Ceded Losses

Study guide: Exam 5

Ceded Losses are the portion of gross losses transferred to reinsurers. They are the reinsurer's share of claim cost and, from the cedant's balance sheet, a recoverable asset rather than a reduction of the underlying claim liability.

\text{Ceded} = \text{Gross} - \text{Net}

\text{Ceded}_{\text{XOL}} = \min\!\left(\max(X - R,\, 0),\, L\right)

\text{Ceded}_{\text{QS}} = c \times \text{Gross}

• Under quota share, ceded is a fixed share c of gross, so the ceded triangle is a scalar multiple of the gross one and develops identically. Under excess of loss, ceded responds only to claims piercing retention R, and the pattern is entirely different — later, steeper, and far more volatile.
• The ceded triangle is thin: a handful of claims in most years, none in some. Development factors estimated from it are unstable, which is why ceded ultimates are often estimated by applying treaty terms to a projected large-claim distribution (exposure rating) instead.
• Ceded losses are leveraged by trend. A 6\% increase in ground-up severity produces far more than 6\% growth in an excess layer, because claims that previously fell short of the retention now pierce it — the same leverage described under Inflation and Increased Limits.
• Ceded history reflects the treaties as they stood. A change in attachment point, limit or structure breaks the series and makes prior ceded years non-comparable; the gross history is unaffected. See Gross Losses.
• Ceded amounts carry credit risk — dispute, commutation, insolvency — and a provision for uncollectible reinsurance may be required. The cedant remains liable to its policyholders regardless.

Ceding Under Two Structures Five claims: \$2{,}600{,}000, \$900{,}000, \$800{,}000, \$500{,}000, \$200{,}000 (\$5{,}000{,}000 gross).

Compute ceded losses under (a) a 30\% quota share and (b) a \$1{,}000{,}000 excess of \$500{,}000 per-risk treaty.

Answer (a) Quota share:

\text{Ceded} = 0.30 \times \$5{,}000{,}000 = \$1{,}500{,}000

spread across all five claims in proportion.

(b) Excess of loss — \min(\max(X-500\text{K},0),\,1\text{M}):

Claim	Gross	Ceded
1	\$2{,}600K	\$1{,}000K (layer exhausted)
2	\$900K	\$400K
3	\$800K	\$300K
4	\$500K	\$0
5	\$200K	\$0
Total	\$5{,}000K	\$1{,}700K

The totals are comparable, the distributions are not. The quota share cedes something on every claim; the excess treaty cedes nothing on two of five and is exhausted on the largest — which means claim 1's excess above \$1.5M (\$1.1M) comes back to the cedant.

Leveraged Trend in the Ceded Layer A book's severity distribution produces \$5{,}000{,}000 of gross losses and \$1{,}700{,}000 ceded to a \$1M xs \$500K layer. Ground-up severity then trends 10\%: each of the five claims above grows by 10\%.

Compute the trend in the ceded layer.

Answer Trended claims: \$2{,}860K, \$990K, \$880K, \$550K, \$220K — gross \$5{,}500K, up 10\% as expected.

Ceded at \$1M xs \$500K:

Claim	Trended	Ceded
1	\$2{,}860K	\$1{,}000K
2	\$990K	\$490K
3	\$880K	\$380K
4	\$550K	\$50K
5	\$220K	\$0
Total	\$5{,}500K	\$1{,}920K

\frac{\$1{,}920}{\$1{,}700} - 1 = +12.9\%

A 10\% ground-up trend produced a 12.9\% trend in the ceded layer — and the effect is concentrated: claim 4 went from ceding nothing to ceding \$50K purely by crossing the retention.

Two consequences. The net layer trends by less than 10\% (3{,}580/3{,}300 - 1 = +8.5\%), so a net analysis understates the ground-up trend. And the reinsurer's own pricing must anticipate this leverage — which is why excess rates move so much more violently than primary rates through an inflationary period.