Case Adequacy

Study guide: Exam 5

Case Adequacy is how close case reserves sit to the eventual settlement cost of the claims they are set on. A change in adequacy over calendar time is one of the two distortions (settlement rate is the other) that make historical development factors misleading.

$\text{Avg Case Outstanding} = \frac{\text{Case Reserves}}{\text{Open Claim Counts}}$

$\text{Adequacy ratio} = \frac{\text{Case reserve at valuation}}{\text{Eventual settlement value}}$

The diagnostic is average case outstanding per open claim, compared down each column of the triangle. It should grow at roughly the severity trend. A jump concentrated on one diagonal, appearing at every maturity at once, is a change in reserving practice, not in claim cost.
Strengthening raises reported losses immediately, so recent age-to-age factors fall (more of the ultimate is already booked). Applying historical factors — built under weaker reserving — to a strengthened diagonal over-states ultimate, because the strengthening is developed a second time.
Weakening does the reverse and understates ultimate, which is the more dangerous direction: the reserves are inadequate and the method that is supposed to catch it is biased in the same direction.
Paid data is immune, so a divergence between paid and reported chain ladder estimates is the corroborating evidence. Rising average case outstanding and reported ultimates running above paid ultimates together confirm a strengthening.
The remedy is the Berquist-Sherman case adjustment: restate historical average case outstanding to the current adequacy level using a selected severity trend, rebuild the reported triangle, and select factors from the restated history.
Adequacy also affects the a priori methods indirectly: the Cape Cod ELR is computed from reported losses, so a strengthening inflates it and the distortion enters twice.

Detecting a Shift Average case outstanding per open claim:

AY 12 mo 24 mo 36 mo

$2020$ $\$5{,}200$ $\$8{,}000$ $\$12{,}000$

$2021$ $\$5{,}500$ $\$8{,}400$ $\$18{,}100$

$2022$ $\$5{,}700$ $\$14{,}000$

$2023$ $\$9{,}400$

What happened, and when?

Answer Read down the columns:

$12$ months: $5{,}200 \to 5{,}500 \to 5{,}700$ (about $+4.7\%$ a year), then $\$9{,}400$ — a $+65\%$ jump.

$24$ months: $8{,}000 \to 8{,}400$ ( $+5.0\%$ ), then $\$14{,}000$ — $+67\%$ .

$36$ months: $12{,}000$ , then $\$18{,}100$ — $+51\%$ .

Every jump is on the latest diagonal, the year ending $12/31/2023$ , and all are of similar magnitude. This is a case reserve strengthening during calendar $2023$ , of roughly $55$ – $65\%$ over and above the $\approx 5\%$ severity trend.

Confirming evidence to look for: reported chain ladder ultimates now exceeding paid chain ladder ultimates, and a stable disposal rate (which would rule out a settlement-speed explanation).

Selecting reported development factors from this triangle unadjusted would over-state ultimate losses substantially — the strengthened diagonal would be multiplied by factors built for a book that reserved $60\%$ lighter.

AY	12 mo	24 mo	36 mo
$2020$	$\$5{,}200$	$\$8{,}000$	$\$12{,}000$
$2021$	$\$5{,}500$	$\$8{,}400$	$\$18{,}100$
$2022$	$\$5{,}700$	$\$14{,}000$
$2023$	$\$9{,}400$

Quantifying the Bias A reported triangle's $24$ – $36$ factor has historically been $1.30$ . Case reserves were strengthened $25\%$ at the end of $2024$ . AY 2023, at $24$ months on $12/31/2024$ , shows paid $\$3{,}000{,}000$ and case reserves $\$2{,}500{,}000$ .

Estimate the size of the bias if the historical factor is used unadjusted.

Answer Unadjusted:

$(\$3{,}000{,}000 + \$2{,}500{,}000) \times 1.30 = \$7{,}150{,}000$

Under the old reserving basis, the same claims would have carried case reserves of about

$\frac{\$2{,}500{,}000}{1.25} = \$2{,}000{,}000$

so reported would have been $\$5{,}000{,}000$ — which is the level the $1.30$ factor was calibrated to:

$\$5{,}000{,}000 \times 1.30 = \$6{,}500{,}000$

The unadjusted estimate is $\$650{,}000$ ( $10\%$ ) too high. The strengthening added $\$500{,}000$ to reported losses, and the factor then developed that $\$500{,}000$ by a further $30\%$ as though it were newly emerged loss rather than a re-estimate of claims already counted.

The Berquist-Sherman restatement fixes the factor rather than the diagonal: the strengthened reserves stay in the estimate (they are the claims department's current best view), but the development applied to them is re-derived from a consistently-restated history.