How to calculate the Value at risk using the percentile approach with 95% confidence level? and with 99% confidence level? (business risk management)

Business Risk Management Class Workshop Week 5 Australian Bank Limited Fraud Loss Data Australian Bank has extracted the following data of losses incurred by industry participants from fraudulent events involving eCommerce (internet banking services). Australian Bankassumes that given the Bank's market profile losses will directly impact on the value of the bank's eCommerce business, i.e a $1 loss will reduce the value of the business by $1 as well. The bank has also calculated the following statistics from this data. Value Loss Frequency Probability % $200 18 0.05% Prob x Value Variance Value (Vv) Vv2 x Prob % 0.0960 -$8,242 32,613 $300 227 0.61% $400 2722 7.26% $450 3807 10.15% $500 4385 11.70% $750 4385 11.70% $1,000 4022 10.73% $2,500 3594 9.59% $5,000 3154 8.41% $7,500 2705 7.21% $10,000 2254 6.01% $15,000 1812 4.83% $25,000 1388 3.70% $8,442 $28,663 Effect on Value and Frequency of Fraud Losses x ( x ) x Std Dev = $35,000 997 2.66% $50,000 654 1.74% $100,000 373 0.99% $250,000 170 0.45% $500,000 50 0.13% $1,000,000 2 0.01% 1.8164 7.2162 29.0409 45.6937 58.4791 87.7187 107.2762 239.6511 420.6231 541.1154 601.1949 724.9547 925.5308 930.7319 872.1861 994.8789 1133.5752 666.8089 53.3447 -$8,142 -$8,092 -$8,042 -$7,992 -$7,942 -$7,692 -$7,442 -$5,942 -$3,442 -$942 $1,558 $6,558 $16,558 $26,558 $41,558 $91,558 $241,558 $491,558 $991,558 401,368 1,350,036 4,695,376 6,485,567 7,377,062 6,919,934 5,941,211 3,384,503 996,616 64,013 145,944 2,078,602 10,150,096 18,756,400 30,126,579 83,399,501 264,577,802 322,241,189 52,447,850 Mean Loss Standard Deviation of Losses Mean = $350 773 2.06% 5000 [(x ) ( ( x))] 2 4500 x Frequency of Losses 4000 Where (x) is the probability of each observation 3500 3000 2500 Loss Frequency 2000 1500 1000 500 0 $ Value of Loss 1. Based on the above data using the statistical approach what is the VaR of the distribution of fraud losses with a 95% confidence level? 2. Based on the above data using the statistical approach what is the VaR of the distribution of fraud losses with a 99% confidence level? 3. What is the VaR (approximate) using the percentile approach with a 95% confidence level? 4. What is the VaR (approximate) using the percentile approach with a 99% confidence level? 5. Why do the values differ? 6. Suggest ways in which this data might be used by Australian Bank to decide what action, if any, it might take to manage this risk. You are not required to suggest how it might be managed but rather how this information might provide information as to how to decide upon the appropriate risk management actions. 7. What other information would you find useful in order to assist with your answer to Q6 above