Roll Forward Analysis

Study guide: Exam 5

Roll Forward Analysis reconciles the reserve balance from one valuation date to the next, decomposing the change into its components so that genuine re-estimation is separated from the ordinary mechanics of new claims and payments.

R_{\text{end}} = R_{\text{begin}} + \text{Incurred on new AY} - \text{Paid} \pm \text{Prior-year development}

\text{Prior-year development} = \sum_{\text{prior AYs}} \left(U_{\text{current}} - U_{\text{prior}}\right)

• The prior-year development term is the only one that reflects a change of view. The other terms are arithmetic: a new accident year arrives, and payments run off the balance. Isolating the development term is the point of the exercise.
• Adverse development (positive) means the prior estimate was deficient; favourable (negative) means it was redundant. Statutory reporting requires this to be disclosed by accident year — Schedule P Part 2 is a one-year and two-year development table across the whole industry.
• Roll forward is also the interim valuation tool: between full reviews, ultimates for prior years are held and the balance is rolled forward on the expected pattern, with A/E used to decide when the held ultimates must be revisited.
• A run of adverse development in the same direction across several roll-forwards is systematic deficiency, not bad luck, and calls for the assumptions to be re-selected rather than for the current estimate to be topped up again.
• Favourable development is not automatically good news: consistent redundancy overstates the current year's loss ratio, which feeds an over-stated rate indication into pricing, exactly as deficiency feeds an under-stated one.

Rolling the Balance Forward Reserves at 12/31/2023 were \$10{,}000{,}000. During 2024: losses incurred on the new accident year \$2{,}500{,}000; payments (all years) \$3{,}200{,}000; adverse development on prior accident years \$400{,}000.

Compute the closing reserve and comment.

Answer

\begin{align*}
R_{\text{end}} &= \$10{,}000{,}000 + \$2{,}500{,}000 \\
&\quad - \$3{,}200{,}000 + \$400{,}000 \\
&= \$9{,}700{,}000
\end{align*}

The balance fell \$300{,}000, which on its own reads as a book running off comfortably. The decomposition says otherwise: the fall is entirely payments outrunning new incurred, and inside that movement is \$400{,}000 of adverse development — a 4\% miss on the opening reserve.

The headline number and the diagnostic number point in opposite directions, which is precisely why the roll forward is done component by component.

A Run of Adverse Development One-year development on prior-year reserves, from successive Schedule P filings:

Calendar year	Opening reserve	Adverse (favourable) development
2021	\$38{,}000K	\$900K
2022	\$41{,}000K	\$1{,}300K
2023	\$44{,}000K	\$1{,}800K
2024	\$47{,}000K	\$2{,}400K

What does the pattern say?

Answer Development as a percentage of the opening reserve: 2.4\%, 3.2\%, 4.1\%, 5.1\%. Adverse in every year, and the percentage is accelerating — this is not random variation around an unbiased estimate.

Two distinct readings, with different implications:

1. The reserving process is systematically low. Factors selected too gently, a tail set too short, or an a priori ELR that has not kept up with rate level and trend. The fix is in the method, and the correction is a one-time catch-up plus a change in selections.
2. The environment is deteriorating faster than the estimates can follow. Social inflation or a legal change raising the cost of all open claims each year. The fix is a calendar-year adjustment, and — critically — the same finding applies to pricing, because the trend selection in the rate indication is stale by the same amount.

Distinguishing them requires the A/E detail: deficiency concentrated at particular maturities points to the method, deficiency spread uniformly across every open year on each diagonal points to the environment.

What is not defensible is a fifth year of topping the reserve up by whatever emerged. Four consecutive misses in the same direction is a demonstrated bias, and the standards expect the assumptions behind it to be revisited.