Premium Trend

Study guides: Exam 5, Exam GI-101

Premium Trend is the change over time in the average premium per exposure at a constant rate level — the drift caused by distributional shifts in the policies written (amounts of insurance, limits, deductibles, mix of business), as distinct from deliberate rate changes, which on-levelling handles, and from inflation in an inflation-sensitive exposure base, which Werner & Modlin treat as exposure trend.

\text{Average Premium at Current Rate Level} = \frac{\text{On-Level Premium}}{\text{Earned Exposures}}

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

• The trend is measured on the average premium per exposure at current rate level, usually from written data — a leading indicator, reflecting distributional shifts sooner than earned premium — often quarterly. An exponential or linear fit may guide the selection, though Werner & Modlin note curve-fitting is usually unnecessary because the changes are normally consistent from period to period.
• The trend period n runs from the average written date of the policies earning premium in the experience period to the average written date of the policies in effect while the new rates are — for calendar-year 2011 earned premium and annual policies written in 2013, 1/1/2011 to 6/30/2013, or 2.5 years. Measuring between average earned dates gives the same 2.5 years, because both dates shift by the same amount; with six-month policies the trend-from date moves to 4/1/2011 and the period is 2.25 years.
• One-step trending applies a single selected annual trend across the whole period. It is adequate when the drift has been steady.
• Two-step trending is used when the recent history contains a shift the historical fit would understate or overstate. Step one brings historical average earned premium up to the current average written premium level (a known, observed figure); step two projects forward from there at a selected prospective trend:

\text{Step 1} = \frac{\text{Latest avg written premium at CRL}}{\text{Historical avg earned premium at CRL}}

\text{Step 2} = (1 + t_P)^{n_2}

• Premium trend matters where the book is drifting — homeowners amounts of insurance indexed to inflation, a move of insureds to higher deductibles, the acquisition of a book of higher-valued homes (Werner & Modlin's three examples). The actuary decides whether an observed shift was a one-time event or will continue, and where the mix is stable the trend is near zero.
• Premium trend is not needed for a Pure Premium Method indication: only the loss ratio approach requires the actuary to estimate the premium to be collected in the future period.

One-Step Premium Trend A homeowners book has on-level earned premium of \$5{,}000{,}000 for accident year 2024. Average premium at current rate level has been rising 3.0\% a year with rising amounts of insurance. The trend period from the average written date of AY 2024 to the average written date of the forecast period is 2.0 years.

Compute trended on-level premium.

Answer

\begin{align*}
\text{Trend factor} &= 1.03^{2.0} \\
&= 1.0609 \\[4pt]
\text{Trended premium} &= \$5{,}000{,}000 \times 1.0609 \\
&= \$5{,}304{,}500
\end{align*}

The projected loss ratio is then computed against \$5{,}304{,}500 rather than \$5{,}000{,}000. Omitting the adjustment would overstate the loss ratio by 6\% relative and indicate a rate increase the insurer does not need — because average premium is already rising on its own as insured values grow.

Two-Step Trending After a Mix Shift An auto insurer introduced a higher-deductible option in mid-2024, and take-up moved quickly. Average premium at current rate level:

Period	Avg. earned premium (CRL)	Avg. written premium (CRL)
AY 2023	\$820	\$835
AY 2024	\$835	\$810
Latest quarter	—	\$798

The historical fitted trend is +1.8\%; the actuary selects +1.0\% prospectively. AY 2024 is the experience year, and the forecast period's average written date is 1.75 years after the latest quarter's.

Trend AY 2024 average earned premium.

Answer The historical fit is misleading — average earned premium rose while average written premium fell, because the earned figures still contain pre-shift policies. One-step trending at +1.8\% would project the average premium upward when the book is actually moving down.

Step 1 — restate AY 2024 average earned premium to the current written level:

\frac{\$798}{\$835} = 0.9557

Step 2 — project forward at the selected trend:

1.010^{1.75} = 1.0176

\begin{align*}
\text{Combined} &= 0.9557 \times 1.0176 \\
&= 0.9725
\end{align*}

AY 2024 premium is trended down by 2.75\%. The deductible shift genuinely reduces the premium the insurer will collect per exposure going forward — and, importantly, it reduces expected losses too, so the corresponding adjustment must also be made on the loss side (Deductible Rating) rather than left to show up as a spurious rate need.