c4a - risk identification measurement

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CHAPTER 3: RISK

IDENTIFICATION AND

MEASUREMENTRisk Management and Insurance

By Harrington & Niehaus

(Class 4)


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AGENDA

Risk Identification Identifying Business Risk Exposures

Identifying Individual Exposures

Basic Concepts from Probability andStatistics Random Variables and Probability Distributions

Characteristics of Probability Distributions

Evaluating the Frequency and Severity ofLosses Frequency, Severity, Expected Loss and

Standard Deviation


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RISK IDENTIFICATION

The first step in the risk management process isrisk identification; the identification of loss

exposures.

There are various methods of identifyingbusiness risk exposures, such as:

Comprehensive checklist of common business

exposures from risk manager / consultant;

Analysis of the firms financial statements;

Discussion with the firms managers;

Surveys of employees etc.


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RISK IDENTIFICATION

Property loss exposures Valuation methodsbook value, market value, firm-specific

value, replacement cost.

Indirect lossesbusiness income exposures and extra expenseexposure.

Liability losses Potential legal liability losses as a result of relationships with

many parties, such as suppliers, customers and members of thepublic.

Losses to human resources

Losses in firm value due to worker injuries, disabilities, death andretirement.

Losses from external economic forces Outside of the firm, such as changes in the prices of inputs and

outputs, changes in exchange rates etc.


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RISK IDENTIFICATION

One method of identifying individual / familyexposures is to analyze the sources and uses of

funds in the present and planned for the future.

Potential events that cause decreases in theavailability of funds or increases in uses of funds

represent risk exposures.

Important risks for most families are drop in

earnings prior to retirement due to death /disability of breadwinner, physical and financial

assets, medical expenses, personal liability etc.


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BASIC CONCEPTS FROM

PROBABILITY AND STATISTICS

Risk assessment and measurement require abasic understanding of several concepts fromprobability and statistics.

Random variables and probability distributions

A random variable is a variable whose outcomeis uncertain.

Example: coin flip, variable X is defined to beequal to $1 if heads appears and -$1 if tailsappears. Prior to the coin flip, the value of X isunknown; that is, X is a random variable.


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BASIC CONCEPTS FROM


Information about a random variable can be

summarized by the random variables

probability distribution.

Probability distribution identifies all the possibleoutcomes for the random variable and the

probability of the outcomes.

Sum of the probabilities must equal 1 There are 2 types of distributions:

Discrete;

Continuous.


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BASIC CONCEPTS FROM


2 ways of presenting discrete

distributions: Numerical listing of outcomes and probabilities;

Graphically.

2 ways of presenting continuous

distributions: Density function (not used in this course);

Graphically.


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BASIC CONCEPTS FROM


Example of a discrete probability distribution in

numerical listing where random variable =

damages from auto accidents.

Possible Outcomes for Damages Probability

$0 0.50

$500 0.30

$1,000 0.10$5,000 0.06

$10,000 0.04


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BASIC CONCEPTS FROM


Example of a discrete probability distribution in

graphical where random variable = damages

from auto accidents.


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BASIC CONCEPTS FROM


Example of a continuous probability distribution

where random variable = an automakers

profits.


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BASIC CONCEPTS FROM


In continuous probability distribution,

important characteristic of density

functions:

Area under the entire curve equals one;

Area under the curve between two points

gives the probability of outcomes falling within

that given range; We can graphically identify the probability

that profits are within certain interval.


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BASIC CONCEPTS FROM


In many applications, it is necessary to compare

probability distributions of different random

variables. Understanding how decisions affect

probability distributions will lead to betterdecisions.

The problem is that most probability

distributions have many different outcomes and

are difficult to compare.

It is therefore common to compare certain key

characteristics of probability distributions.


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BASIC CONCEPTS FROM


Key characteristics of probability distributions:

Expected value of a probability distribution

provides info about where the outcomes tend

to occur, on average. A distribution with a higher expected value will

tend to have a higher outcome, on average.

Formula to calculate the expected value = x1p1+ x2p2 + + xMpM .

(x = denote as possible outcomes and p = denote as

probability)


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BASIC CONCEPTS FROM




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BASIC CONCEPTS FROM



The earlier figure illustrates 2 probabilitydistributions where distribution A has a higher

expected value than distribution B. When distributions are symmetric (like this),

identifying the expected value is relatively easy;it is the midpoint in the range of possible

outcomes and vise-versa. Similarly, to distribution of losses, the

distribution is called a loss distribution and theexpected value is called the expected loss.


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BASIC CONCEPTS FROM



Variance measures the probable variation in

outcomes around the expected value.

If a distribution has low variance, then theactual outcome is likely to be close to the

expected value and vise-versa. A high variance

therefore implies that outcomes are difficult to

predict.

Variance = (Standard Deviation)2


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BASIC CONCEPTS FROM



Standard deviation measure the likelihood that

and magnitude by which an outcome from the

probability distribution will deviate from theexpected value.

Standard deviation (variance) is higher when:

the outcomes have a greater deviation fromthe expected value;

the probabilities of the extreme outcomes

increase.


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BASIC CONCEPTS FROM


Key characteristics of probability distributions:Comparing standard deviation of 3 distributions(distribution 1 has the lowest standard deviation anddistribution 3 has the highest):

Distribution 1 Distribution 2 Distribution 3

Outcome Prob. Outcome Prob. Outcome Prob.

$250 0.33 $0 0.33 $0 0.4

$500 0.34 $500 0.34 $500 0.2$750 0.33 $1000 0.33 $1000 0.4

*Formula, calculation and further workings as per pages 40& 41 of Chapter 3


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BASIC CONCEPTS FROM



The below figure illustrates 2 distributions for accident

losses. Both have an expected value of $ 1,000, but they

differ in their standard deviations


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BASIC CONCEPTS FROM



Sample mean is the average value from a sample ofoutcomes from a distribution.

Sample standard deviation reflects the variation inoutcomes of a particular sample from a distribution.It is calculated with the same formula that we usedabove for the standard deviation but with 3differences: Only the outcomes that occur in the sample are used;

Sample mean is used instead of the expected value;

Squared deviations between the outcomes and the samplemean are multiplied by the proportion of times that theparticular outcome actually occurs in the sample.


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BASIC CONCEPTS FROM



Another statistical concept that is important in

the practice of risk mgt is the skewness of a

probability distribution. Skewness measures thesymmetry of the distribution.

If the distribution is symmetric, it has no

skewness and vise-versa.

Example of skewness can be seen in Figure 3.7

page 44 of Chapter 3

Most loss distributions exhibit skewness.


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BASIC CONCEPTS FROM



A frequently used measure of risk is maximum

probable loss or value-at-risk.

Maximum probable loss usually describes a lossdistribution, whereas value-at-risk describes the

probability distribution for the value of a

portfolio or the value of a firm subject to loss.


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BASIC CONCEPTS FROM



Correlation between random variables

measures how random variables are related.

Correlation = 0, random variables are notrelated (independent / uncorrelated). Example:

correlation between steel prices and product

liability costs of an automaker.

In many cases, random variables will be

correlated. Example: correlation between

demand of new car and steel price.


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BASIC CONCEPTS FROM



Positive correlationimplies that the random

variables tend to move in the same direction

e.g. stocks of different companies.

Negative correlationimplies that the random

variables tend to move the opposite directionse.g. sales of sunglasses and umbrellas on a given

day.


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EVALUATING THE FREQUENCY

AND SEVERITY OF LOSSES

The frequency of loss measures the number oflosses in a given period of time.

The severity of loss measures the magnitude ofloss per occurrence.

Example:

10,000 employees in each of the past five years;

1,500 injuries over the five-year period;

$3 million in total injury costs.

Frequency of injury per year = 1,500 / 50,000 = 0.03

Average severity of injury = $3m/ 1,500 = $2,000 Annual expected loss per employee = 0.03 x $2,000 = $60

c4a - risk identification measurement

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