Ratio Formulas for Insurance

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Practical Considerations

            Casualty Actuarial Society
            2005 Ratemaking Seminar
            John Ferraro FCAS, MAAA
        Philadelphia Insurance Companies
              Price Monitor

• Price Monitor Formulas
• Price Monitor Data Collection
• Price Monitor Reporting
     Price Monitor Formulas
• Renewal Report
• Standard Report
• Benchmark Report
      Price Monitor Formulas
• Renewal Report
  – Calculate rate changes on expiring coverage
  – Adjusts renewal premium to expiring
    coverage level
    • Adjustment to expiring limit and deductible.
  – Calculations not affected by exposure
    • Comparison of renewal and expiring rates not
      Renewal Report Formulas
• Normalization Factor = Current Factors at Renewal Level
                         Current Factors at Expiring Level

• Normalized Renewal Premium =      Renewal Premium
                                    Normalization Factor

• Normalized Renewal Rate = Normalized Renewal Premium
                              Renewal Exposures

• Expiring Rate = Expiring Premium / Expiring Exposures

• Rate Change % = Normalized Renewal Rate / Expiring Rate - 1

• Rate Change Premium =     Rate Change % x Expiring Premium
          Renewal Report Example
                Renewal          Expiring         Change
Premium         13,500           10,000           35%
Exposures       125              110              14%
Limit           1,000,000        500,000
ILF $1M         1.35
ILF $500k       1.25

Normalization Factor = ILF $1M / ILF 500k = 1.35 / 1.25 =     1.08
Normalized Renewal Premium = Premium / NF = 13,500 / 1.08 =   12,500

Normalized Rate = Normalized Renewal Premium / Exposure =     100

Expiring Rate = Expiring Premium / Expiring Exposure =        91

Rate Change =                                                 10%
     Price Monitor Formulas
• Standard Report
  – Measures judgment modification usage
     (e.g. Schedule Credits / Debits)
  – May include Experience Modification
    • As counter-balance to Schedule and IRPM mods
    Standard Report Formulas
• Standard Premium =
            Charged Premium
     Product of Judgment Modifications

• Average Judgment Modifications =
               Sum of Charged Premium
               Sum of Standard Premium
      Price Monitor Formulas
• Benchmark Report
  – Comparison of Final Rates rates across years
    or to a benchmark
   Benchmark Report Formulas
Benchmark Normalizing Factor (BNF) =
  Factor reflecting Policy coverage relative to a common coverage

Normalized Exposure Base = Exposures x BNF

Global Benchmark Rate =      Sum of Charged Premium
                          Sum of Normalized Exposure Base

Policy Level Benchmark Premium =
                Global Benchmark Rate x Policy’s BNF x Exposures

Ratio to Benchmark =       Charged Policy Premium
                       Policy Level Benchmark Premium
        Benchmark Report Example
Premium              13,500
Exposures            125
Limit                1,000,000
ILF $1M              1.35
Basic Limit          100,000

Benchmark Normalizing Factor = ILF $1M =                    1.35

Normalized Exposure Base = Exposures x BNF = 125 x 1.35 =   169

Global Benchmark Rate at Basic Limit = from totals          90

Policy Level Benchmark Premium = 90 x 1.35 x 125 =          15,188

Ratio to Benchmark = 13,500 / 15,188 =                      .89
      Price Monitor Formulas
Renewal & Benchmark Normalizing Factors
• Pertinent to premium determination
• Available & Reliable
• Examples
  – GL – ILF, deductible, term
  – Auto Liability – ILF, deductible, term
  – Fire Building – deductible, coinsurance,
    inflation guard, agreed amount, replacement
  Price Monitor Data Collection
• Matching Pricing to Reporting records

• Reasons Premiums may not be monitored
   Price Monitor Data Collection
  Matching of Pricing to Reporting
• Pricing records are at a very detailed level
      (vehicle, location, building, etc…).
• Pricing records on in-force basis.
• Reporting records are summarized and
  transaction based
   – Summarized to class, territory, coverage levels
   – Includes mid-term end., short-term coverage, cancellations
   – Coverage term not policy term basis
• Pricing fields must be adjusted, summed, or
  averaged to the Reporting record level.
      Price Monitor Data Collection
    Reasons Premiums not Monitored
•   Unable to match Pricing records to Reporting records.
•   Pricing premium does not tie to Reporting premium.
•   Miscoded Pricing records
•   Pricing records lack detail needed for calculations
        (e.g. external rating – umbrella, boiler & machine)
• Rates based on underwriter’s judgment
        (e.g. a-rated GL, inland marine)
• Exclude records or policies that distort the final report.
        (e.g. problems averaging pricing factors)
• Exclusion of insignificant coverages.
             Price Monitor
• Reporting Basics
• Price Monitor Reports
• Price Monitor Premium to Reporting
  Premium Report
• Additional Uses of Data
              Reporting Basics
• Price Monitor calculation fields are on a
  dollar basis to aid in averaging later.

• The records may not pass into all the
  – New policies would not reach Renewal Report
  – Different fields needed for calculations
  – Results may be counter intuitive
     • e.g. Rate Increase with declining Judgment Mod
              Price Monitor Reports
• Senior Management Reports
   –   Year / Quarter / Month
   –   Line / Coverage
   –   New vs. Renewal
   –   Market Segment

• Field & Market Segment Manager Reports
   – Region / Branch Office / Underwriter
   – State
   – Policy

• Price Monitor vs. Reporting Premium Report
          Price Monitor
Price Monitor vs. Reporting Report
• Demonstrates how much reported premium is being

• Provides general description of pockets not monitored.

• Identify blind spots or changes in book

• Satisfy internal control requirements in Sarbanes-Oxley
              Pricing Monitor Data
                   Other Uses
• Provides detailed changes for on-level calculations.
   – Territory and class analysis
   – Only renewed coverages may be considered

• Detailed Rate Effect calculations
   – Underlying rates, factors and exposures readily available
   – Enhance understanding of rating practices.

• Completion of filing forms

• Use of Judgment Modification in Experience Exhibits
   – Assist in explaining effect of schedule mod usage on profitability
   – Assist in developing loss ratio projections.

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