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Private Passenger Auto

Note Section 5.1 • Reading time: ~5 mins

This study note summarizes key ratemaking principles for Private Passenger Auto (PPA) Property Damage (PD) coverage, focusing on policy terms, trend calculations, and credibility application.

Policy Terms and Average Dates

Private Passenger Auto is typically written on 6-month policy terms (though 12-month terms also exist). The policy term length directly impacts the timing of exposures and the projection of average accident dates.

6-Month vs. 12-Month Policy Logic

  • For a block of 6-month policies written uniformly over a calendar year:
    • The average written date is the midpoint of the year (July 1).
    • The average earned date is 3 months later (October 1) because the coverage is fully earned over 6 months.
    • The average accident date for these policies is also the midpoint of the earned period.
  • Key Distinction: When performing rate filings, the trend period is calculated from the average accident date of the historical experience period to the average accident date of the future period when the rates will be in effect.

Trend Calculations (Frequency, Severity, and Pure Premium)

For PPA Property Damage, trend factors are determined by analyzing historical patterns in:

  1. Claim Frequency: Frequency=Claim CountExposures\text{Frequency} = \frac{\text{Claim Count}}{\text{Exposures}}
  2. Claim Severity: Severity=LossesClaim Count\text{Severity} = \frac{\text{Losses}}{\text{Claim Count}}
  3. Pure Premium: Pure Premium=Frequency×Severity=LossesExposures\text{Pure Premium} = \text{Frequency} \times \text{Severity} = \frac{\text{Losses}}{\text{Exposures}}

Trend Selection Guidelines

  • Analyze both linear and exponential models. Property damage severity trends are highly correlated with inflation (parts and labor repair costs) and typically follow exponential growth.
  • Frequency trends may reflect changing driving habits, safety technology, and traffic density.
  • The relationship Pure Premium Trend=(1+Frequency Trend)×(1+Severity Trend)−1\text{Pure Premium Trend} = (1 + \text{Frequency Trend}) \times (1 + \text{Severity Trend}) - 1 must be used to check for consistency.

Credibility and Trended Present Rates

Due to localized data sparsity (e.g., at the territory or class level), credibility weighting is necessary.

  • Complement of Credibility: The Trended Present Rates method is a standard approach for determining the credibility complement.
  • The subject’s present rates are projected forward using the net trend factor (Loss Trend / Premium Trend) to the future effective period, removing any distorting effects of past rate changes that were implemented but not fully indicated.