Pricing by ert554898

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									                                    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        Probability
                           $0              0.95
                      $10,000              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
                               0.15
                 Probability


                                0.1

                               0.05

                                 0
                                          160
                                                320
                                                      480
                                                            640
                                                                  800
                                      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         0.95
                      $10,000         0.05


             • Another Group (YUMs: young unemployed males)

                      Possible Loss   Probability
                           $0         0.90
                      $10,000         0.10




H&N, Ch. 6
                                                              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

                           0.004       MAPs      YUMs

                           0.003
             Probability




                           0.002


                           0.001


                              0
                                   0




                                         500




                                                  1000




                                                         1500
                                         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

            Key Points:

             Profit Maximization
                 +                    ==>   Risk Classification
             Competition




             Lack of Classification
                +                     ==>   Adverse Selection
             Competition



H&N, Ch. 6
                                                                  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 Classification
             Risk Management Alternatives
             to Insurance




             Lack of Classification
                         +                  ==>   Adverse Selection
             Risk Management Alternatives
             to Insurance
H&N, Ch. 6
                                                                        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         Risk Classification
                 +                 ==>      if it is
             Competition                 Cost Effective




H&N, Ch. 6
                                                               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        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




H&N, Ch. 6
                                                                            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%




                            80%
             Cumulative %




                            60%



                                                                             Homeowners
                            40%
                                                                             Auto Liability
                                                                             Workers' Comp
                                                                             Other Liability
                            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

                •   marketing
                •   underwriting
                •   loss adjustment
                •   premium taxes
                •   underwriting income taxes
                •   etc.




H&N, Ch. 6
                                                      T6.30
             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




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

                           $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



H&N, Ch. 6
                                                                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

                           $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



H&N, Ch. 6
                                                                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

                                        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)



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

								
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