External Information in Reserving

Study guide: Exam 5

External Information in Reserving is the use of data originating outside the entity being analyzed — industry development patterns, published loss trends, competitor filings, economic and legal indicators — to supplement or replace an insurer's own experience when that experience is thin, distorted, or newly written. It is the reserving counterpart of the complement of credibility in ratemaking.

When external data is needed: a new line or new company with no history; a small or newly segmented book whose triangle is too volatile to be credible; the immature end of a long-tail triangle where a Tail Factor must be chosen; and as an independent reasonableness check on a selection driven entirely by internal data.
Common sources: industry aggregations (ISO, NCCI, statistical agents, Schedule P compilations for U.S. insurers; GISA and OSFI returns in Canada), rating-bureau loss development patterns, published loss-trend indices, reinsurer experience on the same treaty, and the CAS examiner's-report style benchmarks used for market comparison.
Never use external data unadjusted. It must be reconciled to the subject book on the dimensions that actually drive development: coverage and line of business definitions, policy limits and attachment points, mix of business, jurisdiction and legal environment, case-reserve adequacy philosophy, and settlement speed. Two books with the same nominal line code can have very different development if one is written at higher limits.
Blending, not switching. The usual application is a credibility-weighted selection: $\hat{U} = Z \cdot U_{\text{internal}} + (1-Z) \cdot U_{\text{external}}$ , with $Z$ reflecting the volume and stability of the internal data. The Bornhuetter-Ferguson Method and Expected Loss Method are the natural vehicles, since both need an a priori expected loss ratio that external data can supply.
External information also flags problems. A development pattern far outside the industry range, or a loss ratio that diverges persistently from peers writing the same business, is a signal to re-examine internal assumptions — a diagnostic use that does not require adopting the external numbers at all.
Documentation matters. ASOP 43 requires the actuary to disclose reliance on data supplied by others and the reasonableness review performed; a benchmark adopted without a stated rationale for its applicability is a documentation gap as much as a technical one (see Reserve Communication).

Benchmarking a Tail Factor An insurer's commercial auto liability triangle runs only $60$ months. Internal $48\text{–}60$ age-to-age factors are $1.021$ , $1.018$ , and $1.024$ . Industry patterns for commercial auto liability show a $60$ -months-to-ultimate tail of $1.045$ , but the industry data is written at a $\$1$ M limit while the insurer writes at $\$500$ K.

How should the tail be selected?

Answer The internal data supports continued development past $60$ months — factors are still comfortably above $1.000$ — but the triangle cannot measure how much remains. The industry tail of $1.045$ is the only direct evidence of the unobserved layer, so it is the right starting point.

It must then be adjusted downward for the limit difference. Development beyond $60$ months in liability is dominated by large, slow-settling claims; a book capped at $\$500$ K truncates exactly those claims, so it develops less in the tail than a $\$1$ M book. A selection somewhere between $1.025$ and $1.040$ is defensible depending on the severity distribution, with the reasoning documented.

Selecting the raw $1.045$ would over-state IBNR; selecting $1.000$ because "the triangle ends at $60$ months" would understate it materially. Neither internal nor external data alone answers the question.

A Priori Loss Ratio for a New Line An insurer enters a new state for homeowners in 2024. At $12$ months, AY 2024 reported losses are $\$1{,}150{,}000$ on earned premium of $\$8{,}000{,}000$ . There is no internal history. Industry experience for this state and line shows an ultimate loss ratio of $62\%$ ; the insurer's rates were filed about $4\%$ below the industry average.

Estimate ultimate losses.

Answer With no internal history the Chain Ladder Method is unusable — there are no development factors to select. Use the Bornhuetter-Ferguson Method with an externally derived a priori.

Adjust the industry loss ratio for the rate differential (lower rates → higher loss ratio):

$\text{A priori LR} = \frac{0.62}{1 - 0.04} = 0.646$

$\text{Expected ultimate} = \$8{,}000{,}000 \times 0.646 = \$5{,}168{,}000$

With an industry-benchmark $12$ -month CDF of, say, $1.25$ for homeowners, the percentage unreported is $1 - 1/1.25 = 0.20$ :

$\text{Ultimate}_{\text{BF}} = \$1{,}150{,}000 + 0.20 \times \$5{,}168{,}000 = \$2{,}183{,}600$

Every input here is external. The estimate should be presented with that reliance disclosed, and revisited as soon as the insurer's own experience becomes credible.