Common Berquist-Sherman Calculation Errors

Why Berquist-Sherman Calculations Need Careful Controls

Berquist-Sherman adjustments are intended to reduce distortions caused by changes in claim settlement speed and case reserve adequacy. Their arithmetic is usually straightforward; the risk is applying a reasonable-looking factor to the wrong quantity. A cumulative factor applied to an incremental amount, a closure adjustment applied to incurred losses, or a reserve adequacy change that also alters paid losses can all produce plausible-looking but conceptually incorrect results.

The safest approach is to identify, for every input, whether it is incremental or cumulative, paid or incurred, associated with closed or open claims, and measured at which valuation date. The examples use a clearly specified standardization method. In practice, selections and implementation details can vary, so the analyst must state the method and preserve the relationship between each factor and its intended base.

Keep Triangle Entries on the Correct Basis

A triangle may show incremental amounts, cumulative amounts, or both. An incremental entry records activity during one development interval; a cumulative entry records the total from the start of the claim period through a development age. For example, if paid losses are 400 in the first interval and 500 in the next, cumulative paid losses at the end of the second interval are 900, not 500.

The closure adjustment described here is defined on cumulative paid losses and a cumulative closure proportion at the same development age. Let \(P_{a,d}\) be cumulative paid losses for accident period \(a\) at development age \(d\), and let \(q_{a,d}\) be the proportion of the estimated ultimate claim count closed by that age. Let \(q_d^*\) be the selected target closure proportion at age \(d\). The standardized cumulative paid amount is:

This simplified standardization holds average paid severity per closed claim constant. It is not a claim that every closed claim has the same payment, nor is it appropriate without considering whether claim mix and settlement practices make the comparison credible.

Closure Adjustments Belong to the Paid-Loss Method

A closure adjustment is intended to address how quickly claims have closed and, under the simplified method above, it restates paid losses using a closure proportion. The closure proportion must use the relevant claim-count base: closed claims divided by estimated ultimate claims, not closed claims divided by paid claims, open claims, or a count from a different period.

An incurred amount combines paid losses and case reserves. Applying a closure multiplier to the full incurred amount confounds two distinct components: paid losses and case reserves. If the task is to standardize incurred losses for case reserve adequacy, restate the case reserve component and leave paid losses unchanged. If a separate paid-loss closure adjustment is also being made, keep the two calculations distinct and document how the resulting adjusted data are combined.

Use One Valuation Date for Each Adjustment

A valuation date is the date through which claim and loss information has been recorded. Development age identifies how long a period has developed; it does not, by itself, identify the valuation date. When a closure proportion, paid amount, open-claim count, or reserve benchmark comes from a different valuation date than the other inputs, the resulting adjustment may combine incompatible snapshots.

This matters especially when claim handling changes over calendar time. A closure proportion observed at one valuation date can differ from the proportion for the same development age at another date. A valid calculation therefore matches the numerator, denominator, and loss amount to the intended accident period, development age, and valuation date. If a historical snapshot is required but unavailable, the analyst should not silently substitute a later snapshot.

Why the Closure Ratio Has This Form

The closure multiplier follows from a simple standardization argument. Suppose, as an approximation, that cumulative paid losses equal the number of claims closed multiplied by average paid severity per closed claim. If the average paid severity is held fixed, then paid losses are proportional to the number of claims closed, and hence proportional to the closure proportion when ultimate claim count is fixed.

Write \(P_{a,d}=N_a q_{a,d}s\), where \(N_a\) is estimated ultimate claim count and \(s\) is average paid severity per closed claim. Replacing the observed closure proportion with the target proportion gives \(P_{a,d}^{\text{adj}}=N_a q_d^*s\). Dividing the target expression by the observed expression yields:

This derivation also shows the method's limitations. It relies on the same ultimate count and average paid severity being relevant under both closure patterns. If the claims closing earlier are systematically larger or smaller, or if claim mix changes materially, the proportionality assumption may fail. A factor should not be treated as a mechanical correction that makes unlike claim populations comparable.

Common Error Checks

Before accepting an adjusted triangle, check the calculation in both directions: trace each factor back to its definition, then reconcile the adjusted components to the reported totals. These checks are useful even when the calculation is performed in a spreadsheet or actuarial system.

The central exam trap is to focus on the numerical factor and overlook what it measures. A factor is not meaningful apart from its numerator, denominator, loss basis, and valuation. State those elements explicitly before calculating.