Net Losses

Study guide: Exam 5

Net Losses are what the insurer ultimately bears: gross losses less every recovery — reinsurance cessions, salvage and subrogation, and deductible recoveries.

$\text{Net} = \text{Gross} - \text{Ceded} - \text{S\&S} - \text{Deductible Recoveries}$

$\text{Net Ultimate} = \text{Gross Ultimate} - \text{Ceded Ultimate} - \text{Recovery Ultimate}$

Net is the figure that matters for capital, solvency and the insurer's own results, and it is the basis on which retained profitability is measured.
It should be derived, not developed. Each component — gross, ceded, S&S, deductible recoveries — has its own emergence pattern, so each is projected separately and the net figure falls out of the subtraction. Developing a net triangle directly embeds whatever reinsurance structure was in force in each historical year.
Net experience is smoother than gross because reinsurance truncates the volatility. That makes net data look more credible than it is: the smoothing is bought, and its price is the net cost of reinsurance.
Net loss ratios must be compared against net premium. Gross losses over net premium — or the reverse — misstates the ratio by the whole cost of the reinsurance programme.
Net figures depend on recoveries actually arriving. Reinsurer insolvency, coverage disputes, and an insolvent large-deductible insured all convert an assumed recovery into a retained loss, so a net estimate carries credit risk that a gross estimate does not.

Building the Net Figure Gross incurred losses $\$1{,}000{,}000$ ; excess-of-loss reinsurance recoverable $\$150{,}000$ ; salvage on total-loss vehicles $\$30{,}000$ ; subrogation from an at-fault third party $\$20{,}000$ .

Compute net losses.
Answer
 $\begin{align*} \text{Net} &= \$1{,}000{,}000 - \$150{,}000 \\ &\quad - \$30{,}000 - \$20{,}000 \\ &= \$800{,}000 \end{align*}$ 
The insurer paid claimants $\$1{,}000{,}000$ and will end up bearing $\$800{,}000$ — provided all three recoveries are collected. The $\$150{,}000$ reinsurance recoverable in particular is an asset on the balance sheet, not a reduction of the claim liability: if the reinsurer fails, the insurer still owes the policyholder.

Deriving Net Rather Than Developing It AY 2023 at $24$ months: gross reported $\$8{,}000{,}000$ with a gross CDF of $1.35$ ; ceded reported $\$1{,}500{,}000$ with a ceded CDF of $1.90$ ; S&S reported $\$240{,}000$ with an S&S CDF of $1.45$ .

Compute the net ultimate, and compare with developing the net diagonal at the gross factor.
Answer Component by component:
 $\begin{align*} \text{Gross ultimate} &= \$8{,}000{,}000 \times 1.35 = \$10{,}800{,}000 \\ \text{Ceded ultimate} &= \$1{,}500{,}000 \times 1.90 = \$2{,}850{,}000 \\ \text{S\&S ultimate} &= \$240{,}000 \times 1.45 = \$348{,}000 \\[4pt] \text{Net ultimate} &= \$10{,}800{,}000 - \$2{,}850{,}000 - \$348{,}000 \\ &= \$7{,}602{,}000 \end{align*}$ 
Developing net directly at the gross factor:

$(\$8{,}000{,}000 - \$1{,}500{,}000 - \$240{,}000) \times 1.35 = \$8{,}451{,}000$

The shortcut is $\$849{,}000$ — over $11\%$ — too high, and the error is systematic rather than random: both the ceded layer and the recoveries develop faster than gross, so netting first and developing at the gross factor always under-credits them.

This is the practical argument for the component approach. It costs three triangles instead of one, and it is the difference between an $11\%$ error and none.