Chapter Outline

1
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

2
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

3
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

4
Determinants of Fair Premiums

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

5
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

6
Assumption About Uncertainty

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

7
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

8
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

9
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

10
Implications of Heterogeneous Buyers

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

MAPs
YUMs
11
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

12
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

13
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

14
Implications of Heterogeneous Buyers

• Key Points
• Profit Maximization
• gt Risk Classification
• Competition
• Lack of Classification
• gt Adverse Selection
• Competition

15
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

16
Implications of Heterogeneous Buyers

• Key Points
• Profit Maximization
• gt Risk Classification
• Risk Management Alternatives
• to Insurance
• Lack of Classification
• gt Adverse Selection
• Risk Management Alternatives
• to Insurance

17
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?

18
Implications of Heterogeneous Buyers

• Key Point
• Profit Maximization Risk Classification
• gt if it is
• Competition Cost Effective

19
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)

20
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?

21
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

22
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

23
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

24
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

25
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

26
Return to Determinants of Fair Premiums

• Summary
• Ignoring
• administrative costs
• investment income
• profits
• Fair Premium Expected Claim Costs
• Pure Premium

27
Investment Income

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

28
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

29
Effect of Investment Income Varies Across Lines
of Business - Figure 6-2
30
Administrative Expenses

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

31
Expense Loadings as a Percentage of Premium

32
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

33
Effect of Uncertainty Profit Loading

• Uncertainty gt 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 insurers profit is the owners compensation
  for bearing this risk

34
Summary of Fair Premium Model

• Fair Premium
• PV of Expected Costs Profit loading
• Other terms for profit loading
• risk load
• capital costs

35
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

36
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

37
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

38
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

39
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

40
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

41
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

42
Comparison of the Two Examples

• Note difference in loading on the two policies
• Full coverage Deductible
• 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)

43
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

44
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

45
Premium Increases Following Capital Shocks

• One explanation
• Capital shock depletes insurer capital
• Costly to raise new capital
• Capital becomes scarce gt its required return
  increases
• That is, the risk load increases

46
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

47
Price Regulation

• Types
• Restrict level or change in rates
• prior approval
• file and use
• competitive
• Restrict underwriting criteria

48
Why Regulate Rates?

• Public Interest Perspective
• Correct problems in market place
• collusion among insurers
• lack of consumer information

49
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

50
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)