Various Events

Risk Management Examples

Chapter 3: Cost Assessment Considering Multiple Possible Events
In Book 6: Comprehensive Sensitivity Analysis of Risk for Businesses

ISBN: 978-620-2-91949-4

Author: Vojo Bubevski (Independent Researcher)

Abstract 

This chapter presents a stochastic model for cost assessment considering multiple possible events throughout the year. A simulation model is designed to resolve the cost assessment. Any number of events (up to a maximum) can occur during the year, and a discrete distribution over the months indicates when each of the events occurs. Then for each of these events, a discrete distribution generates the month of occurrence. Also, the costs for all events are generated from a probability distribution. The event’s costs are correlated, so the model applies specified correlations among these costs. The model calculates the outputs including the number of events each month, the total cost each month, and the NPV of costs, using a 10% discount rate.

Keywords: Risk Assessment and Management, Cost Assessment of Possible Events, NPV, Financial Risk, Sensitivity Analysis; Monte Carlo simulation; Stochastic model.

The Results

The calculated Monthly Events (i.e., the number of events that occur in a month) are presented in Table 4.

Table 4: Monthly Events Results

Month

Events

1

0

2

1

3

1

4

0

5

0

6

0

7

0

8

1

9

0

10

0

11

0

12

0
 
 
Table 4 shows that one (1) event occurs in months 2, 3, and 8. In the other months, no events occur. The calculated Monthly Costs (i.e., the costs of events that occur in a month) are presented in Table 5. 

Table 5: Monthly Costs Results

Month

Costs ($)

1

0

2

547,225.71

3

254,160.25

4

0

5

0

6

0

7

0

8

188366.18

9

0

10

0

11

0

12

0

Table 5 shows that the event costs in months 2, 3, and 8 are $547,225.71, $254,160.24, and $188,18 respectively. In the other months, the costs are zero.

The Monthly Costs Mean is graphically presented in Figure 3.

Note: The Mean results, which involve a probability distribution calculation, are not equal to the calculated results. For example, the cost Mean approximation is $100,000 in Month 1, $200,000 in Month 2, $250,000 in Month 3, etc. 

 

 

Chapter 6: Predicting Operational Risk  of Events;

In Book6: Comprehensive Sensitivity Analysis of Risk for Businesses

 

ISBN: 978-620-2-91949-4

Author: Vojo Bubevski (Independent Researcher)

Abstract 

This chapter demonstrates a stochastic model to predict events and associated operational risks in the manufacturing industry. The model calculates the aggregate impact of a number of possible events, which can occur or not. There are 11 events with a given probability of occurring per year. Also, the most likely impact from events (in dollars) is given inputs. These inputs are based on the average values of historical data.   A simulation model is created and runs to predict the occurrence of the events and calculate the impact, including the associated risk factors. In the model, the events’ occurrence and impact are modelled using appropriate probability distributions. Comprehensive Sensitivity Analysis is performed to determine and quantify the risk factors.
Keywords: Risk Management, Manufacturing Industry, Operational Risk of Events, Financial Risk, Simulation. 

The Results

The comparison of the five simulation results, considering the Total Actual Impact, which is calculated with the respective five parameters of the Probable Occurs per Year Vector, and the Total Average Impact, which is calculated with the Probability Occurring per Year Vector, is presented in Table 2.

Table 2: Comparison of Simulation Results ($)

Comparison of Results

Sim#1

Sim#2

Sim#3

Sim#4

Sim#5

Total Actual Impact Mean

0.0

5998999

12747626

18597430

24146875

Actual Standard Deviation

0.0

1348655

2030436

2445578

2793234

Total Average Impact Mean

226000

226000

226000

226000

226000

Average Standard Deviation

4427

4427

4427

4427

4427

The Total Actual Impact Mean starts with zero in Sim#1, and then logarithmically is increased to $24,146,875 in Sim#5. Similarly, the Standard Deviation starts with zero in Sim#1, and then logarithmically is increased to $2,793,234 in Sim#5

The Total Average Impact Mean is constant and equal in all five simulations, i.e., from Sim#1 to Sim#5. Similarly, the Standard Deviation is equal in all five simulations, i.e., from Sim#1 to Sim#5.

It is important to emphasise that the Total Actual Mean and Standard Deviation are logarithmically increased. However, the Total Average Mean and Standard Deviation are constant and linear.