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

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

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 = Ins301 Ch.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

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

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 = $______ Ins301 Ch.4

Risk Pooling with 20 People Ins301 Ch.4

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

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

Effect of Positive Correlation on Risk Reduction Ins301 Ch.4

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

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

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

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

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

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

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

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