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Chapter 8

Chapter 8. Insurance Pricing. Insurance Pricing. Objective: Find the premium that covers an insurer’s expected costs , including a fair return to capital known as the Fair Premium It would prevail in a competitive market. Determinants of Fair Premiums. 4 Determinants

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Chapter 8

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  1. Chapter 8 Insurance Pricing

  2. Insurance Pricing • Objective: • Find the premium that covers an insurer’s expected costs, including a fair return to capital • known as the Fair Premium • It would prevail in a competitive market

  3. Determinants of Fair Premiums • 4 Determinants • Expected Claim Costs • Administrative Costs • Investment Income • Fair Profit Loading • Examine each factor separately

  4. Expected Claim Costs • The premium that just covers expected claim costs is called the pure premium • Example: • Large number of homogeneous buyers, i.e. each has the same loss distribution: Possible LossProbability $0 0.95 $10,000 0.05 • Pure Premium = $500

  5. Assumption About Uncertainty • Actual average claim cost can differ from expected claim costs, but for now we will ignore this uncertainty

  6. Premium Must Cover Expected Claim Costs • To cover claim costs, on average, premiums must equal $500. • if premium = $480, the insurer will lose money, on average • if premium = $640, the insurer will make profits, on average (competition would prevent this) • Conclusion: • Fair Premium must cover expected claim costs

  7. Implications of Heterogeneous Buyers • What if there are two groups of buyers? • One Group (MAPs: middle aged professionals) Possible LossProbability $0 0.95 $10,000 0.05 • Another Group (YUMs: young unemployed males) Possible LossProbability $0 0.90 $10,000 0.10

  8. Implications of Heterogeneous Buyers • Assume initially that • Equal number of each type • Losses are Independent • Full Insurance is mandatory • Costless to distinguish MAPs from YUMs

  9. Implications of Heterogeneous Buyers • Distribution of Average Claims Costs • Again, we will ignore uncertainty MAPs YUMs

  10. Implications of Heterogeneous Buyers • Initial Scenario: • Equal Treatment Insurance Company is only insurer • Premium for everyone = $750 • Does Equal Treatment cover its costs? • _____, the YUMs pay less than their expected cost, but the MAPs pay more

  11. Implications of Heterogeneous Buyers • New Scenario: allow competition • Competition from Selective Insurance Company • If Selective assumes Equal Treatment will continue to charge $750, how does Selective set price to maximize profits, • Premium to MAPs = • Premium to YUMs = • Profit per policyholder =

  12. Implications of Heterogeneous Buyers • What happens to Equal Treatment? • It would experience adverse selection • I.e., it would obtain an adverse selection of policyholders -- only the YUMs will purchase from Equal Treatment • Thus, Equal Treatment will have to classify or lose money

  13. Implications of Heterogeneous Buyers Key Points: Profit Maximization + ==> Risk Classification Competition Lack of Classification + ==> Adverse Selection Competition

  14. Implications of Heterogeneous Buyers • What if full insurance is not mandatory? • Recall, Initial Scenario: • Equal Treatment is only insurer • Equal Treatment charges $750 to everyone • What do MAPs do? • MAPs may purchase less insurance from Equal Treatment • YUMs still buy from Equal Treatment  Equal Treatment experiences adverse selection

  15. Implications of Heterogeneous Buyers Key Points: Profit Maximization + ==> Risk Classification Risk Management Alternatives to Insurance Lack of Classification + ==> Adverse Selection Risk Management Alternatives to Insurance

  16. Implications of Heterogeneous Buyers • What if it is costly to identify MAPs? • Go back to initial situation, but suppose that it costs $100 for each MAP identified • Assuming Equal Treatment continues to charge $750, what does Selective charge? • MAPs? ________ • YUMs? ________ • Redo the analysis assuming the cost per MAP identified = $300.

  17. Implications of Heterogeneous Buyers Key Point: Profit Maximization Risk Classification + ==> if it is Competition Cost Effective

  18. Is Classification Good for Society? • Public Policy Issue: • From a societal perspective, is risk classification desirable? • Some argue that risk classification should be restricted when • insurance is mandatory (e.g., auto liability) • classification is based on inherited traits (e.g., gender, genes) • classification is based on location of residence (e.g., auto, property) • classificationis based on subjective criteria (e.g., “poor moral risks”)

  19. Is Classification Good for Society? • Framework for evaluating public policy issue: • Four effects of restricting classification 1. Restricting classification redistributes income from low risk to high risk • Example: restrict use of gender for auto insurance Is this fair?

  20. Is Classification Good for Society? • Restricting classification will alter insurance prices to certain groups and therefore change behavior • Types of behavior: • amount of insurance purchased • amount of risky activity undertaken • loss control activities • Some changes in behavior may be desirable and some undesirable • Examples: • amount of liability insurance purchased by poor people • smoking • amount of life insurance purchased by people with HIV

  21. Is Classification Good for Society? • Restricting classification may decrease classification costs • Insurers incur costs in classifying, which increases prices on average. We might be better off not incurring these costs and just charge everyone the same price • Many of the controversial issues (gender, age, location) have low classification costs

  22. Is Classification Good for Society? 4. Limiting classification may increase regulatory costs • Monitoring of insurers to enforce restrictions • Need to impose other costly restrictions on insurers • marketing activities • underwriting activities • Restrictions lead insurers to not offer coverage • Leads to residual market (involuntary market) mechanisms • Leads to additional costs

  23. Risk Classification Practices • Consumers are classified by various criteria • Class Rate is applies to all consumers in a given classification • Underwriter decides whether a particular consumer will be offered coverage at the class rate • Schedule rating: modification of the rate by the underwriter based on specific characteristics of the consumer (applies mostly to commercial insurance) • Experience rating refers to practice of basing rates on past experience

  24. Recouping versus Updating • Basing rates on past experience is often controversial • Are insurers • recouping past losses or • updating expected losses on future business? • Competition and low switching costs limit the ability of insurers to recoup

  25. Return to Determinants of Fair Premiums • Summary: Ignoring • administrative costs • investment income • profits Fair Premium = Expected Claim Costs || Pure Premium

  26. Investment Income • Key Point: • Fair premium is reduced to reflect investment income on premiums • Equivalently, • Fair Premium = Present Value of Expected Costs

  27. Example to Illustrate Effect of Investment Income • Assume • no administrative costs • one year policies, premium received at beginning • certain claim costs = $100 paid according to table below Fair Premium

  28. Effect of Investment Income Varies Across Lines of Business

  29. Administrative Expenses • Fair Premium must cover administrative costs, such as • marketing • underwriting • loss adjustment • premium taxes • underwriting income taxes • etc.

  30. Expense Loadings as a Percentage of Premium

  31. Summary of Determinants of Fair Premiums • Ignoring profit loading • Fair Premium = PV of Expected Costs • Fair Premium = PV of Pure Premium + PV of Expenses • Note: Analysis to this point has been based on expected values • Now take into consideration the uncertainty associated with operations

  32. Effect of Uncertainty: Profit Loading • Uncertainty ==> claim costs could exceed premiums • That is, insolvency is possible • Insurers hold capital to reduce the likelihood of insolvency • Thus, capital providers bear the risk associated with insurance operations • Capital providers require compensation

  33. Fair Profit Loadings • Other terms for profit loading: • risk load • capital costs • Determinants of fair profit loading • Amount of capital needed to support the coverage • Cost of capital • Taxes • Agency costs

  34. Conclusion • Fair Premium = PV of Expected Claim Costs + PV of Expected Administrative Costs + Fair Profit Loading • Note fair premiums depend on both notions of risk highlighted in chapter 1 • Expected losses • Unpredictability of losses

  35. Numerical Example $100,000 with prob. 0.02 Loss = $20,000 with prob. 0.08 0 with prob. 0.90 Find Fair Premium if • policy provides full coverage • underwriting costs = 20% of pure premium • claims are paid at end of year • interest rate = 8% • claim processing costs = $5,000 • fair profit = 5% of pure premium

  36. Numerical Example • Solution: • pure premium = $3,600 • PV of expected claims = $3600/1.08 • underwriting costs + fair profit = (0.20 + 0.05) x $3,600 = $900 • expected claim processing costs = $5,000 x 0.10 = $500 • PV of expected claim processing costs = 500/1.08 • Fair premium = 900 + 4,100/1.08 = 900 + 3,796 = $4,696

  37. Capital Shocks and Underwriting Cycles • Fair premium model does not explain everything • Premiums & coverage appear to follow cycles: • “hard” markets (prices high, coverage restricted) • “soft” markets (prices low, coverage available) • Also premiums & coverage change following capital shocks • prices increase, coverage restricted

  38. Capital Shocks and Underwriting Cycles • Cycles and price increases following capital shocks are difficult to explain with fair premium model • Fair premium implies that prices are forward looking • prices depend on expected future costs • prices depend on uncertainty about future costs • What happened in past is irrelevant

  39. Premium Increases Following Capital Shocks • One explanation: • Capital shock depletes insurer capital • Costly to raise new capital • Capital becomes scarce ==> its required return increases • That is, the risk load increases

  40. Underwriting Cycles • Possible explanations • Insurers naively extrapolate from recent past • high (low) losses in the past cause insurers to predict that future losses will be high (low) • Capital shocks, followed by excessive competition • capital shock lowers capital • premiums increase, which replenishes capital • excess capital develops • premiums decrease

  41. Price Regulation Types of regulation: • Restrict level or change in rates • prior approval • file and use • competitive • Restrict underwriting criteria

  42. Effects of Rate Suppression and Compression • Rate suppression - lower rates below costs • Rate compression - restrict differences in rates across classifications • Suppression and/or compression lead insurers to not voluntarily offer coverage to some groups • which leads to creation of residual market mechanisms (e.g., joint underwriting associations) (JUAs)

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