Severity Data Construction Workshop

Why Severity Data Construction Requires Care

A claim file often records payments and recoveries as separate transactions. A single claim may therefore appear on several rows, and its transactions may occur in different accounting periods. A severity response, however, must match the chosen observation unit and loss definition. If the target is net paid loss per claim, the transactions are first combined within each claim; they are not treated as separate severity observations.

This tutorial focuses on building claim-level and grouped severity responses from hypothetical claim records. The key decisions are which transactions belong to the loss measure, which claims belong in the denominator, and which period determines the claim’s group. These decisions must be made consistently before calculating an average.

Definition: For a specified loss basis and valuation date, a claim-level severity response is the loss amount assigned to one claim after all eligible transactions for that claim are combined. A grouped severity is the total of the claim-level responses in a defined group divided by the number of claims included in that group. The group and the denominator must be stated explicitly.

For example, the loss basis might be paid indemnity net of recoveries through a specified valuation date. A transaction that is outside that basis, such as an excluded expense component, should not be added merely because it appears in the same claim system. The loss definition determines which signed transaction amounts enter the calculation.

From Transaction Rows to Claim Responses

Suppose claim $j$ has $m_j$ eligible transactions, with signed amounts $T_{j1},\ldots,T_{jm_j}$. A payment is positive and a recovery or reversal is negative. The net claim response is

Y_j=\sum_{k=1}^{m_j}T_{jk}.

A claim with no eligible transactions in the selected loss basis has a response of zero if it remains in the defined claim population. A net response of zero can also result when payments and recoveries offset. Those situations may look the same in the final response column, but they are different data histories and should remain distinguishable in the audit trail.

The average severity over a specified set of $n$ claims is the sum of their claim responses divided by $n$. If the definition instead includes only claims with positive net responses, the denominator is the number of such claims. The two averages answer different questions; neither denominator should be chosen implicitly.

Worked Example: Combining Eight Transactions Into Three Claim Responses

A hypothetical portfolio extract contains the following eligible paid-loss transactions. Calculate each claim’s net response, the average over all listed claims, the average over claims with positive net responses, and the transaction-row average.

Claim	Signed transactions	Number of rows
A	$1,800, $650, −$300	3
B	$900, −$900	2
C	$1,200, $400, −$100	3

Method. First sum transactions within each claim. The recovery amounts are negative, so they reduce that claim’s net response.

Claim A has response $1{,}800+650-300=\$2{,}150$. Claim B has response $900-900=\$0$. Claim C has response $1{,}200+400-100=\$1{,}500$.

There are three claim responses, and their total is $2{,}150+0+1{,}500=\$3{,}650$. The average over all three listed claims is $3{,}650/3=\$1{,}216.67$, rounded to the nearest cent. There are two claims with positive net responses, so the positive-response average is $3{,}650/2=\$1{,}825.00$.

There are eight transaction rows: $3+2+3=8$. The transaction-row average is $3{,}650/8=\$456.25$. This is an average per transaction row, not a claim severity.

Check. The claim responses sum to $\$3{,}650$, matching the eight signed transaction amounts, whose sum is also $\$3{,}650$. The common mistake is to use the number of transaction rows as the claim denominator. That would produce $\$456.25$, answering a different question from average loss per claim.

Zero-Payment and Net-Zero Claims

A severity calculation must say what counts as a claim in its denominator. Consider a response defined as net paid loss per reported claim as of a stated valuation date. If a reported claim has no eligible payment by that date, its response is zero and it belongs in the average if the target population includes all reported claims. A different target may be defined over claims with positive net paid loss; then that zero-response claim is not in the denominator.

A recovery can also reduce a previously positive payment to zero. Whether to include that claim in the denominator depends on the same stated population rule, not on whether the final number happens to be zero. Do not silently remove zero responses or replace them with small positive amounts. Preserve the response as defined and record the inclusion rule so that the resulting mean can be interpreted.

Worked Example: Keeping the Denominator Consistent

A hypothetical coverage group has three reported claims as of the valuation date. Claim R1 has a payment of $760 and a recovery of $160. Claim R2 has no eligible paid-loss transaction. Claim R3 has a payment of $500 and a recovery of $500. Calculate severity under two stated definitions: net paid loss per reported claim, and average net paid loss among claims with a positive net response.

Method. Aggregate transactions within each claim before applying either denominator rule. R1 is $760-160=\$600$. R2 has response $\$0$. R3 is $500-500=\$0$.

For net paid loss per reported claim, all three reported claims are included. Total response is $600+0+0=\$600$, so the average is $600/3=\$200.00$.

For the positive-net-response definition, only R1 qualifies. The average is $600/1=\$600.00$. The numerator is unchanged, but the population and denominator differ.

Check. The responses total $600 under both definitions. The first mean is $200.00 and the second is $600.00; the difference is entirely due to the denominator. The common mistake is to exclude the two zero responses while describing the result as an average over all reported claims.

Grouped Severity and the Claim Count

A grouped severity summary combines claim responses within a defined cell, such as a coverage and occurrence-period combination. If group $g$ contains $n_g$ eligible claims with responses $Y_j$, its total response is the sum of those claim amounts, and its mean response is the total divided by $n_g$. A group average is not itself an additional claim.

\bar{Y}_g=\frac{\sum_{j\in g}Y_j}{n_g},\qquad n_g>0.

The condition $n_g>0$ matters: a group with no claims has no claim-level severity mean. It should not be represented as a zero-claim average of zero, because that would confuse the absence of observations with observed zero responses.

When combining groups, the overall mean is weighted by their claim counts. To see why, let group $g$ have mean $\bar{Y}_g$ and count $n_g$. By the definition of a group mean, the group total is $n_g\bar{Y}_g$. Summing those totals and dividing by the combined claim count gives

\bar{Y} =\frac{\sum_g n_g\bar{Y}_g}{\sum_g n_g}.

Thus, a simple average of group means is generally wrong unless the groups have equal claim counts or the particular values happen to make the two calculations equal. Claim counts provide the weights because each claim contributes one response to the overall claim-level mean.

Worked Example: Combining Grouped Means Correctly

A hypothetical insurer summarizes claim-level losses for two rating cells. Cell A has two claims with responses of $200 and $600. Cell B has three claims with responses of $100, $300, and $500. Calculate each cell mean and the mean across all five claims. Then compare it with an unweighted average of the two cell means.

Method. Calculate the claim total and count in each cell first. For Cell A, the total is $200+600=\$800$, the count is 2, and the mean is $800/2=\$400.00$. For Cell B, the total is $100+300+500=\$900$, the count is 3, and the mean is $900/3=\$300.00$.

Across both cells, the total is $800+900=\$1{,}700$, and the claim count is $2+3=5$. Therefore the combined mean is $1{,}700/5=\$340.00$.

The unweighted average of the cell means is $(400+300)/2=\$350.00$, which is not the mean across claims. The correct weighted calculation is $(2\times400+3\times300)/(2+3)=1{,}700/5=\$340.00$.

Check. The weighted calculation reproduces the total claim response divided by the total claim count. The common mistake is to give a small cell the same influence as a larger cell by averaging cell means without their claim counts.

Claims That Span Periods

A claim can have payments, adjustments, and recoveries recorded in more than one calendar or accounting period. For an occurrence-period severity view, assign the claim once to the period defined by its occurrence date, then sum all eligible transactions through the valuation date into that claim’s response. The transaction date tells when the amount was recorded; it does not, by itself, determine the claim’s occurrence-period group.

A transaction-period summary can also be useful for a different purpose, but it is not the same as occurrence-period claim severity. If a claim is split across transaction periods, those period amounts should not be treated as separate claims when the intended observation unit is one claim. State the period basis and apply it consistently.

Worked Example: Assigning Claims Paid Across Occurrence Periods

At a valuation date of December 31, 2026, a hypothetical book has three claims. Claim X occurred in 2024 and has payments of $1,000 in 2024 and $500 in 2025, followed by a $100 recovery in 2026. Claim Y occurred in 2024 and has a $600 payment in 2025 followed by a $600 recovery in 2026. Claim Z occurred in 2025 and has payments of $900 in 2025 and $300 in 2026. Calculate claim responses and average severity by occurrence year.

Method. Sum eligible transactions to the valuation date for each claim, then assign each resulting claim response to its occurrence year. Claim X is $1{,}000+500-100=\$1{,}400$. Claim Y is $600-600=\$0$. Claim Z is $900+300=\$1{,}200$.

The 2024 occurrence group contains X and Y. Its total response is $1{,}400+0=\$1{,}400$, its claim count is 2, and its mean is $1{,}400/2=\$700.00$. The 2025 occurrence group contains Z alone, so its total is $1,200, its count is 1, and its mean is $1,200.00.

Across all three claims, the total is $1{,}400+0+1{,}200=\$2{,}600$, and the mean is $2{,}600/3=\$866.67$, rounded to the nearest cent. Claim X remains one 2024 claim even though payments occurred in two calendar years and the recovery occurred in a third.

Check. The occurrence-group totals, $1,400 and $1,200, sum to the overall $2,600. Their counts, 2 and 1, sum to the overall count of 3. The common mistake is to assign Claim X’s later transactions to later occurrence groups or to count each payment as a separate claim.

A Practical Construction Sequence

A reliable data build separates transaction processing from response aggregation. This makes it possible to reconcile the claim totals and to explain why each claim is included in a group. The sequence below is useful whether the final output is an individual claim file or a grouped summary.

Specify the response.
State the loss basis, valuation date, claim population, and period or classification used to form groups.

Filter eligible transactions.
Retain only transaction types and coverage amounts included in the specified loss measure. Preserve payments as positive amounts and recoveries or reversals with their correct signs.

Aggregate within claim.
Sum the eligible transactions for each claim to produce one response. Retain a zero response when the stated population rule includes that claim.

Assign the claim to its group.
Use the stated grouping basis, such as occurrence period, once per claim. Do not let a transaction date create an extra claim observation.

Summarize and reconcile.
Calculate each group’s total response, claim count, and mean. Check that group totals and counts reconcile to the claim-level records under the same inclusion rules.

Common Construction Traps

Using transaction rows as observations. Multiple transactions for one claim do not automatically mean multiple severity observations. Aggregate to the chosen claim unit first.
Dropping recoveries or reversals. If the loss basis is net of eligible recoveries, subtract them. If a different basis is intended, state it and apply it consistently.
Changing the denominator without changing the description. A mean over all defined claims and a mean over only positive-response claims are different statistics. Name the population and count used.
Grouping by the wrong date. For occurrence-period severity, attach the claim response to its occurrence period. Payment dates remain relevant transaction attributes but do not split the claim into several observations.
Averaging group means without weights. Use claim counts when combining claim-level group means. An unweighted mean answers a different question when group counts differ.

Key takeaway: Define the loss basis, claim population, valuation date, and grouping period before calculating severity. Aggregate eligible signed transactions within each claim, apply the stated denominator rule, and use claim counts when combining grouped means. These construction choices keep the response aligned with its intended observation unit.

Check Your Understanding

For each problem, use the stated claim population and period basis. Amounts are hypothetical and stated in dollars.

A claim has eligible transactions of $950, −$150, and $200. What is its net claim response, and how many severity observations does it represent? (Answer: $1,000; one claim-level observation.)
Three reported claims have net responses of $300, $0, and $900. Calculate the mean over all reported claims and the mean over claims with positive net responses. (Answer: $400.00 over all three; $600.00 over the two positive-response claims.)
Two claims occurred in 2024. The first has a $700 payment in 2024 and a $500 payment in 2025, followed by a $200 recovery in 2026. The second has a net response of $0. At a valuation date after all transactions, calculate 2024 occurrence-period average severity over both claims. (Answer: $500.00.)
Cell A has two claim responses, $200 and $600. Cell B has three, $100, $300, and $500. Calculate the combined mean across the five claims and explain why the simple average of the two cell means is not the answer. (Answer: $340.00; the cell means are $400 and $300, and they must be weighted by counts 2 and 3.)
Two claims occurred in 2025. Claim M has a $400 payment in 2025 and a $100 recovery in 2026. Claim N has $700 paid in 2026. Through the end of 2026, what are their claim responses and the 2025 occurrence-period mean? (Answer: M is $300, N is $700, and the mean is $500.00 across two claims.)

What You'll Learn