Decision Models and Analytics
• For simulation models, please answer the questions based on the output of the models. You should include in your spreadsheets the screenshots of the frequency charts of the forecast cells together with the statistics table.
Risk Management
A risk manager of a company has been trying to estimate the aggregated impact of many possible events to the company. The manager has listed potential events that could happen in the coming year, and has assigned a probability of occurrence to each event. The manager has also estimated the financial impact of each event. The data is summarized in Table 1.
Table 1. List of Potential Events
Event Probability per year Impact if Occurs ($1,000,000) Expected Loss ($1,000,000)
IT system, major failure 1.0% 5.0 0.05
Problem with manufacturing process 2.5% 1.0 0.025
Serious illness of a Board member 5.0% 0.1 0.005
Employee wins law suit 8.0% 2.5 0.2
Entry of new competitor 10.0% 10.0 1
Failure of new product launch 7.5% 6.0 0.45
Strengthening of $ Xrate 35.0% 1.0 0.35
Fire in head office 2.0% 2.5 0.05
Fraud 0.5% 5.0 0.025
Confidential data lost 1.0% 3.0 0.03
Large customer goes bankrupt owing money 2.0% 5.0 0.1
Total 2.285
For example, with 1% probability, there will be a major IT system failure, and when it occurs, the company expects a loss of $5 million. Similarly, with 7.5% probability, the launch of a new product will fail, and that will bring a loss of $6 million to the company.
Based on this information, the risk manager has calculated the expected loss of each event. For example, the expected loss of a major failure of the IT system is $0.05 million (1%*5 million). Based on this calculation, the expected total loss of these potential events is $2.285 million.
However, the manager realizes that this simple analysis has at least two issues. First of all, it does not provide useful risk measures such that the standard deviation and 95% Value-at-Risk of the total loss. Second, a fixed amount has been estimated for the financial loss of each event. In order to be more realistic, the loss of each event should be modeled as a probability distribution.
As a first step to address the second issue, the manager has decided to use triangular distributions to model financial loss of the events. For example, the minimum loss of a major IT system failure is $3 million, the maximum loss is $7 million, while the most likely loss is $5 million.
Event Probability per year Most Likely Loss if occured ($1M) Minimum Loss Maximum Loss
IT system, major failure 1.0% 5.0 3 7
Problem with manufacturing process 2.5% 1.0 0.5 1.5
Serious illness of a Board member 5.0% 0.1 0.05 0.15
Employee wins law suit 8.0% 2.5 2 3
Entry of new competitor 10.0% 10.0 5 15
Failure of new product launch 7.5% 6.0 4 8
Strengthening of $ Xrate 35.0% 1.0 0.5 1.5
Fire in head office 2.0% 2.5 2 3
Fraud 0.5% 5.0 4 6
Confidential data lost 1.0% 3.0 2 4
Large customer goes bankrupt owing money 2.0% 5.0 5 5
For the last event, “Large customer goes bankrupt owing money”, the loss is always $5M if the event occurred.
• Build a simulation models to simulate the total aggregated impact (loss) of the potential events listed Table 1 using Crystal Ball with 10,000 trials. (6 points)
• Generate the frequency chart of total aggregated loss. (1 point)
• What is the simulated expected total loss? What is the mean standard error? (1 point)
• What is the standard deviation of the total loss? (1 point)
• What is the 95th percentile of the total loss? (1 point)
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