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 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 OutcomeProbability $10,000 0.05 Loss = $0 0.95 • 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 OutcomeProbability 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: OutcomeProbability $10,000 0.000006 $7,500 0.000475 Loss = $5,000 0.014 $2,500 0.171 $0 0.815 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