Track how reserves perform between full studies, comparing actual emergence to expected and rolling estimates forward at interim valuations.

You run a full reserve study once or twice a year, but management wants a reserve number every quarter. Between studies you do not rebuild everything. You compare what actually emerged to what you expected, and roll the last study forward.

A full study re-estimates every accident year with triangles, selected factors, and multiple methods. That is expensive and slow. Between studies you need a cheaper check: are reserves still holding up? The tool is expected emergence. You predict how much loss should pay or report during the quarter, then compare to what the ledger actually shows.

Start with the prior study. It gives an estimated ultimate for each accident year and a development pattern. The pattern tells you the percent emerged at each age. Percent paid at an age is one divided by the paid CDF to ultimate for that age. Percent reported works the same way with reported factors.

Do not multiply the whole ultimate by the change in percent. Friedland scales the remaining unreported balance.

Common mistakes

• Using the new ultimate to build expected emergence. Expected emergence must use the prior study's ultimate and pattern. Plugging in a freshly recalculated ultimate makes AvE collapse toward zero and hides the signal.
• Using $U\times \Delta \%$ for an off-pattern ultimate. When the ultimate came from BF or expected losses, actual emerged rarely equals ultimate times percent emerged, so scale the unreported balance by dividing by percent unemerged first. Only a development-derived ultimate lets you shortcut to $U\times \Delta \%$.
• Reading the pattern off 1/CDF for a non-development ultimate. 1/CDF is the development pattern. For BF or expected-based ultimates, derive the pattern from ratios of paid or reported claims to the selected ultimates by maturity.

Bottom line

• Expected emergence equals unreported claims (ultimate minus actual reported) divided by percent unreported, times the incremental percent emerged; it collapses to ultimate times delta% only when the ultimate came from the development technique.
• Percent emerged usually equals 1 divided by the CDF, but when ultimates come from another technique, derive the pattern from ratios of paid or reported claims to the selected ultimates by maturity.
• Actual versus Expected (AvE) equals actual emergence minus expected emergence; positive AvE means losses came in faster than the pattern predicted.
• Favorable AvE hints at redundancy; unfavorable AvE hints at deficiency, but is a signal, not proof.

Exam shortcut

Build expected emergence as the unreported balance divided by percent unreported, times the change in percent emerged, and always convert any CDF to percent emerged first with 1 divided by the factor. Only shortcut to old ultimate times the change in percent when the ultimate came from development, because then actual emerged already equals ultimate times percent emerged.

The full lesson (about 3,016 words, 20 min read) adds 2 worked examples, all 8 common mistakes, a self-check, free in the app.

Learning objectives

• B17

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