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
H&N, Ch. 6
T6.1
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
H&N, Ch. 6
T6.2
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
H&N, Ch. 6
T6.3
Determinants of Fair Premiums
• 4 Determinants
•
•
•
•
Expected Claim Costs
Administrative Costs
Investment Income
Fair Profit Loading
• Examine each factor separately
H&N, Ch. 6
T6.4
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
$0
$10,000
Probability
0.95
0.05
• Pure Premium = $500
H&N, Ch. 6
T6.5
Assumption About Uncertainty

Actual average claim cost can differ from
expected claim costs, but for now we will
ignore this uncertainty
Probability
0.15
0.1
0.05
800
640
480
320
160
0
0
Loss
H&N, Ch. 6
T6.6
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
H&N, Ch. 6
T6.7
Implications of Heterogeneous Buyers

What if there are two groups of buyers?
• One Group (MAPs: middle aged professionals)
Possible Loss
Probability
$0
$10,000
0.95
0.05
• Another Group (YUMs: young unemployed males)
Possible Loss
$0
$10,000
H&N, Ch. 6
Probability
0.90
0.10
T6.8
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
H&N, Ch. 6
T6.9
Implications of Heterogeneous Buyers
• Distribution of Average Claims Costs
• Again, we will ignore uncertainty
MAPs
Probability
0.004
YUMs
0.003
0.002
0.001
1500
1000
500
0
0
Average Loss
H&N, Ch. 6
T6.10
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
H&N, Ch. 6
T6.11
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 =
H&N, Ch. 6
T6.12
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
H&N, Ch. 6
T6.13
Implications of Heterogeneous Buyers

H&N, Ch. 6
Key Points:
Profit Maximization
+
Competition
==>
Risk Classification
Lack of Classification
+
Competition
==>
Adverse Selection
T6.14
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 not purchase insurance
• If not, only YUMs buy from Equal Treatment
• Equal Treatment experiences adverse selection
H&N, Ch. 6
T6.15
Implications of Heterogeneous Buyers

Key Points:
Profit Maximization
+
Risk Management Alternatives
to Insurance
Lack of Classification
+
Risk Management Alternatives
to Insurance
H&N, Ch. 6
==>
Risk Classification
==>
Adverse Selection
T6.16
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?
• What if the cost per MAP identified = $300?
H&N, Ch. 6
T6.17
Implications of Heterogeneous Buyers

Key Point:
Profit Maximization
+
Competition
H&N, Ch. 6
==>
Risk Classification
if it is
Cost Effective
T6.18
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”)
H&N, Ch. 6
T6.19
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?
H&N, Ch. 6
T6.20
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
H&N, Ch. 6
T6.21
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
H&N, Ch. 6
T6.22
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
H&N, Ch. 6
T6.23
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
H&N, Ch. 6
T6.24
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
H&N, Ch. 6
T6.25
Return to Determinants of Fair Premiums

Summary:
Ignoring
• administrative costs
• investment income
• profits
Fair Premium = Expected Claim Costs
||
Pure Premium
H&N, Ch. 6
T6.26
Investment Income

Key Point:
• Fair premium is reduced to reflect investment
income on premiums
• Equivalently,
• Fair Premium = Present Value of Expected Costs
H&N, Ch. 6
T6.27
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
Expected Claim Payments
H&N, Ch. 6
Interest Rate
year 1
year 2
year 3
0.1
0.05
$100
$50
$50
$0
$50
$25
$0
$0
$25
$90.91
$86.78
$84.90
$95.24
$92.97
$91.89
T6.28
Effect of Investment Income Varies
Across Lines of Business - Figure 6-2
Cumulative Percentage of Total Losses Paid Over Time
for Accidents in Year t
100%
Cumulative %
80%
60%
Homeowners
Auto Liability
Workers' Comp
Other Liability
40%
20%
0%
1
2
3
4
5
6
7
8
9
10
Year
H&N, Ch. 6
T6.29
Administrative Expenses

Fair Premium must cover administrative
costs, such as
•
•
•
•
•
•
H&N, Ch. 6
marketing
underwriting
loss adjustment
premium taxes
underwriting income taxes
etc.
T6.30
Expense Loadings as a Percentage of Premium
Type of Insurance
Homeowners
Underwriting Expenses
Commissions
General Exp.
Total UW Exp.
15.8%
15.0%
30.8%
Loss Adjustment
Expenses
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
H&N, Ch. 6
T6.31
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
H&N, Ch. 6
T6.32
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
• The insurer’s profit is the owners’ compensation for
bearing this risk
H&N, Ch. 6
T6.33
Summary of Fair Premium Model

Fair Premium
= PV of Expected Costs + Profit loading
• Other terms for profit loading:
• risk load
• capital costs
H&N, Ch. 6
T6.34
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
H&N, Ch. 6
T6.35
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
H&N, Ch. 6
T6.36
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
H&N, Ch. 6
T6.37
Pricing Example 1
Loss =
$100,000
$20,000
0
with prob. 0.02
with prob. 0.08
with prob. 0.90
Find Fair Premium if
•
•
•
•
•
•
H&N, Ch. 6
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
T6.38
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
H&N, Ch. 6
T6.39
Pricing Example 2
Loss =
$100,000
$20,000
0
with prob. 0.02
with prob. 0.08
with prob. 0.90
Find Fair Premium if
•
•
•
•
•
•
H&N, Ch. 6
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
T6.40
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
H&N, Ch. 6
T6.41
Comparison of the Two Examples
• Note difference in loading on the two policies
Premium
Expected claim cost
Dollar loading
Percentage loading
(relative to exp. claim cost)
Full coverage
$4,696
$3,600
$1,096
30.4%
Deductible
$1,974
$1,600
$374
23.4%
Difference is due to the deductible policy eliminating expected
claim processing cost on relatively frequent, low severity claims
(see Chapter 8)
H&N, Ch. 6
T6.42
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
H&N, Ch. 6
T6.43
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
H&N, Ch. 6
T6.44
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
H&N, Ch. 6
T6.45
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
H&N, Ch. 6
T6.46
Price Regulation

Types
• Restrict level or change in rates
• prior approval
• file and use
• competitive
• Restrict underwriting criteria
H&N, Ch. 6
T6.47
Why Regulate Rates?

Public Interest Perspective:
• Correct problems in market place
• collusion among insurers
• lack of consumer information
H&N, Ch. 6
T6.48
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
H&N, Ch. 6
T6.49
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)
H&N, Ch. 6
T6.50