Tracking New-Business and Renewal Cohorts

Why Cohort Definitions Matter

A rate change is implemented at a point in time, but the resulting policies do not all enter the portfolio in the same way. A new customer may receive the new rates immediately, while an existing customer may encounter them only at renewal. Meanwhile, policies have different effective dates, coverage periods, cancellation dates, and transaction histories. If these records are pooled without a clear cohort definition, a monitoring result can combine unlike groups and suggest a change that the data do not establish.

Cohort monitoring organizes policies by a shared event, such as the effective date of a new policy or the effective date of a renewal. It then follows each group over a defined period after that event. This allows the analyst to compare new business with renewals at similar ages, while separately examining earned premium, exposure, and losses. Cohort results should be interpreted alongside segment composition: a group with more high-cost risks can have higher aggregate losses even if results within each segment are unchanged.

Definition: An effective-date cohort is a group of policies assigned according to the date coverage begins for the policy term being studied. A new-business cohort contains newly written policies; a renewal cohort contains policies beginning a subsequent term. A transaction cohort groups records by a specified transaction event or processing date instead. The cohort rule, observation window, and valuation date must be stated so that the population and measured experience are unambiguous.

Set the Cohort Rule Before Calculating

A useful cohort definition answers three separate questions. First, what event assigns a policy to the group: the policy-term effective date, a renewal effective date, or a transaction date? Second, which business is included: new business, renewals, or both? Third, what is the observation age: experience through the first three months after inception, the first six months, or another stated interval?

For monitoring the effect of a rate release, the policy-term effective date is usually the natural anchor because the applicable rating rules are determined for that term. The transaction processing date is still useful for operational questions, such as whether a system applied a change when expected, but it can misclassify experience if processing occurs before or after coverage begins. A midterm endorsement changes a policy transaction record; by itself, it does not create a new policy-term cohort.

For each cohort, keep the measures distinct. Earned exposure records the covered time or units during the observation window. Earned premium is the premium attributable to coverage provided in that window. Losses should be measured on a consistent basis, such as paid losses or incurred losses, and at a stated valuation date. A loss ratio is losses divided by earned premium; loss cost per exposure is losses divided by earned exposure. Neither measure should substitute for the other without considering the question being asked.

\text{Loss ratio}=\frac{\text{losses}}{\text{earned premium}}, \qquad \text{loss cost per exposure}=\frac{\text{losses}}{\text{earned exposure}}, \qquad \text{premium per exposure}=\frac{\text{earned premium}}{\text{earned exposure}}.

These are cohort summaries, not automatically like-for-like comparisons. For instance, a new-business cohort may contain a different mix of territories or coverage levels from a renewal cohort. The earlier material on separating rate effects from portfolio mix changes establishes why composition needs to be examined; cohort tracking supplies the time and transaction structure for doing so.

Worked Example: Comparing New Business and Renewals at a Common Observation Age

A hypothetical insurer monitors two groups through the same six-month observation window. The new-business cohort has 120 earned exposures, $144,000 of earned premium, and $90,000 of incurred losses. The renewal cohort has 300 earned exposures, $330,000 of earned premium, and $231,000 of incurred losses. Calculate premium per exposure, loss cost per exposure, and loss ratio for each group. The incurred amounts are both valued at the same stated date.

Method. Calculate the three ratios separately for each cohort, using earned exposure for per-exposure measures and earned premium for the loss ratio. The common observation age makes the time windows comparable; it does not by itself remove composition differences.

New business. Premium per exposure is $144{,}000/120=\$1{,}200$. Loss cost per exposure is $90{,}000/120=\$750$. The loss ratio is $90{,}000/144{,}000=0.625$, or $62.5\%$.

Renewals. Premium per exposure is $330{,}000/300=\$1{,}100$. Loss cost per exposure is $231{,}000/300=\$770$. The loss ratio is $231{,}000/330{,}000=0.70$, or $70.0\%$.

Check and interpretation. For new business, $\$750/\$1{,}200=62.5\%$; for renewals, $\$770/\$1{,}100=70.0\%$. The calculations reconcile. In this hypothetical data, new business has higher premium per exposure but lower loss cost per exposure, and consequently a lower loss ratio. These aggregate results do not establish that the launch caused the difference; mix, selection, and other differences between the cohorts still need consideration.

Common mistake avoided: dividing losses by written premium or comparing groups with different follow-up periods. The stated loss ratio uses earned premium, and the two cohorts have the same six-month observation window.

Why Aggregate Cohort Results Can Mislead

The aggregate premium and loss measures for a cohort are exposure-weighted summaries of the policies in that cohort. If two cohorts contain different proportions of risk segments, their overall measures can differ even when the measures within every segment are identical. A direct cohort comparison should therefore include segment counts or exposures, segment-level measures, and, where useful, a comparison using a common segment mix.

The standardization calculation has a simple justification. Suppose segment $j$ has loss cost $c_j$, and a cohort has exposure share $w_j$ in that segment, with the shares summing to one. Its aggregate loss cost is the sum of segment loss costs weighted by that cohort's shares. If the segment loss costs are the same between cohorts but the shares differ, the aggregate sums can differ solely because the weights differ. Replacing the cohort-specific shares with common weights isolates this composition effect in the comparison.

\text{Aggregate loss cost for cohort }g =\sum_j w_{gj}c_{gj}, \qquad \sum_j w_{gj}=1.

Worked Example: Distinguishing a Cohort Difference From a Mix Difference

A hypothetical insurer compares new-business and renewal cohorts across two rating segments. New business has 80 exposures in Segment A and 20 in Segment B; its losses are $48,000 in A and $18,000 in B, with earned premiums of $88,000 and $26,000, respectively. Renewals have 20 exposures in A and 80 in B; their losses are $12,000 in A and $72,000 in B, with earned premiums of $22,000 and $104,000, respectively. Compare the aggregate loss costs and then standardize both cohorts to a 50%/50% exposure mix.

Method. First calculate the loss cost within each segment, then calculate each cohort’s actual aggregate. Finally apply the same 50%/50% weights to the segment loss costs. This distinguishes observed mix from within-segment differences.

Segment results. For new business, Segment A loss cost is $48{,}000/80=\$600$ per exposure and Segment B is $18{,}000/20=\$900$. For renewals, Segment A is $12{,}000/20=\$600$ and Segment B is $72{,}000/80=\$900$. The within-segment loss costs match.

Actual new-business aggregate. Total exposures are $80+20=100$. Total losses are $\$48{,}000+\$18{,}000=\$66{,}000$, so aggregate loss cost is $\$66{,}000/100=\$660$. Total earned premium is $\$88{,}000+\$26{,}000=\$114{,}000$, so the loss ratio is $\$66{,}000/\$114{,}000=57.9\%$, rounded to one decimal place.

Actual renewal aggregate. Total exposures are $20+80=100$, and losses are $\$12{,}000+\$72{,}000=\$84{,}000$. Aggregate loss cost is $\$84{,}000/100=\$840$. Earned premium is $\$22{,}000+\$104{,}000=\$126{,}000$, so the loss ratio is $\$84{,}000/\$126{,}000=66.7\%$, rounded to one decimal place.

Common-mix comparison. With 50% weight on each segment, the standardized loss cost for either cohort is $0.50(\$600)+0.50(\$900)=\$750$ per exposure. To check, the actual new-business shares are 80% A and 20% B, giving $0.80(\$600)+0.20(\$900)=\$660$. Renewal shares are 20% A and 80% B, giving $0.20(\$600)+0.80(\$900)=\$840$. Both actual results and the standardized result reconcile.

Interpretation and common mistake avoided: the aggregate loss-cost gap of $\$840-\$660=\$180$ per exposure is consistent with the different segment weights, not a difference in the supplied within-segment loss costs. It would be incorrect to attribute the aggregate gap to the rate launch without examining composition. The standardized calculation is a diagnostic comparison, not a replacement for reporting each cohort’s actual experience.

Track Cohorts Through Coverage and Transactions

A cohort should be followed using the coverage time and premium actually attributable to the observation window. A policy that cancels partway through a term contributes only its covered exposure and earned premium through cancellation. Similarly, an endorsement may alter premium or coverage during a term; it belongs in the policy’s term experience rather than being counted as another newly written policy. Transaction records are needed to reconstruct the policy’s coverage and premium, but the cohort assignment must remain consistent with the chosen rule.

A useful monitoring table separates the cohort identifier from the observation age. For example, one row may represent the first six months after effective date and another the first twelve months after effective date for the same cohort. Each row should show earned exposure, earned premium, loss amount and basis, and the valuation date. Cumulative figures must be clearly distinguished from interval figures: a twelve-month cumulative loss ratio uses all losses and earned premium through twelve months, while a second-half interval ratio uses only second-half amounts.

The following example demonstrates the distinction. All premiums are hypothetical, losses are incurred amounts measured on the same stated basis, and the calculation uses the amounts available at the stated valuation date. It does not project losses beyond that date.

Worked Example: Following New-Business and Renewal Cohorts Through Cancellations

A hypothetical insurer follows two cohorts from their respective term effective dates. The new-business cohort starts with 40 policies, each with annual premium of $1,200. All 40 remain in force for the first six months; 10 cancel at month six, and the other 30 remain for the next six months. First-half losses are $12,000 and second-half losses are $15,000. The renewal cohort starts with 50 policies, each with annual premium of $1,000. All remain for six months; 5 cancel at month six, and the other 45 remain for the next six months. Its first-half losses are $10,000 and second-half losses are $16,000. Calculate exposures, earned premiums, and cumulative loss ratios at six and twelve months for both cohorts. Assume premium is earned uniformly while coverage is in force.

Method. For each half-year, multiply the number of policies in force by $0.5$ year to obtain earned exposure. Under the stated uniform earning assumption, half-year earned premium equals the annual premium per policy multiplied by the number in force and by $0.5$. At each observation age, sum the applicable interval amounts before calculating the cumulative loss ratio.

New business through six months. Exposure is $40(0.5)=20$ policy-years. Earned premium is $40(\$1{,}200)(0.5)=\$24{,}000$. The six-month loss ratio is $\$12{,}000/\$24{,}000=50.0\%$.

New business through twelve months. Second-half exposure is $30(0.5)=15$ policy-years, so cumulative exposure is $20+15=35$. Second-half earned premium is $30(\$1{,}200)(0.5)=\$18{,}000$, and cumulative earned premium is $\$24{,}000+\$18{,}000=\$42{,}000$. Cumulative losses are $\$12{,}000+\$15{,}000=\$27{,}000$. The twelve-month cumulative loss ratio is $\$27{,}000/\$42{,}000=64.3\%$, rounded to one decimal place.

Renewals through six months. Exposure is $50(0.5)=25$ policy-years. Earned premium is $50(\$1{,}000)(0.5)=\$25{,}000$. The six-month loss ratio is $\$10{,}000/\$25{,}000=40.0\%$.

Renewals through twelve months. Second-half exposure is $45(0.5)=22.5$ policy-years, making cumulative exposure $25+22.5=47.5$. Second-half earned premium is $45(\$1{,}000)(0.5)=\$22{,}500$, and cumulative earned premium is $\$25{,}000+\$22{,}500=\$47{,}500$. Cumulative losses are $\$10{,}000+\$16{,}000=\$26{,}000$. The twelve-month cumulative loss ratio is $\$26{,}000/\$47{,}500=54.7\%$, rounded to one decimal place.

Check and common mistake avoided. At twelve months, exposure is less than the starting policy count times one year in both cohorts because cancellations reduce second-half coverage. Earned premium likewise falls by the premium attributable to canceled policies after month six. Using all starting policies for a full year would incorrectly produce 40 new-business exposures and $48,000 of premium, or 50 renewal exposures and $50,000 of premium. The corrected twelve-month cumulative loss ratios are 64.3% and 54.7%, respectively. Both cohorts have equal observation ages, but differences in mix, cancellation patterns, and loss emergence still matter to interpretation.

Operational Checks and Common Traps

Cohort summaries are most useful when their construction can be audited. Before interpreting a difference, verify that policy-term effective dates assign groups as intended, new business and renewal indicators are consistent, and transaction records have been consolidated without duplicating policy exposure. Confirm that cancellations and endorsements affect exposure and earned premium only over the relevant covered periods. Then confirm that both groups use the same observation ages and the same loss basis and valuation date.

A common error is to divide losses from a six-month cohort window by annual written premium. That denominator does not represent the premium earned for the observed coverage and can distort the comparison. Another is to treat the transaction processing month as the effective-date cohort month, even when the transaction is processed later. A third is to compare new-business and renewal aggregates without examining segment shares. The cure is to state the cohort rule, calculate exposure and earned premium for the exact window, and inspect segment-level results before assigning an explanation.

Assign the cohort.
Specify whether assignment uses policy-term effective date or transaction date, and separate new business from renewals when that distinction is relevant.

Set observation age and valuation.
Choose comparable intervals from the cohort event and record the loss basis and valuation date.

Reconstruct coverage and premium.
Account for cancellations and midterm changes so earned exposure and earned premium reflect the coverage actually provided.

Compare, then diagnose.
Calculate cohort measures, check segment composition, and avoid treating an aggregate difference as a launch effect without supporting evidence.

Key takeaway: A defensible new-business versus renewal comparison states the cohort event, transaction class, observation age, valuation basis, exposure, and earned premium. Equal-age cohort results improve comparability; segment analysis is still needed to distinguish changes within segments from changes in portfolio composition.

Check Your Understanding

For each problem, identify the cohort measure requested and use the stated observation window and denominator.

A hypothetical new-business cohort has 75 earned exposures, $90,000 earned premium, and $63,000 losses through six months. A renewal cohort has 125 earned exposures, $137,500 earned premium, and $96,250 losses through the same age. Find both loss costs per exposure and loss ratios. (Answer: New business: $840 per exposure and 70.0%; renewals: $770 per exposure and 70.0%.)
A cohort has 30 policies at $800 annual premium each. All are covered for the first quarter; 6 cancel at the end of that quarter and the remaining 24 stay in force for the next quarter. Assuming uniform earning, find exposure and earned premium through six months. (Answer: 13.5 policy-years and $10,800.)
In Segment A, new business has 40 exposures and $20,000 losses; renewals have 60 exposures and $30,000 losses. In Segment B, new business has 60 exposures and $54,000 losses; renewals have 40 exposures and $36,000 losses. Find each aggregate loss cost, then each loss cost standardized to a 50%/50% mix. (Answer: Actual new business $740 and renewals $660 per exposure; standardized both $700 per exposure.)
A new-business cohort has $18,000 losses and $30,000 earned premium through six months. It has a further $24,000 losses and $30,000 earned premium in months 7–12. Calculate the six-month cumulative and twelve-month cumulative loss ratios, and the months 7–12 interval loss ratio. (Answer: 60.0%, 70.0%, and 80.0%, respectively.)
Policies are assigned to a cohort by effective date. A policy effective March 1 has a midterm endorsement processed May 10, and a new policy effective May 1 is processed May 3. State which event determines each policy’s effective-date cohort and identify the appropriate role of the May 10 transaction. (Answer: The first policy belongs to the cohort determined by its March 1 term effective date, and the second to the cohort determined by its May 1 effective date; the May 10 endorsement is a transaction within the first policy’s term, not a new-business cohort assignment.)

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