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 Positive decision Negative decision 100% 80%

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). uncertainty Absolute certainty Absolute Impossibility 1 0

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 probability Loss value 0.606Zero

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  Standard Deviation, , is a statistical measure of the variability of a distribution around its mean.

Coefficient of Variation standard deviation mean The ratio of the standard deviation of a distribution to the mean of that distribution. RELATIVE It is a measure of RELATIVE risk.  X CV =  /X standard deviation mean The ratio of the standard deviation of a distribution to the mean of that distribution. RELATIVE It is a measure of RELATIVE risk.  X CV =  /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 Amount of loss

Example1 (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. 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:

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.