Short Tail Insurance

Study guide: Exam 5

Short Tail Insurance covers lines whose claims are reported and settled quickly — typically within a year — so that reported losses are close to ultimate almost immediately and IBNR is small relative to case reserves.

$\text{CDF}_{12 \to \text{ult}} \approx 1.0 \text{ for short-tail lines}$

Typical short-tail lines: auto physical damage (collision, comprehensive), homeowners property, inland marine, boiler and machinery, most first-party property covers.
Losses are observable: a damaged car or a burnt building is inspected, appraised and paid. There is no latent injury, little litigation, and the loss amount is not a function of a jury's opinion years later.
Consequently development is compact, tail factors are near $1.000$ , and the chain ladder on paid data is reliable at maturities where a long-tail line would still be guessing.
Fast emergence means fast feedback on rate adequacy: shorter experience periods are acceptable, trend is measurable with less lag, and rate changes show up in results within a year — one reason personal lines can be re-priced annually.
The dominant risk is not development but concentration: a single hail storm or hurricane can produce more loss in a day than a normal year, so catastrophe losses are excluded from the experience and loaded separately. A short-tail line can therefore have low reserve risk and very high underwriting risk at the same time.
Short-tail reserves are also sensitive to seasonality: the December diagonal of a property triangle behaves differently from the June one, which is why quarterly rather than annual cohorts are common.

Short-Tail vs. Long-Tail Development Side by Side An auto comprehensive claim arises from hail damage on $3/5/2024$ . A workers compensation occupational-disease claim also arises from $2024$ exposure.

Trace each claim's life and the implication for reserving.

Answer Comprehensive claim — reported within days, vehicle appraised within a week, paid within a month. At $12/31/2024$ it is closed and its cost is a fact. The AY 2024 comprehensive triangle needs a $12$ -to-ultimate factor of perhaps $1.02$ , and virtually all of that is a handful of claims still in appraisal.

Occupational disease claim — the exposure occurred in $2024$ , but the disease may not manifest until $2029$ and may not be filed until $2031$ ; medical and indemnity payments then run for the claimant's lifetime. At $12/31/2024$ the claim is invisible, sitting entirely in pure IBNR, and the AY 2024 workers compensation CDF at $12$ months may exceed $2.0$ .

Same accident year, same insurer, same valuation date — and one estimate is essentially known while the other is dominated by assumptions about the next thirty years. This is why they are never combined in one triangle (Homogeneity).

Where the Uncertainty Actually Lives A homeowners book has $\$50{,}000{,}000$ of earned premium. Non-catastrophe losses have averaged a $58\%$ loss ratio with little year-to-year variation. Catastrophe losses over the last ten years were: $\$0$ , $\$1$ M, $\$0$ , $\$4$ M, $\$0$ , $\$0$ , $\$38$ M, $\$2$ M, $\$0$ , $\$1$ M.

How should the rate indication treat the two components?

Answer The non-catastrophe portion is short-tail and stable — develop and trend it in the ordinary way.

For catastrophes, the ten-year average is

$\frac{\$46{,}000{,}000}{10} = \$4{,}600{,}000 \text{ per year}$

or a $9.2\%$ catastrophe loss ratio — but the median year is $\$0$ and one year is $\$38$ M. Neither the mean nor the median of ten observations is a credible estimate of a hurricane load.

The correct treatment is to exclude catastrophe losses from the experience period entirely and load a modelled average annual loss (see Catastrophe Loss), so that the indication does not swing by $\pm 8$ points depending on whether the experience period happens to contain the storm.

The line is short-tail in development and highly volatile in result — the two are independent properties, and conflating them is a common error.