Loss Trend

Study guides: Exam ASTAM, Exam 5

Loss Trend is the annual rate of change in loss cost over time — driven by inflation, the legal environment, technology, safety and mix — applied to bring historical losses from the cost level of the experience period to the cost level of the future policy period.

\text{Trend Factor} = (1 + t)^{n}

1 + t_{PP} = (1 + t_{\text{freq}})(1 + t_{\text{sev}})

• t is the selected annual trend and n the trend period, measured from the average date of loss in the experience period to the average date of loss in the forecast period. In Werner & Modlin's example — accident year 2011 losses, annual policies written during 2015 — that is 7/1/2011 to 12/31/2015, or 4.5 years; a common error is measuring it from the wrong end of either period.
• Trend and development answer different questions and must both be applied: development brings immature losses to their own ultimate level; trend restates past losses to the level expected for similar losses in the future period. Werner & Modlin call the belief that doing both double-counts inflation the overlap fallacy: development does include the inflation that raises payments on reported claims after reporting, but that does not prove an overlap.
• Trend is selected, not merely fitted. Linear and exponential regressions are the most common measures; exponential models may be fit to the whole of the data and to more recent periods, supplemented with multi-state, countrywide or industry data and non-insurance indices, and the trend selected with judgment. ASOP 13 asks the actuary to select data appropriate to the trend being analyzed, consider the lengths of the experience and forecast periods in setting the trending period, evaluate each procedure's results for reasonableness, and document the methods, assumptions and data sources.
• Frequency and severity are analyzed separately to understand the drivers of the trend, because they can move in opposite directions — Werner & Modlin's example is a heavily marketed higher deductible, which lowers frequency but is likely to increase severity, a shift that is hard to see in pure premium.
• A two-step trend is used when the trend in the historical period differs from the trend expected in the forecast period (legislative changes are one example): losses are first trended at a current trend from the experience period's average accident date to that of the latest data point in the trend data, then projected at a separately selected trend to the forecast period's average accident date. A benefit-level change is restated in the data, or allowed for in the selection, so that it is not double counted.
• Limits leverage severity trend: for a positive trend, basic-limits losses trend more slowly than total-limits losses and the excess layer faster, so a severity trend measured on total-limits data must be adjusted before it is applied to basic-limits losses, or the trend is measured on basic-limits data (see ILFs).

Getting the Trend Period Right Rates will be in effect for annual policies written from 7/1/2025 to 6/30/2026. The experience period is accident year 2023. Selected annual severity trend is 5\%.

Compute the trend period and the trend factor.

Answer Average date of loss in the experience period. Accident year 2023 runs 1/1–12/31/2023; with losses occurring uniformly, its average loss date is 7/1/2023.

Average date of loss in the forecast period. Policies are written between 7/1/2025 and 6/30/2026; each provides coverage for a year after it is written. The first policy is exposed 7/1/2025–6/30/2026 and the last 7/1/2026–6/30/2027, so the exposure period runs 7/1/2025 to 6/30/2027 and its midpoint — the average loss date — is 7/1/2026.

\begin{align*}
n &= 7/1/2026 - 7/1/2023 = 3.0 \text{ years} \\[4pt]
\text{Trend factor} &= 1.05^{3.0} = 1.1576
\end{align*}

The common mistake is to measure to the start of the policy period (7/1/2025, giving n = 2.0) or to its midpoint (1/1/2026, giving n = 2.5). Both understate the projection — here by 5\% and 2\% of the entire loss provision.

Fitting and Selecting a Trend Annual severity for a liability line:

AY	Severity	Change
2019	\$8{,}000
2020	\$8{,}300	+3.8\%
2021	\$8{,}700	+4.8\%
2022	\$9{,}400	+8.0\%
2023	\$10{,}200	+8.5\%
2024	\$11{,}100	+8.8\%

What trend should be selected?

Answer Annual trends over different windows, from end point to end point (an exponential regression through every point gives 6.9\%, 8.5\% and 8.7\%):

\begin{align*}
\text{5-year } (2019\text{–}2024): \; \left(\tfrac{11{,}100}{8{,}000}\right)^{1/5} - 1 &= 6.8\% \\[6pt]
\text{3-year } (2021\text{–}2024): \; \left(\tfrac{11{,}100}{8{,}700}\right)^{1/3} - 1 &= 8.5\% \\[6pt]
\text{2-year } (2022\text{–}2024): \; \left(\tfrac{11{,}100}{9{,}400}\right)^{1/2} - 1 &= 8.7\%
\end{align*}

The series is not a constant trend — it accelerated around 2022. The five-year figure averages the old regime with the new one and understates the current level of inflation; the two-year figure is responsive but rests on three observations.

A defensible selection is around 8.5\%, supported by: (i) the recent fits clustering at 8.5–8.8\%, (ii) whether external evidence — medical cost indices, jury verdict data, the insurer's own settled-claim severities — corroborates an acceleration, and (iii) a judgment as to whether the acceleration is a level shift or a lasting change.

ASOP 13 asks for the trend estimate to be evaluated for reasonableness and documented so that another actuary could assess it: selecting 6.8\% because it produces a smaller rate increase, without addressing the acceleration visible in the data, would not survive that review.