On This Page

Trends

Note Section 1.4 • Reading time: ~5 mins

ASOP 13 provides guidance on selecting and documenting trends in ratemaking:

  • Scope: Applies to all types of trends including premiums, losses, expenses, retention rates, and marketing response rates.
  • Presentation (Section 3.1): Actuaries can present trends as a point estimate or a range of estimates, depending on the intended purpose.
  • Data Selection (Section 3.2): Can use insurance data (e.g., Fast Track data) or non-insurance data (e.g., Consumer Price Index - CPI). Key considerations include:
    • Credibility of the data.
    • Time period of available data.
    • Relationship of the data to what is being trended.
    • Distortions in the data (e.g., seasonality, change in underwriting/claims practices, change in mix of business, and catastrophe impacts).
  • Influences (Section 3.3): Consider relevant social and economic influences, such as changes in claim consciousness, court practices, and legal precedents.
  • Procedure Selection (Section 3.4): Consider current best practices and methods used in prior analyses.

Why Trend in Rate Level Indications?

Ratemaking is prospective. Actuaries must adjust historical data to reflect the cost and premium levels expected during the future policy period.

  • Premiums: Adjusted for changes in the average premium per exposure (e.g., shifting mix of business).
  • Losses/Expenses: Adjusted for changes in frequency, severity, and price inflation.
  • Historical Premiums Note: We do not use raw historical premium trends because one-time rate changes would distort the trend, and we do not expect these one-time changes to repeat in the same pattern.

An average premium trend can drift even if base rates are unchanged due to:

  • Insureds moving to higher or lower deductibles.
  • Insureds purchasing lesser or greater coverage limits.
  • Changes in the mix of business (e.g., writing more low-risk or high-risk policies).
  • Non-renewing policies of specific risk profiles.

In general, basic limits loss trends are compressed (closer to zero) compared to excess and total loss trends: ∣Basic Limits Trend∣<∣Excess Limits Trend∣\lvert \text{Basic Limits Trend} \rvert < \lvert \text{Excess Limits Trend} \rvert

The Inflation Leverage Effect

When inflation increases loss severities:

  • For claims already above the basic limit, the increase is entirely absorbed by the excess layer, while the basic limits claim is capped.
  • Claims just below the basic limit are pushed into the excess layer, creating new excess losses.
  • Exception: If the loss trend is negative, the basic limits trend is still closer to zero (less negative) than the excess trend (more negative).

[!WARNING] Do not use total or excess loss trends to trend basic limits losses, as total trends ignore the capping constraint of basic limits.

Trend Period Calculations and Average Dates

To determine the trend period, actuaries represent aggregation periods (like Calendar Years or Accident Years) using their average dates.

Simplifying Assumptions

  1. Policies are written uniformly over time.
  2. Premiums are earned uniformly, and claims occur uniformly over the policy period.

Midpoint Formulas (Mental Model)

For a Calendar Year (CY) or Accident Year (AY):

  • Average Earned/Accident Date = July 1 of that year.
  • Average Written Date = Average Earned Date −- Half of the Policy Term (Length).

Example: For a 12-month policy in CY 2020:

  • Average Earned Date = July 1, 2020
  • Average Written Date = January 1, 2020 (6 months prior to July 1)

Two-step trending is appropriate when historical trends are expected to differ from prospective trends (e.g., due to structural shifts or temporary policy limit changes).

[Avg Hist Date] --------(Step 1: Hist Trend)--------> [Latest Avg Date] --------(Step 2: Prospective Trend)--------> [Avg Future Date]
  • Step 1 (Historical): Trend from the historical average earned date to the latest average written date.
  • Step 2 (Prospective): Trend from the latest average written date to the future average earned date.

Formula using OLEP and OLWP

Trended OLEP=Hist. OLEP×Latest Avg. OLWPHist. Avg. OLWP×(1+Prospective Trend)Step 2 Period\text{Trended OLEP} = \text{Hist. OLEP} \times \dfrac{\text{Latest Avg. OLWP}}{\text{Hist. Avg. OLWP}} \times (1 + \text{Prospective Trend})^{\text{Step 2 Period}}

Alternatively, this can be written using average rate levels: Step 1 Trend Factor=Latest Avg. OLWPHist. Avg. OLEP\text{Step 1 Trend Factor} = \dfrac{\text{Latest Avg. OLWP}}{\text{Hist. Avg. OLEP}}

  • Historical Dates: Use average accident dates (July 1 of each Accident Year).
  • Prospective Dates: Use average accident dates of the future policy period.
    • For a future policy period of 7/1/2013 to 7/1/2014, the average written date is 1/1/2014. For 12-month policies, the average accident date is 7/1/2014 (which matches the average earned date).

Trend Estimation and Selection

Exponential Fitting

Trend rates are typically determined by fitting an exponential curve (y=ebxy = e^{bx}) to historical average severities, frequencies, or pure premiums.

  • “12 months ending each quarter”: This phrasing refers to rolling calendar years, meaning the calculated trend rates are annualized.

Selection Rules and Structural Breaks

  • Deductible Shifts: If a deductible shift occurred historically, it affects policy renewals for a full year and earnings for another year. Select data points that exclude the transition period to avoid bias.
  • Structural Shifts: If a structural break is observed in the trend, use two-step trending with a historical trend for the first period and a prospective trend reflecting the post-break environment.

Miscellaneous Considerations

  • Fixed Expenses: Typically trended from the average written date of the experience period to the average written date of the prospective period, because fixed expenses are usually incurred at policy inception.
    • Exception: If fixed expenses are incurred throughout the policy term, trend using average earned dates.
    • No Trend Rule: If fixed expenses and premiums are assumed to trend at the same rate, the fixed expense ratio does not need to be trended.
  • Policy Pricing Incentives: Pricing deductible policies below their indicated rate to incentivize high-deductible adoption can reduce overall profitability if the premium reduction exceeds the expected claim savings.
  • Loss Cost: A common synonym for Pure Premium: Pure Premium=LossesExposures=Frequency×Severity\text{Pure Premium} = \dfrac{\text{Losses}}{\text{Exposures}} = \text{Frequency} \times \text{Severity}

Footnotes