Why Measure Premium When Cash Arrives?
An insurer may record premium when coverage is written, recognize it as coverage is provided, and receive the associated cash on a different date. A cash collection measure answers a specific question: how much premium cash came in during the period being measured? It is useful for understanding cash activity, but it is not a substitute for written or earned premium when a measure of contractual premium or coverage provided is needed.
For a collection measure, the key date is the date the insurer receives the payment, not the policy effective date, invoice date, or date to which the payment relates. A receipt can relate to a policy written earlier, and an amount written during a period may remain unpaid at its end.
The definition is about premium cash, not every cash movement associated with a policy. A receipt should be identifiable as a premium payment under the measure’s data rules. Similarly, a refund should be identified as a return of premium. Other amounts should not be added to or subtracted from the premium measure merely because they appear in the same cash ledger.
Receipt Date Determines the Period
Suppose a policyholder pays an installment in March for a policy that began the previous October. That payment is included in March’s collected premium under a calendar-month measure, even though the policy was not written in March. Conversely, a March invoice that is paid in April does not generate a March cash receipt.
A convenient way to express the calculation is to list premium cash transactions and assign each one a signed amount \(p_j\) and a receipt or refund date \(t_j\). A receipt has a positive amount; a premium refund is negative when calculating net collections. For a period from \(a\) through \(b\), including both boundary dates, net collected premium is:
Here, \(\mathbf{1}\{a\leq t_j\leq b\}\) equals 1 when transaction \(j\) falls within the period and 0 otherwise. For gross collected premium, sum positive premium receipts in the period without subtracting refunds. This is a transaction-date calculation: amounts are selected by when cash was received or returned, not by when the premium was written or earned.
Decide whether the requested result is gross collections or net collections, and specify the included premium transactions.
Use the stated receipt or refund dates. Check whether the period includes its start and end dates.
Add receipts for gross collections. For net collections, subtract qualifying premium refunds paid in the period.
Worked Examples
Worked Example: Installments Received During a Coverage Period
A hypothetical annual property policy is written for a premium of $1,200 on January 1. The policyholder pays four installments of $300 on January 1, March 1, May 1, and July 1. Find the gross collected premium from January 1 through June 30 and compare it with the premium written and earned by June 30. Assume coverage earns uniformly by month, there are no refunds, and all installments are received on their scheduled dates. No interest discounting, mortality assumption, or probability distribution is involved.
Method. Select the installment cash receipts by receipt date. The January 1, March 1, and May 1 receipts fall within the period. The July 1 receipt falls outside it.
The period’s gross collections are:
The full premium written at inception is $1,200. Under the stated uniform monthly earning assumption, six of the policy’s twelve coverage months have elapsed by June 30. The premium earned is therefore:
Thus, the three measures are $900 collected, $1,200 written, and $600 earned. The collection amount is larger than the earned amount because cash receipts do not have to arrive at the same pace as coverage is provided.
Check. The fourth $300 installment is dated July 1, so it is not part of the January-through-June total. The $900 total contains exactly three $300 receipts.
Worked Example: Receipts on a Previously Written Policy
A hypothetical policy runs from October 1 through September 30 and has a written premium of $2,400. An insurer’s transaction record shows a $600 receipt on October 1, a $300 receipt on January 15, a $450 receipt on April 1, a $150 receipt on June 20, and a $600 receipt on July 1. Find gross collected premium from January 1 through June 30. Also find the amount of the January and April installments still unpaid after the June 20 receipt. Assume all listed cash is premium, payments are allocated to the installment dates shown, and there are no refunds. No interest discounting, mortality assumption, or probability distribution is involved.
Method. Apply the date cutoff first. The October 1 receipt is before the measurement period, and the July 1 receipt is after it. The three receipts within January 1 through June 30 total:
The January installment is $600. After the January 15 receipt of $300, its unpaid amount is:
The April installment is also $600. The April 1 and June 20 receipts allocated to it total $450 + $150 = $600, so its unpaid amount is:
The answer is $900 of gross collected premium during the period, with $300 unpaid on the January installment and none unpaid on the April installment. The $2,400 written premium was recorded when the policy was written; it is not the amount of cash received during this six-month period.
Check. The in-period receipts sum to $900, and the January and April installment balances reconcile to $300 and $0, respectively. The July receipt is correctly excluded even though it is associated with the same policy.
Worked Example: Gross Collections Versus Net Collections
In a hypothetical calendar month, an insurer receives $500 against premium on a policy written in an earlier month and $400 against premium on a policy written this month. It also pays a $70 premium refund during the month. The current-month policy has $800 of written premium. Find gross collected premium and net collected premium for the month. Assume each receipt and the refund is correctly classified as a premium transaction. No interest discounting, mortality assumption, or probability distribution is involved.
Method. Gross collections include the two positive premium receipts:
Net collections subtract the refund paid during the same period:
The results are $900 gross collected premium and $830 net collected premium. The $800 of premium written this month does not replace either calculation: $500 of the month’s receipts relates to an earlier-written policy, while the refund is a cash return in the current month.
Check. Net collections are $70 less than gross collections, exactly the refund amount. A common mistake is to count only the $400 received on the policy written this month, and then call that the month’s total collections. That gives $400, but it omits the $500 receipt on the earlier-written policy. The correct gross total is $900; the net total is $830 after the refund.
How Collections Differ From Written and Earned Premium
Written premium measures premium recorded for coverage when it is written or when a premium-changing transaction is recorded, according to the applicable data convention. Earned premium measures the portion associated with coverage already provided. Collected premium measures cash received during a period. These measures can refer to the same policies while recording different events.
| Measure | What determines inclusion? | Question it answers |
|---|---|---|
| Written premium | The date premium is recorded as written | How much premium was written or recorded in the period? |
| Earned premium | The coverage provided during the period | How much premium corresponds to coverage already provided? |
| Collected premium | The date premium cash is received | How much premium cash came in during the period? |
The distinction follows from the event each measure records. A written premium can exist before the policyholder pays it, so it is possible to have written premium without a matching cash receipt in that period. Cash can also arrive after the policy was written, so collections can include premium associated with an earlier period. And cash timing need not match the passage of coverage, so collections in a period need not equal premium earned in that period.
This is not an assertion that the three measures must always differ. They can happen to be equal in a particular set of data. Equality does not make their definitions interchangeable; it means only that the underlying amounts and timing happen to produce the same total for that case.
Common Measurement Traps
- Using the invoice date as the receipt date. An invoice documents an amount due; it does not establish that cash was received. Include the payment when the cash receipt occurs under the stated data convention.
- Using the policy effective date to assign cash. A policy can be effective in one period while its installment is collected in another. For a cash measure, classify the receipt by its receipt date.
- Counting only premium written in the current period. Collections can relate to policies written earlier. Do not discard an in-period receipt just because the policy was written before the period.
- Ignoring the gross-versus-net convention. Gross collections and net collections differ when refunds occur. State whether refunds are subtracted and use that definition consistently.
- Including transactions outside the cutoff. A receipt on the first day after period-end is not an in-period receipt. Apply the stated dates consistently, including boundary rules.
Check Your Understanding
For each problem, apply the stated collection convention and pay close attention to transaction dates.
- A hypothetical insurer receives premium payments of $180 on February 2, $220 on March 31, and $140 on April 1. What is gross collected premium for the first quarter, January 1 through March 31, inclusive? (Answer: $400)
- A hypothetical one-year policy is written for $1,600 on January 1. The policyholder pays $400 on January 1 and $400 on April 1. Assuming no refunds, what is gross collected premium from January 1 through March 31, and what is earned premium over those three months if it earns uniformly by month? (Answer: $400 collected; $400 earned)
- During a hypothetical month, an insurer receives $320 and $280 in premium payments and pays $45 in premium refunds. What are gross and net collected premium for the month? (Answer: $600 gross; $555 net)
- A hypothetical policy has $1,000 of written premium recorded in August. The insurer receives $250 in September, $300 in October, and $450 in November. How much is collected in October, and how much has been collected in total by the end of November? (Answer: $300 in October; $1,000 cumulatively by the end of November)
- A hypothetical insurer measures net collections for June. It receives premium payments of $510 on June 30 and $290 on July 1, and pays a $60 premium refund on June 15. What is June net collected premium? Explain the cutoff. (Answer: $450; include the June 30 receipt and June refund, but exclude the July 1 receipt)