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CHAPTER 3 THE CALCULATIONS OF RISK Basic risk calculations Risk severity: Severity reaches a maximum when we are in a complete uncertainty (where it is difficult to make a decision). Complete certainty reach where risk severity is zero (the possibility of loss = zero) or the possibility of loss = one true). Risk severity %100 %80 Positive decision 0.1 Negative decision 0.4 0.5 0.6 0.7 Probability is a measure or estimation of how likely it is that something will happen or that a statement is true. Probabilities are given a value between 0 (0% chance or will not happen) and 1 (100% chance or will happen). 0 uncertainty Absolute Impossibility 1 Absolute certainty Risk measures The expected loss value: The expected loss value = loss value x probability of the loss. Quantitative measures of risk: measuring risk given the impact of loss: The following table shows the probability distribution of the total losses of five cars, each worth 10,000 ryal Loss value probability Zero 0.606 500 0.274 1000 0.100 2000 0.014 5000 0.003 10000 0.002 20000 0.001 Exercise (continued) Required: May not achieve any financial losses for those cars. Prospect of financial losses for those cars. Prospect of losses equal to or greater than 2000 ryal. Prospect of losses of more than 5000 ryal. Prospect of losses worth 10,000. Determining Standard Deviation (Risk Measure) Standard Deviation, s, is a statistical measure of the variability of a distribution around its mean. Coefficient of Variation The ratio of the standard deviation of a distribution to the mean of that distribution. It is a measure of RELATIVE risk. CV = s/X EXAMPLES The following examples illustrate methods of calculating the loss in different situations Example (1): The following data gives losses due to the fire of a factory in five successive years year 1999 2000 2001 2002 2003 Amount of loss 20 21 0 22 17 Example1 (continued) Using the information’s in the table above calculate the following 1. Average loss x(expected value of loss for the following) 2. The standard deviation of the loss . 3. Coefficient of variation of loss C.V. SOLUTION We Symbolizes the amount of (loss per thousand) as the symbol x we have the following table: X X2 20 400 21 441 0 0 22 484 17 289 80 1614 solution(continued) The value of each: the expected value of loss , the standard deviation and the coefficient of variation of loss are calculated as the follows: = Solution (continued) Example2 A transport company for tourism and travel Owns 800 cars, the following table gives the frequency distribution of non-motor vehicle accidents of the company and the resulting losses estimated (in ryal thousands) Example2 (continued) Using the information’s in the table above calculate the following 1. Average loss (expected value of loss for the following) 2. The standard deviation of the loss . Categories of loss (in 0-20 20-40 40-60 60-80 80-100 100-120 thousand ryal Number of cars 300 220 140 80 42 18 Fx Fx2 10 3000 30000 220 30 6600 198000 40- 140 50 7000 350000 60- 80 70 5600 392000 80- 42 90 3780 34200 100-120 18 110 1980 217800 total 800 -------- 27960 1528000 Categories of Number of Center loss)per cars categories thousand ryal) F X 0- 300 20-