Why Integrate Loss and Expense Data?
A ratemaking experience table brings several records together: policy-period premium and exposure, claim payments and case reserves, recoveries, loss adjustment expenses, and underwriting expenses. The table is useful only when each amount is assigned to the intended period and classified consistently. A claim payment is not the same measure as incurred loss, and underwriting expense is not part of loss adjustment expense.
The earlier material on accident-year, policy-year, and calendar-year loss measures distinguishes the period basis used for experience. Here, the central task is to combine the relevant records into one table after a period basis has been selected. The examples use hypothetical data and state the selected basis. They do not apply on-leveling, trending, or loss development.
Build the Table in a Consistent Order
Start by deciding which period records the table will summarize. Then aggregate claim and expense records into that period, using the appropriate policy, coverage, and period assignments. For a period total, a typical calculation is:
This expression assumes the case reserves are unpaid indemnity amounts at the valuation date, the recoveries shown are applicable to the same loss measure, and there are no other relevant adjustments. If expected but not yet received recoveries are separately reserved, those amounts must also be treated consistently. Do not subtract a recovery twice merely because it appears in both a claim record and a summary.
For ALAE, use paid ALAE plus its unpaid case reserves. Add ULAE separately to obtain total loss adjustment expense. Then add incurred loss and loss adjustment expense to obtain total losses and LAE. Underwriting expenses remain a separate amount. Earned premium and earned exposure provide the denominators for common experience measures; they must refer to the same selected period basis as the experience being summarized.
Specify the experience period, policy or coverage scope, valuation date, and whether monetary amounts are dollars or thousands of dollars.
For claims in scope, total paid indemnity, case reserves, and applicable recoveries. Calculate net incurred loss without treating payments and reserves as duplicate amounts.
Combine paid ALAE with ALAE case reserves. Add ULAE assigned to the period, and keep underwriting expenses in a different column.
Use earned premium and earned exposure for the same period basis and scope. Calculate ratios only after checking the totals and units.
Worked Period Table
The following example builds a period summary from claim-level and period-level records. It illustrates why the components should be shown separately before calculating a combined measure.
Worked Example: Combining Claims, LAE, Premium, and Exposure
A hypothetical insurer is preparing an accident-year 2025 summary for one coverage. The period has 120 earned exposures and $60,000 of earned premium. Claim A has $12,000 of indemnity paid, a $3,000 case reserve, a $1,000 recovery received, $2,000 of ALAE paid, and a $500 ALAE case reserve. Claim B has $8,000 of indemnity paid, no case reserve or recovery, and $1,000 of ALAE paid with no ALAE reserve. ULAE assigned to the period is $1,200, and assigned underwriting expenses are $4,800. Build the summary and calculate the main ratios. No interest, mortality, or probability distribution is assumed; all amounts are hypothetical accounting values.
1. Calculate incurred loss by claim. For Claim A, net incurred loss is $12,000 + $3,000 − $1,000 = $14,000. For Claim B, it is $8,000 + $0 − $0 = $8,000. Total net incurred loss is $14,000 + $8,000 = $22,000.
2. Calculate ALAE. Claim A has $2,000 + $500 = $2,500 of incurred ALAE. Claim B has $1,000 + $0 = $1,000. Total incurred ALAE is $3,500. Adding $1,200 of ULAE gives total LAE of $3,500 + $1,200 = $4,700.
3. Combine the period amounts. Total losses and LAE are $22,000 + $4,700 = $26,700. Underwriting expenses remain separate at $4,800.
| Accident year 2025 measure | Amount |
|---|---|
| Earned exposures | 120 |
| Earned premium | $60,000 |
| Net incurred loss | $22,000 |
| Incurred ALAE | $3,500 |
| Assigned ULAE | $1,200 |
| Total LAE | $4,700 |
| Total losses and LAE | $26,700 |
| Underwriting expenses | $4,800 |
4. Calculate ratios and check. The net incurred loss ratio is $22,000 / $60,000 = 36.67%. The LAE ratio is $4,700 / $60,000 = 7.83%. The losses-and-LAE ratio is $26,700 / $60,000 = 44.50%. The underwriting expense ratio is $4,800 / $60,000 = 8.00%. Including both losses and LAE and underwriting expenses gives $31,500 / $60,000 = 52.50%. As an exposure-based check, $26,700 / 120 = $222.50 of losses and LAE per earned exposure. The ratios are rounded to two decimal places.
The totals reconcile: $22,000 of loss plus $4,700 of LAE equals $26,700 of losses and LAE; adding $4,800 of underwriting expenses gives $31,500. No underwriting expense has been included in LAE.
Why the Incurred-Loss Formula Works
The paid amount records the part of the loss already settled by the valuation date. The case reserve estimates the remaining unpaid part of the covered loss. Together, paid loss and case reserve represent the gross loss amount recognized to date under this accounting view. A recovery reduces the insurer’s net cost of that loss, so it is subtracted once.
For example, if a claim has $5,000 paid, a $2,000 case reserve, and a $500 recovery, its net incurred loss is $5,000 + $2,000 − $500 = $6,500. The formula does not mean that the recovery is necessarily received in cash at the same time as the claim payment. It means the recovery is included as a reduction in the selected measure, provided its scope and period treatment are consistent.
Worked Example: Summarizing Policy-Period Records
Policy-period records often provide earned premium and earned exposure, while claim and expense records must be matched to the applicable policy and coverage. The following example treats the supplied claim totals as already matched to the corresponding policy-period records.
Worked Example: Comparing Two Policy-Period Records
A hypothetical portfolio contains two policy-period records for the same coverage. Policy-period A has 0.5 earned exposures, $900 earned premium, $450 indemnity paid, a $150 case reserve, $80 ALAE paid, and a $40 ALAE reserve. Policy-period B has 1.0 earned exposure, $1,800 earned premium, $700 indemnity paid, a $200 case reserve, $100 ALAE paid, and a $50 ALAE reserve. There are no recoveries. The period has $90 assigned ULAE and $360 of underwriting expenses. Calculate the portfolio totals, ratios, and loss-and-LAE amount per earned exposure. No interest, mortality, or probability distribution is assumed; all amounts are hypothetical accounting values.
1. Calculate net incurred loss. Policy-period A has $450 + $150 − $0 = $600. Policy-period B has $700 + $200 − $0 = $900. Total net incurred loss is $600 + $900 = $1,500.
2. Calculate total LAE. Incurred ALAE is $80 + $40 = $120 for A and $100 + $50 = $150 for B. Total ALAE is $120 + $150 = $270. Adding $90 of ULAE gives total LAE of $360.
3. Sum the denominators and calculate total losses and LAE. Earned premium is $900 + $1,800 = $2,700; earned exposure is 0.5 + 1.0 = 1.5. Total losses and LAE are $1,500 + $360 = $1,860. Underwriting expenses are $360, kept separate.
4. Calculate the measures. The net incurred loss ratio is $1,500 / $2,700 = 55.56%. The LAE ratio is $360 / $2,700 = 13.33%, and the losses-and-LAE ratio is $1,860 / $2,700 = 68.89%. The underwriting expense ratio is $360 / $2,700 = 13.33%; including all three components gives ($1,860 + $360) / $2,700 = 82.22%. Losses and LAE per earned exposure are $1,860 / 1.5 = $1,240. Ratios are rounded to two decimal places; the per-exposure result is in dollars.
The portfolio result is a premium-weighted aggregate: its ratio uses total amounts divided by total earned premium, not the unweighted average of the two policy-period ratios. The totals also check: $1,500 loss + $360 LAE = $1,860 losses and LAE.
Worked Example: A Full Expense Reconciliation
A second reconciliation makes the distinction among paid loss, reserves, recoveries, LAE, and underwriting expenses especially visible. Amounts below are stated in thousands of dollars.
Worked Example: Reconciling a Small Claims Portfolio
A hypothetical accident-year portfolio has $15,000 of earned premium and 25 earned exposures. Claim C has $4.0 thousand of indemnity paid, a $2.0 thousand case reserve, a $0.5 thousand recovery, $0.4 thousand of ALAE paid, and a $0.1 thousand ALAE reserve. Claim D has $3.0 thousand of indemnity paid, a $1.0 thousand case reserve, a $0.5 thousand recovery, $0.3 thousand of ALAE paid, and a $0.2 thousand ALAE reserve. Assigned ULAE is $0.6 thousand and assigned underwriting expenses are $1.2 thousand. Calculate the period totals, ratios, and losses and LAE per exposure. No interest, mortality, or probability distribution is assumed; all amounts are hypothetical accounting values.
1. Total indemnity paid and reserves. Paid indemnity is $4.0 + $3.0 = $7.0 thousand. Case reserves are $2.0 + $1.0 = $3.0 thousand. Recoveries total $0.5 + $0.5 = $1.0 thousand.
2. Calculate net incurred loss. Net incurred loss is $7.0 + $3.0 − $1.0 = $9.0 thousand.
3. Calculate LAE and total losses and LAE. ALAE paid is $0.4 + $0.3 = $0.7 thousand, and ALAE reserves are $0.1 + $0.2 = $0.3 thousand. Incurred ALAE is $0.7 + $0.3 = $1.0 thousand. Total LAE is $1.0 + $0.6 ULAE = $1.6 thousand. Total losses and LAE are $9.0 + $1.6 = $10.6 thousand.
4. Calculate ratios and exposure measure. The net incurred loss ratio is $9.0 / $15.0 = 60.00%. The LAE ratio is $1.6 / $15.0 = 10.67%. The losses-and-LAE ratio is $10.6 / $15.0 = 70.67%. The underwriting expense ratio is $1.2 / $15.0 = 8.00%. Including all three components gives ($10.6 + $1.2) / $15.0 = 78.67%. Losses and LAE per exposure are $10,600 / 25 = $424. Ratios are rounded to two decimal places.
The reconciliation is $9.0 thousand net loss + $1.6 thousand LAE = $10.6 thousand of losses and LAE; adding $1.2 thousand underwriting expense gives $11.8 thousand of total experience cost. The units are consistent because the ratio calculations use $15.0 thousand of premium and the per-exposure calculation converts $10.6 thousand to $10,600.
Common Mistakes and Checks
A common mistake is to treat paid loss as the whole incurred loss. In the last example, using only the $7.0 thousand paid amount and subtracting recoveries gives a wrong loss of $6.0 thousand. The correction is to include the $3.0 thousand case reserves: $7.0 + $3.0 − $1.0 = $9.0 thousand. A case reserve represents estimated unpaid loss, not a second recording of paid loss.
Other checks help catch classification and aggregation errors before a table is used:
- Keep ALAE and ULAE distinct. ALAE is tied to specific claims; ULAE is assigned to the period at an aggregate level. Both contribute to LAE, but ULAE should not be added again if it is already included in a stated total.
- Keep underwriting expenses outside losses and LAE. They can be shown alongside those amounts for a broader expense measure, but they are not claim losses or LAE.
- Match period and scope. Claim, expense, premium, and exposure totals must refer to the intended period and coverage. A total can add correctly and still be inappropriate if its records belong to a different period or scope.
- Check units and denominators. Do not divide dollars by premium stated in thousands, or divide a total-period amount by an exposure count from a different scope. State units before calculating ratios or per-exposure amounts.
- Reconcile subtotals. Confirm that paid amounts plus reserves produce the intended gross incurred amount, applicable recoveries are subtracted once, and the LAE and underwriting expense subtotals sum to their displayed totals.
Check Your Understanding
For each hypothetical problem, calculate the requested measure and keep the stated units and expense categories separate.
- A claim has $6,200 of indemnity paid, a $1,800 case reserve, and a $500 recovery. Calculate net incurred loss. (Answer: $7,500)
- For one period, incurred ALAE is $2,400 and assigned ULAE is $600. Earned premium is $30,000. Calculate total LAE and the LAE ratio. (Answer: $3,000 and 10.00%)
- A portfolio has $18,000 of earned premium, $10,000 of net incurred loss, $1,500 of ALAE, and $500 of ULAE. Underwriting expenses are $2,000. Calculate total losses and LAE, the losses-and-LAE ratio, and the ratio including underwriting expenses. (Answer: $12,000; 66.67%; 77.78%)
- Two policy-period records have earned exposures of 0.4 and 0.6, and net incurred losses of $280 and $520. Calculate total loss per earned exposure. (Answer: $800 per earned exposure)
- In a hypothetical period, indemnity paid is $9.0 thousand, case reserves are $4.0 thousand, and recoveries are $1.0 thousand. Incurred ALAE is $1.5 thousand, ULAE is $0.5 thousand, earned premium is $20.0 thousand, and underwriting expenses are $2.0 thousand. Calculate net incurred loss, total LAE, and the ratio including losses, LAE, and underwriting expenses. (Answer: $12.0 thousand; $2.0 thousand; 80.00%)