T6.1H&N, Ch. 6

Chapter Outline

6.1 Insurance Costs and Fair Premiums

6.2 Expected Claim Costs

Homogeneous buyers

Heterogeneous buyers

Competition, Risk Classification, and Societal Welfare

Redistributive Effects of Classification

Behavioral Effects of Classification

Classification Costs

Risk Classification Practices

6.3 Investment Income and the Timing of Claim Payments

6.4 Administrative costs

6.5 Profit Loading

Summary

T6.2H&N, Ch. 6

Chapter Outline

6.6 Capital Shocks and Underwriting Cycles

Fair Premiums are Forward Looking

Large Losses And Capital Shocks

The Underwriting Cycle

6.7 Price Regulation

Regulation Of Rate Changes

Why Regulate Rate Changes?

Effects of Regulating Rate Changes

Regulation of Rating Factors

Incentives for Risk Control

Fairness, Imperfect Classification, and Control/Causality Issues

Excessive Classification and Use of Subjective Assessments

Ensuring Availability When Regulation Depresses Rates

6.8 Summary

T6.3H&N, Ch. 6

Insurance Pricing

Objective:

• Find the premium that equals expected costs, including a fair return to capital

• known as the Fair Premium

• It would prevail in a competitive market

T6.4H&N, Ch. 6

Determinants of Fair Premiums

• 4 Determinants

• Expected Claim Costs

• Administrative Costs

• Investment Income

• Fair Profit Loading

• Examine each factor separately

T6.5H&N, Ch. 6

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

T6.6H&N, Ch. 6

Assumption About Uncertainty

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

0

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T6.7H&N, Ch. 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

T6.8H&N, Ch. 6

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)

Possible Loss Probability

$0 0.90

$10,000 0.10

T6.9H&N, Ch. 6

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

T6.10H&N, Ch. 6

Implications of Heterogeneous Buyers

• Distribution of Average Claims Costs• Again, we will ignore uncertainty

0

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0.002

0.003

0.004

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Average Loss

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MAPs YUMs

T6.11H&N, Ch. 6

Implications of Heterogeneous Buyers

Initial Scenario:

• Equal Treatment Insurance Company is only insurer

• Premium for everyone = $750

• Does Equal Treatment cover its costs?

• Yes, the YUMs pay less than their expected cost, but the MAPs pay more

T6.12H&N, Ch. 6

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 =

T6.13H&N, Ch. 6

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

T6.14H&N, Ch. 6

Implications of Heterogeneous Buyers

Key Points:

Profit Maximization

+ ==> Risk Classification

Competition

Lack of Classification

+ ==> Adverse Selection

Competition

T6.15H&N, Ch. 6

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 not purchase insurance

• If not, only YUMs buy from Equal Treatment

• Equal Treatment experiences adverse selection

T6.16H&N, Ch. 6

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

T6.17H&N, Ch. 6

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?

• What if the cost per MAP identified = $300?

T6.18H&N, Ch. 6

Implications of Heterogeneous Buyers

Key Point:

Profit Maximization Risk Classification

+ ==> if it is

Competition Cost Effective

T6.19H&N, Ch. 6

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”)

T6.20H&N, Ch. 6

Is Classification Good for Society?

Framework for evaluating public policy issue:

• Four effects of restricting classification

1. Redistributes income

• From low risk to high risk

• Examples:

• Is this fair?

T6.21H&N, Ch. 6

Is Classification Good for Society?

2. Classification will alter insurance prices to certain groups and therefore change behavior

• Types of behavior:

• amount of insurance purchased

• 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

T6.22H&N, Ch. 6

Is Classification Good for Society?

3. May decrease classification costs

• Ignoring fairness issues (point #1), if there are no behavioral effects of classification (point #2), then costly classification is a waste;

• I.e., classification simply redistributes income

• Controversial issues: (gender, age, location) have low classification costs

T6.23H&N, Ch. 6

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

T6.24H&N, Ch. 6

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

T6.25H&N, Ch. 6

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

T6.26H&N, Ch. 6

Return to Determinants of Fair Premiums

Summary:

Ignoring• administrative costs

• investment income

• profits

Fair Premium = Expected Claim Costs ||

Pure Premium

T6.27H&N, Ch. 6

Investment Income

Key Point:

• Fair premium is reduced to reflect investment income on premiums

• Equivalently,

• Fair Premium = Present Value of Expected Costs

T6.28H&N, Ch. 6

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

Expected Claim Payments Interest Rate

year 1 year 2 year 3 0.1 0.05

$100 $0 $0 $90.91 $95.24$50 $50 $0 $86.78 $92.97$50 $25 $25 $84.90 $91.89

T6.29H&N, Ch. 6

Effect of Investment Income Varies Across Lines of Business - Figure 6-2

0%

20%

40%

60%

80%

100%

10987654321

Year

Cu

mu

lati

ve

%

Homeowners

Auto Liability

Workers' Comp

Other Liability

Cumulative Percentage of Total Losses Paid Over Timefor Accidents in Year t

T6.30H&N, Ch. 6

Administrative Expenses

Fair Premium must cover administrative costs, such as

• marketing

• underwriting

• loss adjustment

• premium taxes

• underwriting income taxes

• etc.

T6.31H&N, Ch. 6

Expense Loadings as a Percentage of Premium

Underwriting Expenses Loss Adjustment Type of Insurance Commissions General Exp. Total UW Exp. Expenses

Homeowners 15.8% 15.0% 30.8% 11.5%

Personal Auto Liability 8.5 14.0 22.5 13.0

Personal Auto Physical Damage 8.5 13.9 22.4 8.6

Workers' Compensation 5.6 14.3 19.9 12.0

Other Liability 11.0 15.1 26.1 28.1

T6.32H&N, Ch. 6

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

T6.33H&N, Ch. 6

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

• The insurer’s profit is the owners’ compensation for bearing this risk

T6.34H&N, Ch. 6

Summary of Fair Premium Model

Fair Premium

= PV of Expected Costs + Profit loading

• Other terms for profit loading:

• risk load

• capital costs

T6.35H&N, Ch. 6

Determinants of Profit Loadings

• Actuarial Models:

• Variance of distribution of claim costs for that line of business determines risk load

• Risk load increases with the unpredictability of claim costs

T6.36H&N, Ch. 6

Determinants of Profit Loadings

• Financial Models:

• Optimal level of capital given its costs and benefits

• Benefits of capital depend on

• variance of claim costs

• covariance of claim costs across lines and with assets

• Cost of holding capital:

• tax costs

• agency costs

T6.37H&N, Ch. 6

Conclusion

Fair Premium

= PV of Expected Claim Costs

+ PV of Expected Administrative Costs

+ Profit Loading

Note two meanings of risk

• expected losses

• unpredictability of losses

T6.38H&N, Ch. 6

Pricing Example 1

$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

T6.39H&N, Ch. 6

Pricing Example 1

• 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

T6.40H&N, Ch. 6

Pricing Example 2

$100,000 with prob. 0.02

Loss = $20,000 with prob. 0.08

0 with prob. 0.90

Find Fair Premium if

• policy has a $20,000 deductible

• 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

T6.41H&N, Ch. 6

Pricing Example 2

• Solution:

• pure premium = 0.02 x $80,000 = $1,600

• PV of expected claims = $1600/1.08

• underwriting costs + fair profit = (0.20 + 0.05) x $1,600 = $400

• expected claim processing costs = 0.02 x $5,000 = $100

• PV of expected claim processing costs =$100/1.08

• Fair premium = $400 + $1,700/1.08 = $400 + $1574 = $1,974

T6.42H&N, Ch. 6

Comparison of the Two Examples

• Note difference in loading on the two policies

Full coverageDeductible

Premium $4,696 $1,974

Expected claim cost $3,600 $1,600

Dollar loading $1,096 $374

Percentage loading 30.4% 23.4%

(relative to exp. claim cost)

Difference is due to the deductible policy eliminating expected claim processing cost on relatively frequent, low severity claims (see Chapter 8)

T6.43H&N, Ch. 6

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)

• Change following capital shocks• prices increase, coverage restricted

T6.44H&N, Ch. 6

Capital Shocks and Underwriting Cycles

Cycles and price increases following capital shocks are difficult to explain

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

T6.45H&N, Ch. 6

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

T6.46H&N, Ch. 6

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

T6.47H&N, Ch. 6

Price Regulation

Types

• Restrict level or change in rates

• prior approval

• file and use

• competitive

• Restrict underwriting criteria

T6.48H&N, Ch. 6

Why Regulate Rates?

Public Interest Perspective:

• Correct problems in market place

• collusion among insurers

• lack of consumer information

T6.49H&N, Ch. 6

Why Regulate Rates?

Economic Theory of Regulation Perspective

• Regulation benefits politically influential groups

• Possible beneficiaries of price regulation:

• Insurers as a group

• Inefficient insurers

• High risk consumers

T6.50H&N, Ch. 6

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)