Recoveries

Study guide: Exam 5

Recoveries are amounts an insurer collects that offset the claims it pays — deductibles billed back to insureds, salvage and subrogation, reinsurance, and collateral sources. In reserving they are estimated alongside the gross claims, and their unreceived portion (the recoverable) reduces the estimate of net unpaid claims.

$\begin{aligned} \text{Net Ultimate} &= \text{Gross Ultimate} \\ &\quad - \text{Ultimate Recoveries} \end{aligned}$

$\begin{aligned} \text{Recoverable} &= \text{Ultimate Recoveries} \\ &\quad - \text{Recoveries Received} \end{aligned}$

Know how the data record them (Friedland Ch. 3). Some insurers keep separate payment and case-outstanding data by recovery type; others combine them, record payments only, or book recoveries as negative claim payments. Deductibles differ by line: first-party auto physical damage payments are made net of the deductible, while general liability claims are paid in full and the deductible recovered afterwards; case reserves may be set net or gross. A change in any of these conventions is a changing condition.
Salvage and subrogation (Friedland Ch. 14) are projected either by the development technique on reported or received S&S, or by the ratio approach: develop the ratio of received S&S to paid claims to an ultimate ratio, and multiply by selected ultimate claims gross of S&S. The ratio's development factors are less leveraged than those of S&S dollars, and the ultimate ratio is easier to select for immature years. Salvage (property) arrives quickly; subrogation (liability) can arrive years after the claim is paid, giving age-to-age factors below $1.000$ at older ages.
Reinsurance. Analyze gross and ceded and derive net, or gross and net and derive ceded — then test what is implied. Checks: net claims and premium do not exceed gross; a quota share shows up as a stable net-to-gross ratio triangle; large claims are ceded consistently with each year's retention; net development and tail factors are generally no larger than gross; and net IBNR is generally no larger than gross (exceptions include provisions for uncollectible reinsurance and disputed runoff). Aggregate or stop-loss covers are usually applied as a final step. See Net of Reinsurance, Ceded Losses.
Consistency across years. A change in retention makes historical net data non-comparable; restate history at the current retention where claim-level data allow, or project gross and ceded separately.
Recoveries carry collection risk — insured insolvency on deductibles, reinsurer insolvency or disputes on cessions — which is why the recoverable is reported and assessed as a separate item rather than netted away silently.

The S&S Ratio Approach Auto physical damage. Historical ratios of cumulative received S&S to cumulative paid claims settle at $0.108$ , having been $0.060$ at $12$ months and $0.095$ at $24$ months.

AY $2023$ at $24$ months: paid claims $\$9{,}600{,}000$ , received S&S $\$912{,}000$ , selected ultimate claims $\$12{,}000{,}000$ .

AY $2024$ at $12$ months: paid claims $\$6{,}000{,}000$ , received S&S $\$312{,}000$ , selected ultimate claims $\$12{,}500{,}000$ .

Estimate ultimate S&S and the S&S recoverable for each year.
Answer Ratio development to ultimate: $0.108 / 0.095 = 1.137$ from $24$ months; $0.108 / 0.060 = 1.800$ from $12$ months.
 $\begin{align*} \text{AY 2023 ratio} &= 912{,}000 / 9{,}600{,}000 = 0.0950 \\ \text{Ultimate ratio} &= 0.0950 \times 1.137 = 0.1080 \\ \text{Ultimate S\&S} &= 0.1080 \times \$12{,}000{,}000 = \$1{,}296{,}000 \\ \text{Recoverable} &= \$1{,}296{,}000 - \$912{,}000 = \$384{,}000 \end{align*}$ 
 $\begin{align*} \text{AY 2024 ratio} &= 312{,}000 / 6{,}000{,}000 = 0.0520 \\ \text{Developed} &= 0.0520 \times 1.800 = 0.0936 \end{align*}$ 
AY $2024$ 's developed ratio is well below the $0.108$ of every mature year. Before accepting it, ask whether recording or recovery practice changed or one large claim is distorting the ratio. Absent a reason, a selection near the historical level is typical — at $0.107$ , ultimate S&S is $\$1{,}337{,}500$ and the recoverable $\$1{,}025{,}500$ , against $\$858{,}000$ from the mechanical projection. Friedland makes the same kind of judgmental selection for her most recent year.

Gross, Net and Implied Ceded AY $2024$ under a per-occurrence excess of loss treaty: gross reported $\$8{,}000{,}000$ with a selected gross CDF of $1.50$ ; net reported $\$6{,}500{,}000$ with a selected net CDF of $1.35$ . Derive ceded ultimate and check the result.
Answer
 $\begin{align*} \text{Gross ultimate} &= \$8{,}000{,}000 \times 1.50 = \$12{,}000{,}000 \\ \text{Net ultimate} &= \$6{,}500{,}000 \times 1.35 = \$8{,}775{,}000 \\ \text{Ceded ultimate} &= \$12{,}000{,}000 - \$8{,}775{,}000 \\ &= \$3{,}225{,}000 \\ \text{Implied ceded CDF} &= 3{,}225{,}000 / 1{,}500{,}000 = 2.15 \end{align*}$ 
Net IBNR ( $\$2{,}275{,}000$ ) is below gross IBNR ( $\$4{,}000{,}000$ ), and the ceded layer develops far more than gross ( $2.15$ vs. $1.50$ ) — as expected, since the reinsurer takes the large, late-developing part of claims. Had the retention risen from $\$500{,}000$ to $\$1{,}000{,}000$ for AY $2024$ , the net CDF of $1.35$ — selected from years capped at $\$500{,}000$ — would be too low, and net IBNR understated; the net history would need restating at the new retention.