CHAPTER 3THE 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%

0.1 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).

uncertainty

Absolute certaintyAbsolute Impossibility

10

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 ryalLoss valueLoss value probabilityprobability

ZeroZero 0.6060.606

500500 0.2740.274

10001000 0.1000.100

20002000 0.0140.014

50005000 0.0030.003

1000010000 0.0020.002

2000020000 0.0010.001

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

Coefficient of Variation

The ratio of the standard deviation standard deviation of a distribution to the mean mean of that

distribution.

It is a measure of RELATIVERELATIVE risk.

CV = /XX

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 (expected value of loss for the following)2. The standard deviation of the loss .3. Coefficient of variation of loss C.V.

x

SOLUTION We Symbolizes the amount of (loss per

thousand) as the symbol xwe 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 thousand ryal

0-20 20-40 40-60 60-80 80-100 100-120

Number of cars 300 220 140 80 42 18

Categories of loss(per

thousand ryal)

Number of

cars

F

Center

categories

X

Fx Fx2

0- 300 10 3000 30000

20- 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