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-