kurtosis & 2.99 \\ \hline Coefficient of variability & 4.92 \\ \hline Minimum & 1,183,572.09 \\ Maximum & 1,286,217.07 \\ \hline Mean standard error & 17,260.77 \\ \hline \end{tabular} Table 6.1 Exced Model of Imvertment \begin{tabular}{|l|l|} \hline Forecast & Forecast \\ \hline Statistic & Forecast values. \\ Trials & 500 \\ Mean & 96,022.98 \\ Median & 304,091.58 \\ Mode & - \\ \hline Standard Deviation & 1,124,864.11 \\ Variance & 1,265,319,275,756.19 \\ Skewness & -7.92 \\ Kurtosis & 90.69 \\ Coefficient of variability & 11.71 \\ Minimum & 14,706,919.79 \\ Maximum & 1,265,421.71 \\ Mean standard error & 50,305.45 \\ \hline \end{tabular} Table 6.2 Output statistics for operating income \begin{tabular}{|l|l|} \hline Forecast & Operating Income \\ \hline Statistic & Forecast values. \\ \hline Trials & 500 \\ Mean & 78,413.99 \\ Median & 67.861 .89 \\ Mode & - \\ \hline Standard Deviation & 385,962.44 \\ Variance & 148,967,005,823.21 \\ \hline Skewness & -0.0627 \\ \hline Kurtosis & 2.99 \\ \hline Coefficient of variability & 4.92 \\ \hline Minimum & 1,183,572.09 \\ Maximum & 1,286,217.07 \\ \hline Mean standard error & 17,260.77 \\ \hline \end{tabular}