uum-bwrr3033-risk management--chapter 04 risk measurement

8/13/2019 UUM-BWRR3033-Risk Management--CHAPTER 04 Risk Measurement

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Chapter 4: Risk Measurement

Frequency and severity of losses

Probability

Probability distribution Fault tree

Pooling arrangement and diversification of

risk

BWRR3033_Rodziah(c)


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Learning Objective

Review the concepts of probability and statistics

Apply mathematical concepts to understand the

frequency and severity of losses

Understand the concepts of expected value andvariance of random variables

Distinguish between binomial distribution and

poisson distribution, and which is more appropriatefor different situations

Show how pooling of independent loss exposures

reduces risk

BWRR3033_Rodziah(c) 2


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RISK MEASUREMENT



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Random Variables & Probability Distribution

BINOMIAL

DISTRIBUTION

POISSONDISTRIBUTION

PROBABILITY TREE

DIAGRAM

RV is a variable which outcome is uncertain. Example: Flipping a coin.

Each flips result is uncertain.

Probability Distribution identifies all of the

possible outcomes, associates a probability with

each outcome.



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0

0.1

0.2

0.3

0.4

0.5

0.6

RM0 RM500 RM1,000 RM5,000 RM10,000

Probability

Probability

BINOMIAL

DISTRIBUTION

POISSONDISTRIBUTION

Possible Outcomes for Damages()

Probability

1 RM0 0.50

2 RM500 0.30

3

RM1,000 0.10

4 RM5,000 0.06

5 RM10,000 0.04

The question now

How we make decision based on these data?

Use

Expected Value

Variance or Standard Deviation

Skewness

Correlation



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Expected Value

it is where the outcomes tend to occur, on

average.

,

=



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Expected Value

Probability

Outcome

B A



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Variance & Standard Deviation

=

Variance

Standard Deviation

=



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Expected Value

Probability

Outcome

B

A



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Expected Value & Skew

Probability

Outcome

D

C



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MPL : Worst loss in worst scenario

PML: Worst loss in normal scenario

Maximum Probable Loss

Vs

Probable Maximum Loss



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Maximum Probable Loss

(Value At Risk)

Probability

Annual Liability Loss RM20m

area= 0.05

Area = 0.01

RM30m



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Area: 0.05

Value at Risk

Probability

-RM7.5m -RM5m

Area: 0.01

0

Monthly change in value of portfolio



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When discussing about many types of risk, it is

important to study the relationship among

random variables.

Correlation = 0the random variables are

not related.

:: outcome of one random variables will not

give info about the other random variables.

:: random variables are said to be

independent or uncorrelated.

Correlation



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REVISION

INDEPENDENT

EVENTS

MUTUALLY

EXCLUSIVE

EVENTS

COLLECTIVE

EXHAUSTED

EVENTS

ALTERNATIVE

EVENTSJOINT EVENTS



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Pooling Arrangements and

Diversification of Risk Basic Idea:

Replace your loss with the average loss of a group

Issues:

What happens to each persons Expected loss

Standard deviation of loss

Maximum probable loss

How do these results change with More participants

Correlation in losses among the participants increases



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Uncorrelated Risk Pooling Example

with 2 People Two people with same distribution (w/o pooling)

Outcome Probability

$2,500 0.20

Loss =$0 0.80

Assume losses are uncorrelatedExpected value =

Standard deviation =



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with 2 People Two people with same distribution (w/o pooling)

Outcome Probability

$2,500 0.20

Loss =$0 0.80

Assume losses are uncorrelatedExpected value =

2500 0.2 + 00.8

$500Standard deviation =

2500500 0.2 + 0 500 0.8 $1000



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with 2 People

Loss

No

Loss

Loss

Loss

No

Loss

No

Loss

0.2

0.8

0.2

0.2

0.8

0.8

Tree Diagram Loss Amount to be shared

2500 x 2/2 = 2500

2500 / 2 = 1250

2500 / 2 = 1250

0



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with 2 People Pooling Arrangement changes distribution of

accident costs for each individualOutcome Probability

$0

Cost = 1,250

2,500

Expected Cost =

SD =



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with 2 People Pooling Arrangement changes distribution of

accident costs for each individualOutcome Probability

$0 0.64

Cost = 1,250 0.32

2,500 0.04

Expected Cost = $500

SD = $707



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Effect on Expected Loss

w/o pooling, expected loss = $500

with pooling, expected loss = $500

Effect on Standard Deviation

w/o pooling, standard. deviation = $1,000

with pooling, standard. deviation = $707

Risk Pooling Example with 2 People



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Risk Pooling Example with

More People



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The Effect of Risk Pooling Arrangements on Probability

Distributions for a large number of small business

Without Pooling

With Pooling

P

robabilityDistributions

Cost paid by each business20000 40000 60000BWRR3033_Rodziah(c) 24


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Risk Pooling of Uncorrelated Losses

Main Points: Pooling arrangements

do not change expected loss

reduce uncertainty (variance decreases,losses become more predictable, maximum

probable loss declines)

distribution of costs becomes moresymmetric (less skewness)



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Effect of positive correlation on Risk Reduction

Pro

babilityDistrib

utions

Loss

Positive Correlated

Uncorrelated



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Effect of positive correlation on Risk Reduction

Standard

Deviation

ofAverageLoss

Number of participants in risk pooling

Uncorrelated

Less than perfect correlation

Perfect Correlation



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RISK MEASUREMENT (Analyze)DEFINITION

(What?)

ESTIMATION

(How)

LOSS

FREQUENCY

Number of times loss occurs

during a specific time on record.

nil/ slight/ moderate/ ultimate

Very likely/ likely/ unlikely

LOSS

SEVERITY

Size of loss per occurrences. Critical/ important/

unimportant fatal,/ major/ minor/

negligible



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RISK MEASUREMENT (Evaluate)

BWRR3033 Rodziah(c) 29

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