Reserving Diagnostics and the Berquist–Sherman Adjustment

Development-factor methods (see Loss Development Triangles, Reserving Methods) implicitly assume that claims processes — how quickly claims are reported, reserved, and settled — are stable over time. Reserving diagnostics exist to test that assumption, and the Berquist–Sherman technique exists to correct the data before applying chain-ladder methods when the assumption fails.

Core diagnostic ratios

Three diagnostics, tracked by origin year and development age, reveal changes in claims department behavior that would otherwise silently distort development factors:

• Paid-to-incurred ratio: $\text{P/I}_{i,k} = \text{Paid}_{i,k}/\text{Incurred}_{i,k}$. A rising P/I ratio at a given age across successive origin years suggests either faster claim settlement (more of the ultimate is paid earlier) or weakening case reserve adequacy (incurred is understated); a falling ratio suggests the reverse. Distinguishing between these two causes requires the other diagnostics below.
• Closure rate: $\text{Closure Rate}_{i,k} = \text{Closed Counts}_{i,k}/\text{Reported Counts}_{i,k}$. An increasing closure rate at a given maturity across origin years indicates claims are being resolved faster — a genuine operational change (e.g., a new claims management initiative, or catch-up after a prior backlog) that will shorten the paid development tail if not recognized.
• Average case reserve (ACR): $ACR_{i,k} = \text{Case Reserves}_{i,k}/\text{Open Counts}_{i,k}$. Tracking ACR by age across origin years, adjusted for inflation, reveals whether case reserve adequacy (the average reserve carried per open claim, in real terms) is strengthening, weakening, or stable. A change here directly signals that the incurred triangle's historical development pattern no longer applies to current and future case reserves.

These diagnostics are typically displayed as a triangle of ratios (mirroring the loss triangle's shape) so that trends can be read along diagonals (calendar-year effects, e.g., a new claims system implemented in a specific year) as well as along age (maturity effects).

Why level shifts break chain-ladder

Chain-ladder development factors are estimated from historical relationships between successive evaluations. If claims handling changes mid-history — say, case reserves become more conservative (larger) starting in calendar year 2023 — then the incurred triangle will show an artificial jump in incurred losses on the 2023 diagonal, contaminating every age-to-age factor that straddles that diagonal, for years that have not yet reached the new, more-adequate reserving regime. Naively applying the resulting (distorted) development factors to recent, still-immature accident years — which are already reserved under the new, more-adequate regime — would double-count the strengthening, since the factor was inflated based on years that hadn't yet been strengthened. Berquist–Sherman corrects for exactly this by restating history as if the current claims-handling regime had always been in place.

The Berquist–Sherman case reserve adequacy adjustment

The idea: restate all historical average case reserves onto a current-level basis (adjusting only for inflation to a common cost level, since case reserve adequacy, once inflation-adjusted, should be roughly stable if reserving philosophy hasn't changed), then re-derive "adjusted" incurred triangle values consistent with that current reserving level.

Method: (1) compute the trend in ACR over time — for a stable reserving philosophy this equals only the severity inflation trend; select the trend from the most recent, presumed-stable diagonals; (2) restate each historical cell's ACR to the latest diagonal's level: $\text{Adj ACR}_{i,k} = ACR_{i,k}^{latest\,diagonal\,trended\,back}$, i.e., compute what the ACR at age $k$ would have been if the current reserving adequacy and only the trend applied; (3) rebuild the adjusted incurred triangle as $\text{Adj Incurred}_{i,k} = \text{Paid}_{i,k} + \text{Adj ACR}_{i,k}\times\text{Open Counts}_{i,k}$; (4) re-derive development factors from this adjusted triangle, which are now free of the reserve-adequacy distortion, and apply them to project ultimates.

The Berquist–Sherman settlement rate adjustment

A parallel procedure corrects the paid triangle when closure rates have changed. If claims are closing faster than historical averages, the historical paid development pattern (which reflects the old, slower closure rate) will understate how quickly current-year paid losses will emerge, understating reserves if applied naively. The adjustment restates historical closed claim counts to be consistent with the current settlement rate, then interpolates a revised paid-loss triangle consistent with that adjusted closure pattern (using the average severity of closed claims by age, which is a much more stable quantity than the count of closures itself), and re-derives paid development factors from this adjusted triangle.

Worked mini-example: case reserve adequacy

Actual data for AY 2021 and AY 2023, both evaluated at 24 months, and the current (2024) inflation-adjusted target ACR level trended to 24 months is 6,500:

Suppose the diagnosed severity-only trend (from stable years) is 5%/year, so trending the AY2021 24-month evaluation forward two years to a 2023-equivalent cost level gives $5{,}000\times1.05^2 = 5{,}513$ — but the actual current adequacy level (from the most recent diagonal, inflation-trended) is 6,500, well above 5,513. This gap (6,500 vs. trended 5,513) indicates reserve strengthening beyond inflation — i.e., a genuine adequacy-level change, not just cost inflation.

Adjusted ACR for AY2021 @24mo $= 6{,}500$ (current adequacy level, since after removing pure inflation the philosophy is deemed applicable uniformly): Adjusted case reserves $=6{,}500\times40=260{,}000$ (vs. actual 200,000). Adjusted incurred $=\text{Paid}_{2021,24}+260{,}000$ instead of $\text{Paid}_{2021,24}+200{,}000$ — a 60,000 upward restatement reflecting that 2021's case reserves, at that age, were on average 60,000 short of what today's more-adequate reserving philosophy would carry.

Repeating this restatement across every historical cell and re-running the chain ladder on the adjusted triangle yields development factors — and hence ultimates — consistent with today's reserving adequacy, rather than a blend of eras.

Pitfalls

• Confusing a rising average case reserve with case-strengthening when it is actually pure claims-cost inflation — always separate the inflation trend from the adequacy-level trend before adjusting.
• Applying Berquist–Sherman when the real driver is a genuine mix shift (e.g., more large claims in recent years) rather than a claims-handling change — the adjustment should not be used to paper over real underlying loss trend changes.
• Adjusting only the incurred triangle for a case-reserve issue while ignoring a concurrent settlement-rate change — the two often occur together (e.g., a claims department overhaul changes both reserving and closing practices) and should both be diagnosed.
• Applying the adjustment mechanically without first confirming the diagnostic evidence (P/I ratios, closure rates, ACR trends) actually shows a level shift.

Exam relevance

Reserving diagnostics and the Berquist–Sherman technique are classic, frequently tested topics on CAS Exam 6 and Exam 8.

Further reading

• Berquist & Sherman, Loss Reserve Adequacy Testing: A Comprehensive, Systematic Approach, PCAS LXIV, 1977.
• Friedland, Estimating Unpaid Claims Using Basic Techniques, CAS Study Note.
• Feldblum, Reserving and Financial Statement Insight, CAS Study Note.