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 Expected Claim Costs Administrative Costs Investment Income Fair Profit Loading Examine each factor separately

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 Loss Probability $0 0.95 $10,000 0.05 Pure Premium = $500

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

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

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

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

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

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

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 =

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

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

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

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

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.

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

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) classification is based on subjective criteria (e.g., “poor moral risks”)

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?

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

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

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

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

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

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

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

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

Effect of Investment Income Varies Across Lines of Business

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

Expense Loadings as a Percentage of Premium

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

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

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

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

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

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

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

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

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

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

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

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)