Adjustments to Ratemaking Data

AY 2021 shows a 58% loss ratio. Looks profitable, until you realize losses are only 80% developed, costs rose 6% annually, and a mid-2022 rate increase isn't reflected. After adjusting: 83%. Every number in the ratemaking dataset is distorted by time. Skip any one of three adjustments and the indicated rate change is wrong.

HIGH-FREQUENCY: Trend factor calculations and the parallelogram method are among the most frequently tested concepts.

$$\text{Ultimate Losses}=\text{Reported Losses}\times \text{LDF}$$

More immature years have larger LDFs. A fully developed year has LDF = 1.00.

TRAP: If the problem says losses are "developed to ultimate," the LDF was already applied. Multiplying by LDF again double-develops the losses, a common exam error.

Trend adjusts historical cost levels to the future policy period. Apply separately to frequency and severity or as a combined pure premium trend:

$$\text{PP Trend}=(1+f_{\text{trend}})(1+s_{\text{trend}})-1$$

The trend period runs from the average historical loss date to the average future loss date. For AY data with annual policies and rates effective January 1:

Common mistakes

• Using the wrong trend period. For AY 2023 with rates effective Jan 1 2026: midpoint is July 1 2023 to July 1 2026 = 3.0 years, not 2.5 (Jan 2024 to July 2026). Trap: $1.05^{2.5}=1.1314$ instead of $1.05^{3.0}=1.1576$.
• Applying the parallelogram with the wrong $f$. April 1 gives $f=0.25$, not 0.75. Swapping gives $(0.25{)}^2/2=0.03125$ instead of 0.28125. Trap: a much lower on-level factor.
• Adding rate changes instead of compounding. +6% then +4% gives $1.06\times 1.04=1.1024$, not 1.10. Trap: slightly off, compounding over more changes.

Bottom line

• Three adjustments (D-T-O): develop losses to ultimate, trend losses, and on-level the premium; all three are required.
• Adjusted LR = (Ultimate Losses $\times$ Trend Factor) / On-Level EP.
• Trend factor = $(1+t{)}^n$, where $n$ runs from the historical-year midpoint to the future policy-period midpoint.
• Compound frequency and severity multiplicatively, never add the two trends.

Exam shortcut

Draw a timeline for every trend problem: mark the midpoint of the experience year, the rate effective date, and the midpoint of the future policy period. The trend period is the distance between the first and last marks (always "mid to mid." For the parallelogram, remember "one minus f, squared, over two") $f$ is how far through the year the change occurs.

The full lesson (about 2,164 words, 14 min read) adds 4 worked examples, all 5 common mistakes, a self-check, free in the app.

Learning objectives

• 5c

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