Risk Diversification and Insurance

1
Risk Diversification and Insurance

• Risk without pooling arrangement
• Risk with pooling arrangement
• Uncorrelated losses
• Correlated losses
• The role of insurance in risk diversification

2
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

3
Expected Losses and Standard Deviation without
Pooling Arrangement

• Two people with same distribution
• Outcome Probability
• 10,000 0.05
• Loss
• 0 0.95
• Expected losses and standard deviation for each
  person
• Expected value
• Standard deviation

4
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

5
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 _____

6
Risk Pooling with 4 People

• Pooling Arrangement between 4 people
• Outcome Probability
• 10,000 0.000006
• 7,500 0.000475
• Loss 5,000 0.014
• 2,500 0.171
• 0 0.815
• Expected Loss ______
• Variance ______

7
Risk Pooling with 20 People
8
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)

9
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 persons large loss does not tend to be
  offset by others small losses
• Therefore pooling does not reduce risk as much

10
Effect of Positive Correlation on Risk Reduction
11
Summary of Risk Pooling

• Pooling reduces each participants risk
• i.e., costs from loss exposure become more
  predictable
• Predictability increases with the number of
  participants
• Predictability decreases with correlation in
  losses

12
Insurance

• Why do we need insurance companies to deal with
  risk pooling?

13
Pooling Arrangements is Costly

• Adding Participants
• Distribution cost
• Underwriting cost
• Verifying Losses
• Collecting Assessments

14
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)

15
More on Insurance Distribution

• Marketing in Insurance
• Exclusive agents
• Independent agents
• Brokers
• Direct marketing
• Internet

16
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

17
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

18
Other Diversification Methods

• stock market diversification
• diversification across lines of business within a
  firm