Why Three Loss Amounts Matter
A claim can involve a larger loss than the policy covers, and the amount eligible for coverage can in turn be larger than the insurer’s payment. Keeping these amounts separate makes it easier to read policy terms, calculate a settlement, and explain what remains with the insured. This distinction is aligned with the SOA Exam FAM (Fundamentals of Actuarial Mathematics) syllabus.
Consider a hypothetical property claim. The damage might total $10,000, but $1,500 could relate to an excluded item. Of the remaining amount, a deductible or policy limit could further reduce the insurer’s payment. Calling all three amounts “the loss” hides the sequence and can lead to an incorrect answer.
These terms describe different stages of a claim, not necessarily three different physical events. In the usual indemnity setting, assume the same claim is being considered throughout; covered and excluded amounts have been identified using the contract; and there are no additional payments, such as defense costs, interest, or claim expenses, outside the stated loss amount. Under those assumptions, the covered loss cannot exceed the ground-up loss, and the insurer’s payment cannot exceed the covered loss.
Separate the Loss Before Calculating the Payment
Start with the full loss as measured for the problem. Then identify which components are eligible under the contract. The difference between the ground-up loss and the covered loss is the amount that is not eligible for coverage in that calculation. Reasons can include an exclusion, an uncovered property or activity, or a valuation rule that produces a lower covered amount than the total economic loss.
Only after identifying the covered loss should you apply payment provisions. A deductible leaves part of the covered loss with the insured. Coinsurance assigns a stated share of eligible costs to the insured. A limit caps the insurer’s payment. The policy wording determines which provisions apply and in what order; do not assume an order that the problem does not specify.
| Amount | Question it answers | Typical effect of policy terms |
|---|---|---|
| Ground-up loss | How much total loss is being considered? | Measured before coverage adjustments |
| Covered loss | How much of that loss is eligible? | Exclusions and valuation terms can reduce it |
| Insurer payment | How much does the insurer pay? | Deductibles, coinsurance, and limits can reduce it further |
| Amount retained by the insured | How much of the ground-up loss is not paid by the insurer? | May include both ineligible loss and covered loss left unpaid |
For a simple claim in which the ground-up amount is split into covered and ineligible parts, define \(X\) as the ground-up loss, \(C\) as the covered loss, \(I\) as the insurer payment, and \(U\) as the ineligible part. Then \(X=C+U\). If the covered loss is fully divided between insurer payment and the amount retained by the insured, write \(R_C=C-I\) for the covered amount not paid by the insurer. The total amount not paid by the insurer is therefore \(X-I=U+R_C\).
Worked Settlements
For each example, first separate eligible from ineligible loss. Then apply the stated payment terms to the eligible amount. Any calculation involving a limit assumes that the limit is a maximum insurer payment, as specified in the hypothetical contract.
Worked Example: An Exclusion, a Deductible, and a Payment Limit
A hypothetical storm causes $18,400 of total damage to a small workshop. The policy covers $15,900 of the damage; the remaining $2,500 is excluded. The policy has a $1,000 deductible and a $12,000 maximum payment for this claim. The deductible is applied to the covered loss, and the limit caps the payment after the deductible. Find the ground-up loss, covered loss, insurer payment, and total amount not paid by the insurer.
Method. Separate covered and excluded amounts first, then apply the deductible and the payment limit to the covered loss. This avoids treating excluded damage as though it were eligible.
Ground-up loss: \(X=\$18{,}400\), as stated.
Covered loss: \(C=\$15{,}900\). The excluded amount is \(U=\$2{,}500\), and the amounts reconcile: \(\$15{,}900+\$2{,}500=\$18{,}400\).
Amount after the deductible: \(\$15{,}900-\$1{,}000=\$14{,}900\).
Insurer payment: the payment before the limit would be $14,900, which exceeds the $12,000 maximum. Therefore, \(I=\$12{,}000\).
Amount not paid by the insurer: \(\$18{,}400-\$12{,}000=\$6{,}400\). This consists of $2,500 excluded loss and \(\$15{,}900-\$12{,}000=\$3{,}900\) of covered loss left unpaid.
Check: \(\$2{,}500+\$3{,}900=\$6{,}400\), matching the ground-up loss less the insurer payment.
Common mistake avoided: applying the limit to the ground-up loss without first identifying the covered amount. The limit caps the insurer’s payment; it does not make excluded damage eligible.
Worked Example: A Deductible Does Not Make Excluded Damage Covered
In a hypothetical equipment claim, total damage is $7,600. Of this amount, $6,200 is eligible under the policy and $1,400 is excluded. The contract has a $500 deductible and a maximum payment of $8,000 for this claim. The deductible applies to covered loss, and the limit applies to the insurer payment after the deductible. Calculate the three loss amounts and the amount retained by the insured.
Method. Determine the covered loss before calculating the insurer payment. This keeps the excluded component out of the payment calculation.
Ground-up loss: \(X=\$7{,}600\).
Covered loss: \(C=\$6{,}200\), with \(U=\$1{,}400\) excluded. Check that \(\$6{,}200+\$1{,}400=\$7{,}600\).
Covered amount after the deductible: \(\$6{,}200-\$500=\$5{,}700\).
Insurer payment: $5,700 is below the $8,000 maximum, so the limit does not reduce it. Thus, \(I=\$5{,}700\).
Amount retained: the total not paid is \(\$7{,}600-\$5{,}700=\$1{,}900\). It comprises $1,400 of excluded damage and the $500 deductible.
Check: the covered loss is \(\$5{,}700+\$500=\$6{,}200\), and adding the excluded amount gives the ground-up loss of $7,600.
Common mistake avoided: calculating the payment as \(\$7{,}600-\$500=\$7{,}100\). That calculation incorrectly treats the $1,400 excluded amount as covered. The correct payment is based on $6,200, not $7,600.
Worked Example: Coinsurance and a Binding Limit
A hypothetical commercial claim has a ground-up loss of $30,000. The policy’s valuation terms and exclusions leave $26,000 eligible for coverage. A $2,000 deductible applies first. The insurer then pays 80% of the remaining eligible amount, subject to a $15,000 maximum payment. Calculate the covered loss, payment, and total amount not paid by the insurer. For this contract, the 80% share is applied after the deductible, and the limit caps the resulting payment.
Method. Apply the specified sequence: identify covered loss, subtract the deductible, calculate the insurer’s 80% share, and then check the maximum payment. This prevents the limit or coinsurance percentage from being applied to the wrong amount.
Ground-up loss: \(X=\$30{,}000\).
Covered loss: \(C=\$26{,}000\). The ineligible amount is \(U=\$30{,}000-\$26{,}000=\$4{,}000\).
Amount after the deductible: \(\$26{,}000-\$2{,}000=\$24{,}000\).
Payment before the limit: \(0.80\times\$24{,}000=\$19{,}200\). The insured’s 20% share of this post-deductible amount is \(0.20\times\$24{,}000=\$4{,}800\).
Insurer payment: $19,200 exceeds the $15,000 maximum, so \(I=\$15{,}000\).
Amount not paid: \(X-I=\$30{,}000-\$15{,}000=\$15{,}000\). This consists of $4,000 ineligible loss and $11,000 of covered loss not paid. Within that $11,000, $2,000 is the deductible, $4,800 is the insured’s 20% share, and $4,200 is the reduction caused by the payment limit.
Check: \(\$4{,}000+\$2{,}000+\$4{,}800+\$4{,}200=\$15{,}000\). Adding this amount to the insurer’s $15,000 payment reconciles to the $30,000 ground-up loss.
Common mistake avoided: stopping at the 80% calculation and reporting $19,200 as the payment. The stated maximum payment is binding, so the insurer pays $15,000.
Why the Separation Is Useful
The separation is more than a bookkeeping preference. Ground-up loss describes the full amount being considered; covered loss describes the amount within the contract’s scope; payment describes the settlement after the contract’s sharing and caps. Keeping the stages distinct shows which policy term caused each reduction. It also helps check a result: if the insurer’s payment exceeds the covered loss under the assumptions in this tutorial, the calculation needs review.
This framework also helps avoid a misleading interpretation of the insured’s retained amount. If the insured retains $6,400, that does not mean the deductible was $6,400. The retained amount can combine exclusions, a deductible, coinsurance, and the effect of a limit. To explain it correctly, identify those components rather than assigning the whole difference to one term.
Common Mistakes
- Starting the payment calculation with the entire ground-up loss. An excluded component is not made eligible just because it is part of the total damage.
- Calling the covered loss the insurer payment. A deductible, coinsurance provision, or limit can leave some covered loss unpaid.
- Applying a limit to the wrong amount. Use the limit in the manner specified by the contract; a maximum payment is not automatically a cap on the ground-up loss or the covered loss.
- Reporting only the insurer payment. When asked to distinguish the three amounts, state each amount and show how the difference is accounted for.
Check Your Understanding
For each hypothetical claim, identify the requested amount or amounts. Assume each stated deductible applies to covered loss and each stated limit caps insurer payment after the other specified calculations.
- A claim has a $9,400 ground-up loss, of which $8,500 is covered. The deductible is $750, and the maximum payment is $9,000. Find the insurer payment and total amount not paid by the insurer. (Answer: insurer payment $7,750; total not paid $1,650.)
- A $12,500 loss includes $2,000 that is excluded. The policy has a $1,500 deductible, pays 90% of the covered loss remaining after the deductible, and has a $9,000 maximum payment. Find the covered loss and insurer payment. (Answer: covered loss $10,500; insurer payment $8,100.)
- A $41,000 ground-up loss includes $5,000 ineligible for coverage. The covered loss is subject to a $3,000 deductible, after which the insurer pays 75%, subject to a $22,000 maximum payment. Find the insurer payment and total amount not paid. (Answer: insurer payment $22,000; total not paid $19,000.)
- A claim has a $16,000 ground-up loss. After exclusions and the contract’s valuation basis, $13,500 is covered. The deductible is $1,000, and the insurer pays 80% of the covered loss after the deductible; the $10,000 payment limit applies afterward. Find the payment and identify each component of the amount not paid. (Answer: insurer payment $10,000; total not paid $6,000, comprising $2,500 ineligible loss, $1,000 deductible, $2,500 insured share, and no further reduction from the limit.)
- A covered loss is $24,000, and a separate $3,000 portion of the ground-up loss is excluded. The deductible is $2,000. After the deductible, the insurer pays 100% of the remaining covered amount, subject to a $20,000 maximum payment. Find the ground-up loss, insurer payment, and amount retained by the insured. (Answer: ground-up loss $27,000; insurer payment $20,000; amount retained $7,000, comprising $3,000 excluded loss, $2,000 deductible, and $2,000 due to the limit.)