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
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 Loss Probability $
$10,
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 Loss Probability $
$10,
Another Group (YUMs: young unemployed males) $
$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

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

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)
classification is 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 = ( ) 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 = ,100/1.08 = ,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)