Allocated Loss Adjustment Expense

Study guide: Exam 5

Allocated Loss Adjustment Expense (ALAE) is claim adjustment cost that can be attributed to a specific claim — defence counsel fees, expert witnesses, independent adjusters, court costs — as opposed to ULAE, the claims-department overhead that cannot.

$\text{Loss \& ALAE} = \text{Indemnity} + \text{ALAE}$

$\text{ALAE Ratio} = \frac{\text{ALAE}}{\text{Indemnity}}$

Because ALAE attaches to a claim, it is captured in case reserves and can be developed in a triangle exactly like indemnity. Friedland gives three approaches: develop a combined loss-and-ALAE triangle, develop ALAE separately in its own triangle, or develop a ratio of ALAE to loss and apply it to projected losses.
Combining is simplest and is the usual choice, but it assumes ALAE develops like indemnity. It often does not: defence costs accrue steadily through litigation while indemnity lands at settlement, so an ALAE-only triangle can have a different shape and a different tail.
The ALAE ratio varies enormously by line — roughly $30$ – $50\%$ of indemnity in professional liability, $15$ – $25\%$ in general liability, $10$ – $15\%$ in auto liability, and a few percent in property. A load taken from one line and applied to another is a substantial error.
ALAE can be countercyclical to indemnity: money spent defending a claim vigorously may reduce the indemnity paid. A "defence and settle" strategy shift moves both components, in opposite directions, and shows up in the triangles as a change in the ALAE ratio.
Whether ALAE sits inside "losses" matters for the reinsurance treaty too: treaties differ on whether ALAE is included within the limit, shared pro rata, or added on top — which changes both ceded and net figures.

ALAE on a Litigated Claim A general liability claim settles with an indemnity payment of $\$100{,}000$ . Along the way the insurer paid defence counsel $\$25{,}000$ , an expert witness $\$8{,}000$ , and court costs $\$2{,}000$ .

Compute total incurred and the ALAE ratio, and state how the claim appears in the triangles.
Answer
 $\begin{align*} \text{ALAE} &= \$25{,}000 + \$8{,}000 + \$2{,}000 = \$35{,}000 \\[4pt] \text{Loss \& ALAE} &= \$100{,}000 + \$35{,}000 = \$135{,}000 \\[4pt] \text{ALAE ratio} &= \frac{\$35{,}000}{\$100{,}000} = 35\% \end{align*}$ 
In a combined triangle the claim contributes $\$135{,}000$ . In separate triangles it contributes $\$100{,}000$ to the indemnity triangle and $\$35{,}000$ to the ALAE triangle — and the two will develop differently, since the defence fees were largely paid before the indemnity settlement.

A $35\%$ ratio is at the high end for GL and would be worth investigating: is it one unusually litigated claim, or has the book's mix shifted toward disputed claims?

Estimating Unpaid ALAE by the Ratio Approach An actuary has projected ultimate indemnity of $\$12{,}000{,}000$ for an accident year and $\$7{,}500{,}000$ of indemnity paid to date. Historical ratios of ultimate ALAE to ultimate indemnity for mature years are $0.18$ , $0.19$ , $0.20$ and $0.19$ . ALAE paid to date on this year is $\$1{,}400{,}000$ .

Estimate unpaid ALAE.
Answer Select an ultimate ALAE ratio of $0.19$ :
 $\begin{align*} \text{Ultimate ALAE} &= 0.19 \times \$12{,}000{,}000 \\ &= \$2{,}280{,}000 \\[4pt] \text{Unpaid ALAE} &= \$2{,}280{,}000 - \$1{,}400{,}000 \\ &= \$880{,}000 \end{align*}$ 
The check worth doing: ALAE is $61\%$ paid ( $1{,}400/2{,}280$ ) while indemnity is $63\%$ paid ( $7{,}500/12{,}000$ ) — close enough that the ratio approach is defensible here.

If instead ALAE were $85\%$ paid against $63\%$ on indemnity, the ratio method would be projecting ALAE that has largely already been spent, and a separate ALAE triangle would be the better estimator. That comparison — the relative maturity of the two components — is what decides between the methods.