1. Chapter 3: risk measurement
A way of calculating risk

2. CHARACTERISTICS OF RISK DATA
Topic 3.1
CHARACTERISTICS OF RISK DATA

3. DATA Factual information Information in form of facts or figures
Acquired from experiments, surveys, etc
Used as a basis for making calculations or drawing conclusions
Importance
Better loss prediction leads to an appropriate response towards risk
It is important to analyze risk in terms of frequency and severity

4. Characteristic of risk data
FREQUENCY
SEVERITY
Example: road accident
Many minor car accident happened in a year whereby each accident caused little damage
High frequency but low severity event
Example: Aircraft accident
Smaller quantity of aircraft accident happened in a year yet each accident caused severe damage
Low frequency but high severity event

5. Techniques for representing risk data
POPULATIONS
Full set/number of objects, people or situation which is to be the subject of the study
Example: populations of fires, branch offices, injured people, motor claims, houses, and etc.
SAMPLES
A smaller sub-section of the entire set of population
Example: A small number of injured people were used as sample for the population of injured people.

6. DATA COLLECTION METHOD
Topic 3.2
DATA COLLECTION METHOD

7. Sources of data (published data)
THE GOVERNMENT: Statistics provided by the government such as basic information on population, government income and expenditure, etc. are all collected and available to the general public.
BANK NEGARA MALAYSIA: Information related to insurance companies (insurers) obtained by BNM which the insurers need to submit for regulatory purposes.

8. Sources of data (published data)
The main drawback of using published sources of data is the fact that the insurers had no control over how the data was created in the first place.

9. Methods of collecting/ gathering data
Direct observation
Interviews
Experiments
Questionnaires

10. Methods of collecting/ gathering data
1. DIRECT OBSERVATION
Risk manager directly come to a particular place to gather data
Example: a risk manager could observe the number of times that defective products were produced
Advantages: most accurate method, limited ambiguity, not to rely on the interpretation of others
Disadvantages: cost of collecting data is expensive

11. Methods of collecting/ gathering data
2. INTERVIEWS
Risk manager interviews a particular person/ group of people to gather data
Example: a risk manager interviews a client in order to find out information about the risk faced by the client
Advantages: face to face, attitude study
Disadvantages: possibility of error, wrong interpretation

12. Methods of collecting/ gathering data
3. EXPERIMENTS
Risk manager develops a set of new experiment to create new loss control device so as to collect data
Example: a risk manager develops an experiment on new design of safety belt
Advantages: improve effectiveness of loss control device
Disadvantages: time consuming, expensive

13. Methods of collecting/ gathering data
4. QUESTIONNAIRES
Risk manager designed a form and sent to people for their completion and receive the completed form so as to collect data
Example: a risk manager designed questionnaires to ask clients on their perception toward certain insurance policy
Advantages: speed, cost saving
Disadvantages: poor response rate, incomplete answers

14. THE MEASUREMENT OF RISK
Topic 3.3
THE MEASUREMENT OF RISK

15. Risk measurement
Process of evaluating the importance of an exposure of risk to an organization
Importance: pricing of individual contracts, management of insurance and reinsurance companies & overall regulation of the industry
It provides fundamental support to decision making within the insurance industry

16. HOW TO MEASURE THE RISK?
Step 1: collect all the relevant data such as the number & size of losses suffered
Step 2: collate the data. Data must be presented in an ordered manner to reveal loss trends, patterns of behavior, relationship between variables.

17. MEASURING FREQUENCY & SEVERITY
The distribution of the number of losses per year from a given exposure
Probability of a loss exposure = Number of losses/ Number of exposures
Measuring frequency
The distribution of the Ringgit Malaysia amount lost when a loss occurs
Average severity of loss per occurrence = amount of losses/ number of losses
Measuring severity

18. MEASURING FREQUENCY & SEVERITY
Measuring Frequency Example: A construction company had 1,000 workers in each of the past 10 years and over the 10 years period there were 2,000 workers injured. What is the probability that the particular worker will be injured per year? Answer: Probability of a loss exposure = Number of losses Number of exposures = 2,000/ 10,000 = 0.2 (A particular worker becoming injured would be 0.2 or 20% per year)

19. MEASURING FREQUENCY & SEVERITY
Measuring Severity Example: A construction company had 1,000 workers in each of the past 10 years and over the 10 years period there were 2,000 workers injured. The 2,000 workers injured cost RM4,000,000. What is the average severity per occurrence? Answer: Average severity per occurrence = Amount of losses Number of losses = 4,000,000/ 2,000 = RM2,000 (each worker injury imposed RM2,000 loss on the construction company)

20. Reasons to measure potential severity
To classify the risks into critical, important, or unimportant exposures. The potential losses should be ordered in importance according to their loss severity.
To determine the amount of insurance to buy. Over insuring will result in unnecessary costs, while inadequate cover may mean unbearable costs.

21. Relationship between loss frequency & severity
LOW
HIGH
LOSS SEVERITY
These risks are generally appropriately retained
Example: Theft of shopping basket
These risks are often appropriately retained
Example: shoplifting
These risks are often appropriate for insurance
Example: fire
These risks are often appropriate for risk avoidance
Example: Liability risk

22. Risk measurement stage 1
Identify the technique to represent the risk data
Construct bar chart from raw data
Use frequency distributions to represent suitable data

23. Ways of presentation of risk data
Frequency distribution
Relative frequency
Cumulative frequency
Histogram

24. THE PROBABILITY – EXAMPLE 1
The frequency distribution table is given as below:

25. THE PROBABILITY – EXAMPLE 1
Based on the following, calculate:- a) Relative frequency for all level of claims. (5 marks) b) Cumulative frequency for all level of claims. (5 marks) c) Percentage of claims: (5 marks) i) less than RM500 ii) less than RM1,500 iii) more than RM1,000 iv) more than RM2,000. d) Present the data above using histogram.(5 marks)

26. Claim Cost (RM) Number of claims Relative Frequency
THE PROBABILITY – EXAMPLE 1 a) Relative frequency for all level of claims
Claim Cost (RM)
Number of claims
Relative Frequency
0<500 10
10%
500<1000 20
20%
1000<1500 15
15%
1500<2000
2000<2500 35
35%
TOTAL
100%

27. THE PROBABILITY – EXAMPLE 1 b) Cumulative frequency for all level of claims
Claim Cost (RM)
Number of claims
Relative Frequency
Cumulative Frequency
Less than
More than
0<500 10
10%
100%
500<1000 20
20%
30%
90%
1000<1500 15
15%
45%
70%
1500<2000
65%
55%
2000<2500 35
35%
TOTAL

28. THE PROBABILITY – EXAMPLE 1 c) Percentage of claims
Claim Cost (RM)
Number of claims
Relative Frequency
Cumulative Frequency
Less than
More than
0<500 10
10%
100%
500<1000 20
20%
30%
90%
1000<1500 15
15%
45%
70%
1500<2000
65%
55%
2000<2500 35
35%
TOTAL

29. THE PROBABILITY – EXAMPLE 1 d) Histogram

30. Risk measurement stage 2
Represent the frequency distribution
Represent the severity distribution
Find the expected value

31. THE PROBABILITY – EXAMPLE 2
SSO Insurance Bhd has been running a special scheme for the owners of medium sized grocery shops. The scheme provides burglary insurance cover and has been running for a year with eight hundred shops. The loss record for the year 2006 is as follows:

32. THE PROBABILITY – EXAMPLE 2
i) Change the above frequency distribution into a probability distribution.(5 marks) ii) What is the probability of an event of theft happening and the probability of a shop having more than one loss? (4 marks) iii) What is the expected number of theft per shop? (6 marks)

33. THE PROBABILITY – EXAMPLE 2 i) Probability Distribution
No. of thefts (x)
(b)
No. of shops
(c)
P(x) = (b) / 800
550
0.69 1
105
0.13 2 55
0.07 3 50
0.06 4 40
0.05
Total
800
1.00

34. THE PROBABILITY – EXAMPLE 2 ii) Probability of an event of theft happening is 0.13
No. of thefts (x)
(b)
No. of shops
(c)
P(x) = (b) / 800
550
0.69 1
105
0.13 2 55
0.07 3 50
0.06 4 40
0.05
Total
800
1.00

35. THE PROBABILITY – EXAMPLE 2 ii) Probability of a shop having more than one loss is = 0.18
(a)
No. of thefts (x)
(b)
No. of shops
(c)
P(x) = (b) / 800
550
0.69 1
105
0.13 2 55
0.07 3 50
0.06 4 40
0.05
Total
800
1.00

36. Expected no. of thefts per shops = (a) x (c)
THE PROBABILITY – EXAMPLE 2 iii) The expected number of theft per shop is 0.65
(a)
No. of thefts (x)
(b)
No. of shops
(c)
P(x) = (b) / 800
(d)
Expected no. of thefts per shops = (a) x (c)
550
0.69 1
105
0.13 2 55
0.07
0.14 3 50
0.06
0.18 4 40
0.05
0.2
Total
800
1.00
0.65

37. PRESENTATION OF RISK DATA
Topic 3.4
PRESENTATION OF RISK DATA

38. Presentation of risk data
Tables
Graphs
Bar charts
Pie charts
Histogram

39. Presentation of risk data - TABLE
CLAIM COST (RM)
NUMBER OF CLAIMS
0 < 500 10
500 < 1000 20
1000 < 1500 15
1500 < 2000
2000 < 2500 35

40. Presentation of risk data - GRAPH

41. Presentation of risk data – BAR CHARTS

42. Presentation of risk data – pie CHARTS

43. Presentation of risk data – histogram

44. revision Characteristics of risk data Frequency Severity
Techniques representing risk data
Population
Sample
Sources of published data
The government
BNM
Methods collecting data
Direct observation
Interview
Experiment
Questionnaires
How to measure risk
Collect data
Collate data
Measuring frequency & severity
Probability of a loss exposure = Number of losses/ Number of exposures
Average severity of loss per occurrence = amount of losses/ number of losses
Risk measurement I
Identify the technique to represent the risk data
Construct bar chart from raw data
Use frequency distributions to represent suitable data
Risk measurement II
Represent the frequency distribution
Represent the severity distribution
Find the expected value

45. Group activity: DISCUSS AND ANSWER
Group 1: Explain the characteristic of risk data.
Group 2: Explain the techniques used to represent risk data.
Group 3: Explain the sources of published data.
Group 4: Explain four methods used to collect data.

46. Individual assignment
FIND ANY IMPORTANT STATISTIC/DATA RELATED TO INSURANCE FROM ANY OF THESE SOURCES:
GOVERNMENT WEBSITE
BNM WEBSITE
INSURANCE COMPANIES OR INSTITUTIONS’ WEBSITE
NEXT, TRANSFORM ALL THE OBTAINED DATA INTO ANY TYPE OF RISK PRESENTATION DATA BELOW:
TABLES
GRAPHS
BAR CHARTS
PIE CHARTS
HISTOGRAM