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Homeowners

Note Section 5.2 • Reading time: ~5 mins

Homeowners ratemaking involves unique complexities due to catastrophe exposure, changes in the average Amount of Insurance (underinsurance trends), and expense trending.

Catastrophe Ratemaking

Because catastrophes (e.g., hurricanes, earthquakes) are low-frequency, high-severity events, using standard historical experience to price them is inadequate. Actuaries separate catastrophe losses into modelled catastrophes (using external computer simulation models) and non-modelled catastrophes (smaller storm losses smoothed over a long historical period).

Non-Modelled Catastrophe Formula

To project non-modelled catastrophe loss costs, the historical ratio of catastrophe losses to the Amount of Insurance Years (AIY) is calculated and applied to the projected AIY:

Projected Catastrophe Pure Premium=[Average(Non-Modelled Catastrophe LossesAIY)]×Projected AIYEarned Exposures\text{Projected Catastrophe Pure Premium} = \left[ \text{Average}\left(\frac{\text{Non-Modelled Catastrophe Losses}}{\text{AIY}}\right) \right] \times \frac{\text{Projected AIY}}{\text{Earned Exposures}}

Where:

  • Amount of Insurance Year (AIY): Measures both the number of exposures and the amount of coverage provided (e.g., a home insured for $300,000 for one year represents 3.0 AIY, assuming $100,000 units).
  • Catastrophe-to-AIY Ratio: Reflects the loss severity per unit of coverage. This ratio is typically not on-leveled or trended because it compares loss dollars directly to coverage limits.
  • AIY-to-Exposures Ratio: Represents the average policy limit. This ratio changes over time due to inflation and coverage updates and must be projected forward.

Projecting Average AIY

To project the average AIY to the future rating period:

  1. Fit a linear (y=mx+by = mx + b) or exponential (y=abxy = ab^x) trend model to historical average AIY data.
  2. Identify the average earned date of the historical periods and the future policy period.
  3. Interpolate or project using the chosen trend model.
    • Example: If the target future policy period has an average earned date of January 1, 2018, and historical data points are centered at July 1, 2017 and July 1, 2018, the target average AIY is calculated using a 50%/50%50\% / 50\% interpolation between the two years.

Calculation of Annual Expense Trend

Like losses, expenses must be trended to the future period. Expenses are typically split into variable expenses (which change automatically with premium, e.g., commissions) and fixed expenses (which are subject to general cost inflation, e.g., rent, salaries).

Methodology

  1. Select an Expense Index: Use external economic indicators (e.g., Consumer Price Index (CPI) for services, or compensation indices) to measure cost inflation.
  2. Fit a Trend Line: Apply exponential regression to the expense index over a 3- to 5-year historical period to determine the annual expense trend rate (ff).
  3. Project to Future Period: Apply the trend factor to the current base fixed expenses: Projected Fixed Expense=Current Fixed Expense×(1+f)Trend Period\text{Projected Fixed Expense} = \text{Current Fixed Expense} \times (1 + f)^{\text{Trend Period}}