Including Loss Adjustment Expenses

Why Loss Adjustment Expenses Belong in the Indication

A prospective rate indication must account for the costs the insurer expects to pay for covered claims. Those costs can include both indemnity payments and the expenses of investigating, evaluating, defending, and settling claims. If the loss measure includes only indemnity, but the rate indication is intended to fund indemnity and claim-adjustment costs, omitting loss adjustment expenses (LAE) understates the projected cost.

The calculation is not simply “add every expense number to losses.” The expense estimate must match the loss measure, exposure period, and premium basis used in the indication. In particular, the treatment of allocated loss adjustment expense (ALAE) and unallocated loss adjustment expense (ULAE) depends on how each is measured and on what the target loss ratio is defined to include.

For a rate indication, let \(L\) denote projected losses, \(A\) projected ALAE, and \(U\) projected ULAE. These are dollar amounts for the same coverage, experience period, and prospective basis unless otherwise stated. The combined projected loss-and-LAE cost is \(L+A+U\), but that sum is appropriate only when the amounts are measured on compatible bases. All numerical examples below use deterministic selected prospective amounts; no interest or mortality assumption is used.

Match Each Expense to Its Measurement Basis

ALAE is often collected by claim, so an actuary may project it claim by claim, by claim type, or as a ratio to a defined loss measure. ULAE is not attached to individual claims and may instead be estimated per exposure, per claim, as a percentage of losses, or as a percentage of premium. These are different measurement bases, not interchangeable labels.

Before combining amounts, confirm that loss and LAE estimates refer to the same coverage and prospective period. If losses are adjusted to a particular gross or net basis, the LAE treatment should be consistent with that basis. If LAE is estimated as a percentage, identify its denominator: a percentage of losses is not automatically a percentage of premium. Also confirm that the target loss ratio includes the LAE components placed in its numerator.

Pure-Premium Indications Including LAE

In a pure-premium indication, projected cost is divided by the corresponding exposure count. If projected losses, ALAE, and ULAE are all dollar amounts on the same basis, the indicated pure premium is their sum per exposure. If an expense estimate is already stated per exposure, multiply it by the exposure count before adding it to aggregate dollars—or add it directly to the other per-exposure amounts after converting all components to that basis.

where \(N\) is the number of matching exposures. To express an indicated change, compare this indicated pure premium with the current average rate or premium per exposure for the same exposure basis. The comparison is meaningful only when both rates apply to comparable exposures and coverage.

Loss-Ratio Indications Including LAE

A loss-ratio indication uses projected loss-and-LAE dollars and a target ratio defined on a premium basis. Let \(P\) be indicated premium and \(q\) the target loss-and-LAE ratio. If the target ratio includes the projected losses and all the LAE being added, and those dollar costs do not vary with indicated premium, then the target condition is that the costs equal \(qP\). Solving gives the indicated premium.

This formula does not apply as written if the target ratio excludes one or more LAE components, if an expense is already included in the loss amount, or if an expense varies as a percentage of indicated premium. Those cases require either a consistent reformulation of the numerator and target or an equation that accounts for the premium-dependent expense.

When ULAE Is a Percentage of Premium

A percentage-of-premium ULAE estimate depends on the premium being solved for. It therefore cannot be treated as a fixed dollar amount known before the indication. Suppose projected losses and ALAE together are \(C\), ULAE is a fraction \(r\) of indicated premium \(P\), and the target loss-and-LAE ratio \(q\) includes that ULAE. The target equation is \(C+rP=qP\). Rearranging yields the indicated premium, provided \(q>r\).

The condition \(q>r\) is necessary for a positive finite premium when \(C>0\). If \(q=r\), the equation would require \(C=0\); if \(q<r\), the rearranged denominator is negative. Either result signals that the stated assumptions do not produce a valid positive indication. The formula also does not apply if the stated ULAE percentage is defined on a different premium basis or is already included elsewhere.

A Practical Consistency Check

A brief reconciliation can expose most errors before an indication is finalized. The purpose is to make the bases explicit, not to replace judgment in selecting the prospective estimates. Use the same coverage, exposure period, and gross-or-net definition for the loss and LAE amounts being combined.

For example, an ALAE estimate stated as 12% of projected losses is calculated from that loss base; it is not 12% of premium. Likewise, ULAE stated as $20 per exposure must be multiplied by the matching exposure count before being added to aggregate loss dollars. A basis mismatch can create a plausible-looking number while answering a different question from the one intended.

Common Exam Traps

• Omitting LAE from the cost numerator. If the indication is intended to fund losses and LAE, include the projected LAE components unless the problem states that they are already included.
• Adding the same expense twice. Check the definitions of the loss and expense data. A combined amount must not include ALAE in both the loss figure and a separate ALAE estimate.
• Using an unspecified target ratio. A loss-ratio calculation needs the numerical target and a clear statement of what the target includes. Without both, the indicated premium is not uniquely determined.
• Confusing percent-of-loss with percent-of-premium. The former is calculated from a stated loss base; the latter generally requires solving an equation involving indicated premium.
• Comparing unlike premium bases. A rate change is valid only when the current and indicated premium correspond to the same portfolio or exposure basis.