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
Ins301 Ch.4
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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 =
Ins301 Ch.4
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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
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Effect on Expected Loss
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w/o pooling, expected loss = _____

with pooling, expected loss = _____
Effect on Standard Deviation
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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
Ins301 Ch.4
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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
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Result: uncertainty is not reduced as much
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Intuition:
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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
Ins301 Ch.4
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Effect of Positive Correlation on Risk
Reduction
Ins301 Ch.4
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Summary of Risk Pooling
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Pooling reduces each participant’s risk
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i.e., costs from loss exposure become more predictable
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Predictability increases with the number of
participants
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Predictability decreases with correlation in losses
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Insurance
 Why do we need insurance companies to deal with
risk pooling?
Ins301 Ch.4
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Pooling Arrangements is Costly
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Adding Participants
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Distribution cost
Underwriting cost
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Verifying Losses
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Collecting Assessments
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Function of Insurance Companies
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Insurers are intermediaries that lower the cost of
pooling arrangements by
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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
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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)?
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Collecting assessments is costly
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With assessments, there might be a delay in
payments to those who have claims
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Assessments impose greater uncertainty to
policyholders than fixed premiums
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Implications of Fixed Premiums
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Revenues may not match costs
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Someone must be the residual claimant
 i.e., someone must bear unexpectedly high losses and
receive profits when losses are lower than expected
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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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