From Extracts to Ratemaking Targets
A policy extract describes coverage and exposure; a claim extract describes claim events and their recorded financial amounts. Neither extract, by itself, is necessarily a ready-to-use ratemaking target. The records must be aligned to a defined experience period, coverage basis, valuation date, and loss level. A defensible construction also makes explicit which claim events count and which loss amounts are included.
The goal is a set of compatible measures for a defined portfolio or rating segment: earned exposure, eligible claim count, and selected adjusted losses. From those totals, frequency is claims per exposure, severity is loss per claim, and pure premium is loss per exposure. These are portfolio measures; if targets are required for individual policies, retain the policy-level exposure and count information rather than relying only on portfolio averages.
A claim event is counted once under a stated claim-count convention, even if it has multiple payment or reserve transactions. The selected loss basis must match that convention. For example, a count of eligible claim events paired with incurred losses is not the same construction as a count of payments paired with payment amounts. Define the experience period and loss valuation date before joining or aggregating records.
Construct the Data in a Controlled Sequence
Specify the experience period, segment, exposure unit, claim-count convention, valuation date, loss basis, and target period to which adjusted losses will be brought.
Intersect each policy’s covered dates with the experience period. Apply the stated earning convention, exclude uncovered time, and aggregate exposure at the intended target level.
Use claim identifiers to count events once. Apply the stated rules for coverage, occurrence date, segment, and experience period; do not treat transaction rows as separate claims.
Use the specified paid, incurred, or ultimate basis. Apply any required development to the selected valuation level, then trend from the historical loss level to the target level.
Sum exposures from policy records and claim counts and adjusted losses from eligible claim events. Calculate the targets and verify both the arithmetic and the units.
Earned exposure is not automatically the number of policies, nor is it necessarily the number of days in the experience period. It measures the portion of covered risk included under the chosen exposure convention. For a daily pro-rata convention on a 365-day basis, for example, an otherwise eligible policy covering 92 days contributes \(92/365\) policy-years. A monthly convention may instead assign \(1/12\) policy-year per earned month. Use the convention required for the portfolio and state it; do not mix conventions within a target.
Eligibility rules should be applied to claim events, not to individual transaction rows. A claim may have multiple payments, reserve changes, or administrative records. Conversely, a claim extract can contain a reported event that falls outside the experience period or outside the policy’s covered dates. Define the event-date rule and coverage test, then count only claim events satisfying both.
Worked Example: Earning Exposure and Counting Events
A hypothetical portfolio is evaluated for calendar year 2025. Exposure uses daily pro-rata earning on a 365-day basis, with both policy effective and expiration dates treated as covered. Policy A is in force for all of 2025. Policy B is in force from April 1, 2025, through March 31, 2026. Policy C is in force from July 1 through December 31, 2025. The claim extract has two transaction rows for Policy A claim A1, one row for Policy A claim A2, one row for Policy B claim B1, one row for Policy B claim B2 dated March 15, 2026, and one row for Policy C claim C1 dated June 30, 2025. Count claims with occurrence dates in calendar 2025 that fall within the policy coverage.
Exposure. Policy A contributes \(365/365=1.0000\) policy-year. Policy B contributes the covered part of its term within 2025: April through December has \(30+31+30+31+31+30+31+30+31=275\) days, so its exposure is \(275/365\). Policy C contributes July through December, or \(31+31+30+31+30+31=184\) days, so its exposure is \(184/365\).
The total is \((365+275+184)/365=824/365=2.2575\) policy-years, rounded to four decimals. The calculation includes only the portions of the terms that overlap calendar 2025.
Eligible claim count. Claim A1 is one event even though it has two transaction rows. Claim A2 is a second event. Claim B1 is a third event and is within Policy B’s coverage and the experience period. Claim B2 is outside the experience period, and C1 is dated before Policy C’s coverage begins. Therefore \(N=3\).
The resulting frequency is \(3/(824/365)=1.3289\) claims per policy-year, rounded to four decimals. The method avoids counting payment transactions as claims and avoids counting events outside the defined period or coverage. The exposure and frequency are consistent with the stated daily convention.
Selecting, Developing, and Trending Losses
A selected loss basis is the financial measure to be used before any adjustments required for the target. It might be paid, incurred, or ultimate loss, depending on the stated purpose and data maturity. The basis must be applied consistently across eligible claim events. For instance, do not combine paid amounts for some claims with incurred amounts for others unless the construction explicitly defines and supports that treatment.
When historical claims are not yet at the selected ultimate level, a development factor may be applied. In a simple claim-level construction, an amount at an earlier valuation is multiplied by the selected factor from its current development age to the desired loss level. A trend factor then brings that loss level from its historical period to a stated target period. For an annual trend rate \(r\) over \(t\) years, the factor is \((1+r)^t\). The rate and time unit must agree: an annual rate applied over two years uses a two-year exponent.
The order and interpretation matter because development and trend address different changes. Development adjusts for the amount expected to emerge as claims mature; trend adjusts the loss level between time periods. If the selected factors are multiplicative, their product gives the same numerical result in either order, but that does not make the adjustments interchangeable: each factor still needs the correct input basis, period, and purpose.
Worked Example: Adjusting Historical Incurred Losses
A hypothetical segment has two eligible claims. The selected historical incurred amounts are $8,000 at 12 months of development and $12,000 at 24 months. The selected development factors to ultimate are 1.15 and 1.05, respectively. The annual trend rate is 5%, applied from the historical loss level to the target level: two years for the first claim and one year for the second. Calculate total adjusted loss and average adjusted severity.
Claim 1. Develop the incurred amount to ultimate: \($8{,}000\times1.15=$9{,}200\). The two-year trend factor is \(1.05^2=1.1025\). The adjusted loss is \($9{,}200\times1.1025=$10{,}143.00\).
Claim 2. Develop to ultimate: \($12{,}000\times1.05=$12{,}600\). The one-year trend factor is \(1.05^1=1.05\). The adjusted loss is \($12{,}600\times1.05=$13{,}230.00\).
Total adjusted loss is \($10{,}143+$13{,}230=$23{,}373.00\). There are two eligible claims, so average adjusted severity is \($23{,}373/2=$11{,}686.50\) per claim. The calculation uses each claim’s stated development and trend periods; it does not apply a single period to both merely because the claims are in the same segment.
Deriving the Relationship Among the Targets
Frequency, severity, and pure premium are not three unrelated calculations. For a segment with \(E>0\) and \(N>0\), the definitions imply:
The claim count cancels, so frequency times severity equals pure premium when all three use the same population of eligible claims, exposure base, and adjusted loss total. This identity is useful as a construction check, but it does not guarantee the inputs are correct: duplicated claims or mismatched loss bases can still produce internally consistent arithmetic.
If \(N=0\), severity \(L/N\) is undefined. Do not report it as zero; report no claim-level severity for that segment. If \(E>0\) and there are no eligible losses, frequency and pure premium can be zero under the stated convention. A segment with no exposure has no defined per-exposure frequency or pure premium.
Worked Example: Building and Checking a Complete Target
A hypothetical rating segment has three policies in calendar year 2025. The company’s stated monthly convention assigns \(1/12\) policy-year per earned month. Policy A earns six months, Policy B earns twelve months, and Policy C earns nine months. The three eligible claim events have historical incurred amounts of $10,000, $5,000, and $8,000. Their selected development factors are 1.10, 1.20, and 1.00. The selected annual trend rate is 5%; the trend periods to the target level are two years for the first claim and one year for each of the other claims. Calculate the adjusted target totals and the three measures.
Exposure. Policy A contributes \(6/12=0.50\) policy-year, Policy B contributes \(12/12=1.00\), and Policy C contributes \(9/12=0.75\). Thus \(E=0.50+1.00+0.75=2.25\) policy-years. The three eligible events give \(N=3\).
Adjusted claim losses. For the first claim, \($10{,}000\times1.10=$11{,}000\) at ultimate, and the two-year trend factor is \(1.05^2=1.1025\). Its adjusted loss is \($11{,}000\times1.1025=$12{,}127.50\).
For the second claim, \($5{,}000\times1.20=$6{,}000\) at ultimate. Its one-year trend factor is 1.05, giving \($6{,}000\times1.05=$6{,}300.00\). For the third claim, \($8{,}000\times1.00=$8{,}000\) at ultimate; trending one year gives \($8{,}000\times1.05=$8{,}400.00\).
The adjusted loss total is \(L=$12{,}127.50+$6{,}300.00+$8{,}400.00=$26{,}827.50\). Frequency is \(N/E=3/2.25=1.3333\) claims per policy-year, rounded to four decimals. Severity is \(L/N=$26{,}827.50/3=$8{,}942.50\) per claim. Pure premium is \(L/E=$26{,}827.50/2.25=$11{,}923.33\) per policy-year, rounded to cents.
Check. Frequency times severity is \(1.333333\ldots\times$8{,}942.50=$11{,}923.33\) per policy-year, matching pure premium after rounding. The method preserves the monthly exposure convention and adjusts each claim using its own stated factors.
Common Traps and Practical Checks
A common mistake is to calculate from a joined table in which each policy is repeated once per claim transaction. That can multiply policy exposure when the joined records are summed. Another is to count every claim transaction as a claim event. Calculate and validate exposure at policy-term level, and count unique eligible claim events under the chosen convention before combining the totals.
A second trap is to adjust a loss amount at the wrong starting level. If the input is already ultimate, multiplying by a development factor again overstates the loss. If trend is annual, using an annual rate as though it applied only once when the target is two years away understates the result. Record, for every adjusted claim, its starting basis, development age, selected development factor, trend interval, and adjusted amount.
- Reconcile policy counts and earned exposure before and after any data join.
- Confirm claim eligibility from the event date and covered policy period.
- Check that one claim identifier represents one event under the selected count convention.
- Verify that the selected loss basis and adjustment factors are consistent across the target population.
- Check that frequency times severity agrees with pure premium when both are defined.
These controls make the resulting target interpretable as well as numerically correct. A clear target record should preserve the period, segment, exposure convention, count rule, loss basis, valuation date, adjustment factors, and final totals. This supports review and makes it possible to trace a surprising result back to the policy or claim records that produced it. The construction is aligned with the CAS Exam 8 (Advanced Ratemaking) syllabus.
Check Your Understanding
For each problem, use only the stated conventions and keep the exposure, count, and loss bases aligned.
- A hypothetical portfolio uses monthly exposure earning. Two policies earn three and nine months, respectively. The claim extract has three eligible claim identifiers, one of which appears on two transaction rows, and one additional event outside the experience period. What are total earned exposure and eligible claim count? (Answer: 1.0000 policy-year and 3 claims.)
- Two eligible incurred claims are $4,000 and $6,000. Their development factors to ultimate are 1.10 and 1.00. The annual trend rate is 4%; the trend intervals are one and two years. What is total adjusted loss and average adjusted severity? (Answer: $11,065.60 total and $5,532.80 per claim.)
- A segment has earned exposure of 0.75 and 1.25 policy-years on two policy records. There are three eligible claims and adjusted losses total $24,000. Calculate frequency, severity, and pure premium. (Answer: 1.5000 claims per policy-year, $8,000.00 per claim, and $12,000.00 per policy-year.)
- A claim has a historical incurred amount of $7,500, a development factor to ultimate of 1.20, and a 3% annual trend rate for two years. A segment has 1.5 earned policy-years and this is its only eligible claim. Find the adjusted loss, severity, frequency, and pure premium. (Answer: $9,549.90 adjusted loss; $9,549.90 per claim; 0.6667 claims per policy-year; $6,366.60 per policy-year.)
- A segment has 2.4 earned policy-years and four eligible events. Two claims have adjusted losses of $5,200 and $8,000; the other two have adjusted losses of $0 and $2,800 under the stated loss basis. Calculate total loss and the three targets, and state the reconciliation. (Answer: $16,000 total loss; 1.6667 claims per policy-year; $4,000.00 per claim; $6,666.67 per policy-year; frequency times severity equals pure premium, subject to rounding.)