1. 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

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
Ins301 Ch.4

3. Expected Losses and Standard Deviation without Pooling Arrangement
Two people with same distribution
Outcome Probability
$10,
Loss = $
Expected losses and standard deviation for each person:
Expected value =
Standard deviation =
Ins301 Ch.4

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 =
Ins301 Ch.4

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 = _____
Ins301 Ch.4

6. Risk Pooling with 4 People
Pooling Arrangement between 4 people:
Outcome Probability
$10,
$7,
Loss = $5,
$2, $
Expected Loss = $______
Variance = $______
Ins301 Ch.4

7. Risk Pooling with 20 People
Ins301 Ch.4

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)
Ins301 Ch.4

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 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

10. Effect of Positive Correlation on Risk Reduction
Ins301 Ch.4

11. 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
Ins301 Ch.4

12. Insurance
Why do we need insurance companies to deal with risk pooling?
Ins301 Ch.4

13. Pooling Arrangements is Costly
Adding Participants
Distribution cost
Underwriting cost
Verifying Losses
Collecting Assessments
Ins301 Ch.4

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)
Ins301 Ch.4

15. More on Insurance Distribution
Marketing in Insurance
Exclusive agents
Independent agents
Brokers
Direct marketing
Internet
Ins301 Ch.4

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
Ins301 Ch.4

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
Ins301 Ch.4

18. Other Diversification Methods
stock market diversification
diversification across lines of business within a firm
Ins301 Ch.4