Transcript Document
Risk Diversification and Insurance
Risk without pooling arrangement
Risk with pooling arrangement
Uncorrelated losses
Correlated losses
The role of insurance in risk diversification
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Pooling Arrangements
Pooling arrangement -- every participant agrees to
share losses equally, each paying the average loss.
How does pooling arrange reduce risk?
Uncorrelated losses
Correlated losses
Ins301 Ch.4
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Expected Losses and Standard Deviation
without Pooling Arrangement
Two people with same distribution
Outcome
$10,000
Probability
0.05
Loss =
$0
0.95
Expected losses and standard deviation for each person:
Expected value =
Standard deviation =
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Expected Losses and Standard Deviation with
Pooling Arrangement
Pooling Arrangement changes distribution of accident costs
for each individual
Outcome
Probability
Cost =
Expected Cost =
Standard Deviation =
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The Effect of Pooling Arrangement
Effect on Expected Loss
w/o pooling, expected loss = _____
with pooling, expected loss = _____
Effect on Standard Deviation
w/o pooling, standard. deviation = _____
with pooling, standard. deviation = _____
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Risk Pooling with 4 People
Pooling Arrangement between 4 people:
Outcome
$10,000
$7,500
Loss =
Probability
0.000006
0.000475
$5,000
0.014
$2,500
$0
0.171
0.815
Expected Loss = $______
Variance = $______
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Risk Pooling with 20 People
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Effect of Risk Pooling of Uncorrelated Losses
do not change expected loss
reduce uncertainty (variance decreases, losses become
more predictable, maximum probable loss declines)
distribution of costs becomes more symmetric (less
skewness)
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Effect of Risk Pooling of Correlated Losses
Now allow correlation in losses
Result: uncertainty is not reduced as much
Intuition:
What happens to one person happens to others
One person’s large loss does not tend to be offset by
others’ small losses
Therefore pooling does not reduce risk as much
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Effect of Positive Correlation on Risk
Reduction
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Summary of Risk Pooling
Pooling reduces each participant’s risk
i.e., costs from loss exposure become more predictable
Predictability increases with the number of
participants
Predictability decreases with correlation in losses
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Insurance
Why do we need insurance companies to deal with
risk pooling?
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Pooling Arrangements is Costly
Adding Participants
Distribution cost
Underwriting cost
Verifying Losses
Collecting Assessments
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Function of Insurance Companies
Insurers are intermediaries that lower the cost of
pooling arrangements by
reducing the number of contracts
employing people with expertise in
marketing, underwriting, and claims processing
Insurers also provide services needed by businesses
loss control
claims processing (third party administrators)
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More on Insurance Distribution
Marketing in Insurance
Exclusive agents
Independent agents
Brokers
Direct marketing
Internet
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Fixed Premiums Versus Assessments
Why do insurers charge fixed premiums (as
opposed to having ex post assessments)?
Collecting assessments is costly
With assessments, there might be a delay in
payments to those who have claims
Assessments impose greater uncertainty to
policyholders than fixed premiums
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Implications of Fixed Premiums
Revenues may not match costs
Someone must be the residual claimant
i.e., someone must bear unexpectedly high losses and
receive profits when losses are lower than expected
Insurers can fail (become insolvent)
Examine the implications of these observations in
Ch. 5
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Other Diversification Methods
stock
market diversification
diversification across lines of business
within a firm
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