Calculate projected losses using trend analysis. | Free Exam ASTAM Lesson

Trend analysis turns yesterday's losses into tomorrow's expected losses. Skip the trend factor and your rate filing prices last year's claims, not next year's.

Why trend. Historical losses reflect the cost level of the past: average claim severity, claim frequency, and mix of business at that time. The future policy period operates under a different cost level (medical inflation, wage growth, jury awards, claim frequency drift). Trend bridges the gap.

Three trend pieces. Severity trend is dollars per claim. Frequency trend is claims per exposure. Pure premium trend is dollars per exposure, equal to severity times frequency.

Pure premium trend combines multiplicatively, not additively:

$(1 + t_{P P}) = (1 + t_{S}) (1 + t_{F})$

If severity trends at 5% and frequency at 2%, pure premium trends at $1.05 \times 1.02 - 1 = 0.071$ , or 7.1%. Adding 5% + 2% = 7% underprices by 10 basis points (the cross-product $t_{S} t_{F}$ is the missing piece).

Trend period: mid-point to mid-point. The trend period runs from the average loss date in the experience period to the average loss date in the future policy period.

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Common mistakes

Adding severity and frequency trends instead of compounding. The correct combination is $(1 + t_{S}) (1 + t_{F}) - 1$ , not $t_{S} + t_{F}$ .
Trending start-of-year to start-of-year. Always mid-point to mid-point, otherwise the period is off by up to a full year.
Using the calendar year writing mid-point as the loss mid-point. For annual policies, the loss mid-point sits six months past the writing mid-point.

Bottom line

Projected loss = historical loss × trend factor × loss development factor (other adjustments as needed).
Trend factor = $(1 + t)^{n}$ , where $t$ is the annual trend rate and $n$ is the trend period in years, measured mid-point to mid-point.
Two-step trend: past trend (experience mid-point to anchor), future trend (anchor to future policy mid-point); rates can differ but windows must abut.
Pure premium trend = $(1 + t_{S}) (1 + t_{F}) - 1$ ; combine frequency and severity multiplicatively, never additively.

Exam shortcut

Memorize the mid-point shift: annual policies push the loss mid-point six months past the writing mid-point. AY 2024 anchors at July 1, 2024; CY 2026 policies anchor at January 1, 2027. For combined severity-frequency trends under 10%, the multiplicative result is approximately $t_{S} + t_{F} + t_{S} t_{F}$ . The cross-product is small but non-zero; do not drop it. Two-step shortcut: write the trend timeline left to right, mark the anchor, multiply two factors.

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Learning objectives

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