Your loss experience comes from policies priced at last year's rates, but you want to project next year's premium. Before those old premiums can predict anything, you must restate them as if today's rates had always been in force.
Historical earned premium reflects whatever rates were charged then. If you raised rates 10% last July, a policy written in June carries less premium than the identical policy today. Comparing that stale premium to projected losses understates the true rate need. On-leveling removes the distortion by asking a single question: what would this premium have been at today's rates?
The answer is a multiplier. The on-level factor scales historical premium up (or down) to the current rate level.
KEY: On-leveling changes the price level, not the exposure level. It answers "what if today's rates had always applied," holding the historical mix of business fixed.
Every rate change compounds. Chain them into a running index. Suppose rates rose 10% then 6%.
Index after the first change is 1.000 × 1.10 = 1.100. After the second, 1.100 × 1.06 = 1.166. The current rate level is the latest index value, here 1.166.
Common mistakes
- Adding rate changes instead of chaining them. Treating +10% then +6% as 1.16 rather than 1.166 understates the current rate level and the on-level factor.
- On-leveling before developing premium. Applying the on-level factor to unaudited PY premium of $3,000,000 instead of the developed $3,150,000 leaves the premium base short.
- Confusing the two triangle formulas. A change during the year earns 0.5(1 − x)² at the new rate; a change before the year leaves 0.5(1 + t)² at the old rate. Swapping them mislabels the 0.125 and 0.28125 portions.
Bottom line
- On-leveling restates historical premium as if the current rate level had always applied; the multiplier is the on-level factor, also called the current rate level factor.
- Two methods exist: extension of exposures (re-rate every record at current rates, exact, class-accurate) and the parallelogram method (approximates the average rate level from geometric areas, uses aggregate data).
- Parallelogram on-level factor equals the current cumulative rate index divided by the average rate index for the period; build the index by chaining changes, so the index is the product of (1 plus each rate change).
- Changes at policy issuance are diagonal lines; a law-mandated change to in-force policies is a vertical line that splits each region into pre-change and post-change sub-areas.
Exam shortcut
If the question gives policy-level exposures and current rates, reach for extension of exposures and skip the geometry; if it gives only calendar-year aggregate premium, the parallelogram is intended. For any parallelogram, the new-rate corner triangle is always 0.5(1 − x)² and the old-rate corner from a prior-year change is 0.5(1 + t)². Weight indices by these areas, then divide current by the weighted average.
The full lesson (about 3,381 words, 23 min read) adds 6 worked examples, all 8 common mistakes, a self-check, free in the app.
Learning objectives
- A7
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