Ins301 Ch.4 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$10,000 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

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$10,000 0.000006

$7,500 0.000475Loss = $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