Chapter 3: risk measurement A way of calculating risk

CHARACTERISTICS OF RISK DATA Topic 3.1 CHARACTERISTICS OF RISK DATA

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

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

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.

DATA COLLECTION METHOD Topic 3.2 DATA COLLECTION METHOD

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.

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.

Methods of collecting/ gathering data Direct observation Interviews Experiments Questionnaires

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

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

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

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

THE MEASUREMENT OF RISK Topic 3.3 THE MEASUREMENT OF RISK

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

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.

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

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)

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)

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.

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

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

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

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

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)

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%

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

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

THE PROBABILITY – EXAMPLE 1 d) Histogram

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

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:

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)

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

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

THE PROBABILITY – EXAMPLE 2 ii) Probability of a shop having more than one loss is 0.07 + 0.06 + 0.05 = 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

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

PRESENTATION OF RISK DATA Topic 3.4 PRESENTATION OF RISK DATA

Presentation of risk data Tables Graphs Bar charts Pie charts Histogram

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

Presentation of risk data - GRAPH

Presentation of risk data – BAR CHARTS

Presentation of risk data – pie CHARTS

Presentation of risk data – histogram

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

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.

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