Ratemaking Fundamentals

Ratemaking answers one question: is current premium adequate for expected future losses and expenses, and if not, by how much should rates change? This article covers the fundamental equation, the two classical indication methods, and the on-leveling and trending mechanics that make historical data usable.

The fundamental insurance equation

$\text{Premium} = \text{Losses} + \text{LAE} + \text{Underwriting Expenses} + \text{Underwriting Profit}.$

Rearranged, the permissible loss ratio is $PLR = 1 - V - Q$, where $V$ is the variable expense ratio (commission, premium tax — expenses that scale with premium) and $Q$ is the target underwriting profit provision, after loading fixed expenses separately. Ratemaking is the exercise of comparing projected losses to this permissible level.

Loss ratio method

$\text{Indicated rate change} = \frac{\text{Trended \& developed loss ratio}}{\text{Permissible loss ratio}} - 1.$

This method needs no separate exposure count — only premium and losses — and is standard when a rate level (not a full rate rebuild) is being adjusted.

Pure premium method

$\text{Indicated rate} = \frac{\text{Trended \& developed pure premium} + \text{Fixed expense per exposure}}{1 - V - Q}, \qquad PP = \frac{\text{Losses}}{\text{Exposures}}.$

This method is used when exposures are stable and reliable (e.g., car-years) and is preferred for ground-up rate calculations rather than percentage rate changes.

On-leveling: the parallelogram method

Historical premium was collected at past rate levels; it must be adjusted to the current rate level before use. The parallelogram method plots cumulative rate level changes on a calendar timeline against the accident/policy year being on-leveled, computing the average rate level as the area-weighted (time-weighted) average of the rate levels in effect during the period, then

$OLF = \frac{\text{current rate level}}{\text{average historical rate level}}.$

For annual policies, a rate change effective April 1 that increases rates by 8% affects three-quarters of the following accident year (if the change persists) — this fractional-year overlap is exactly what the "parallelogram" geometry computes.

Trending

Losses (and sometimes premium, if measured via average premium per exposure) must be trended from the historical experience period to the future policy period during which the new rates will apply, because frequency and severity drift over time (inflation, judicial trends, inflationary medical costs). Trend is typically fit as an exponential: $\hat y_t = a\,e^{bt}$, fit by regressing $\ln(y_t)$ on $t$; the annual trend is $e^b - 1$. The trend period runs from the average date of loss in the experience period to the average date of loss under the new rates (experience period midpoint to the future policy period midpoint) — commonly 2–4 years for annual policies with an effective date well in the future.

Development

Losses in recent accident years are immature — not all claims have been reported or fully valued — so they must be developed to an ultimate basis using loss development factors (see Loss Development Triangles) before being used in an indication; skipping this step is one of the most common ratemaking errors for long-tailed lines like WC and GL.

Worked example

A WC book had accident-year 2022 earned premium of $10,000,000 at an average historical rate level 4% below current rates ($OLF = 1.0417$), incurred losses (undeveloped) of $6,200,000 developed to ultimate with a CDF of 1.15, and a selected annual severity/frequency trend of 3.5% applied over a 2.5-year trend period. Variable expenses are 25% of premium and the target profit provision is 5% ($PLR = 0.70$).

On-leveled premium = $10,000,000 × 1.0417 = $10,417,000.

Developed losses = $6,200,000 × 1.15 = $7,130,000.

Trended losses = $7,130,000 × $1.035^{2.5}$ = $7,130,000 × 1.0904 = $7,774,552.

Trended, developed loss ratio = $7,774,552 / $10,417,000 = 74.63%.

Indicated rate change = 74.63% / 70.00% − 1 = +6.6%.

Pitfalls

• Applying trend to already-developed losses without checking the trend period dates align to the midpoint of the future policy period, not its start.
• Using calendar-year incurred losses (which mix accident years) instead of accident-year triangles for the indication.
• Forgetting that fixed expenses do not scale with premium — loading them as a percentage overstates the indication when a rate increase is large.
• Applying a single trend rate to a line with diverging frequency and severity trends (e.g., declining frequency, rising severity) rather than trending each component separately.

Exam relevance

The fundamental ratemaking equation and both indication methods are the core of CAS Exam 5, and reappear in real filings tested implicitly on CAS Exams 8 and 9.