The completion factor method is widely used across the industry to set healthcare reserves. The method works by looking at the lag between when claims are incurred and when they are paid. It then calculates development factors (i.e. age-to-age factors) and averages those factors across several months to predict future payment patterns.
While the calculation of the development factors follows a prescriptive formula, the selection of the averaging method is largely left to the discretion of the actuary. That single choice can have a substantial impact on the final reserve amount.
If you are new to the mechanics of building a triangle and computing development factors, start with The Completion Factor Method. This article picks up at Step 4 of that process, where the development factors have already been calculated and the actuary must decide how to average them.
Why the Averaging Method Matters#
Individual development factors can be volatile. A single large claim, a processing delay, or a one-time data anomaly can distort the factor for a given period. Because these factors are multiplied together to produce age-to-ultimate factors, and then inverted into completion factors, a distortion in even one lag can ripple through to the final reserve.
Averaging is how the actuary smooths out that noise. But averaging is not a single, fixed operation. The actuary chooses which factors to include, how many recent periods to look back over, and whether to exclude extreme values. Each of these choices reflects a view about what the data is telling us and how much weight recent experience should carry.
The Most Common Methods#
Two averaging approaches account for the majority of completion factor work in practice.
- Simple average. The arithmetic mean of the most recent x development factors for a given lag (for example, the last 3 or last 6 months). Every included factor receives equal weight.
- Medial average. The middle x sorted development factors from the most recent y months. The notation "4 of 6," for example, means the highest and lowest of the six most recent factors are dropped, and the middle four are averaged.
The key advantage of the medial average is that it mitigates the impact of abnormally high and low values by removing them before averaging. When a lag column contains an outlier, the medial average keeps that outlier from pulling the selected factor away from the central tendency of the data.
How the Medial Average Handles Outliers#
Consider a single lag column with six recent development factors. Five of them cluster tightly together, but one month contains an unusually large claim that inflates its factor.
| Month | Development Factor |
|---|---|
| Month 1 | 1.20 |
| Month 2 | 1.22 |
| Month 3 | 1.19 |
| Month 4 | 1.21 |
| Month 5 | 1.85 |
| Month 6 | 1.23 |
The single 1.85 factor is clearly out of line with the rest of the column. Watch how each method responds:
- Simple average of the last 6 = (1.20 + 1.22 + 1.19 + 1.21 + 1.85 + 1.23) / 6 = 1.3167
- Medial average 4 of 6 drops the lowest (1.19) and the highest (1.85), then averages the middle four: (1.20 + 1.21 + 1.22 + 1.23) / 4 = 1.2150
The simple average is pulled up to 1.32 by the one anomalous month, while the medial average lands at 1.22, in line with the five well-behaved factors.
That gap of roughly ten points in a single lag may look small, but it compounds. Because age-to-ultimate factors are the product of every subsequent lag's selected factor, an inflated factor at an early, low-completion lag can move the ultimate estimate, and therefore the reserve, by a meaningful amount.
The Same Effect on Real Data#
The distinction is not only visible in a contrived example. Using the Lag 1 development factors from the triangle in The Completion Factor Method, here are three averaging methods applied to the same column:
| Method | Lag 1 Factor |
|---|---|
| Simple Average Last 6 | 1.3842 |
| Medial Average 4 of 6 | 1.3924 |
| Simple Average Last 3 | 1.3781 |
In this case the three methods land within a fraction of a point of one another, which is itself a useful signal: it suggests the underlying data is relatively stable and predictable. When the methods disagree materially, that disagreement is a prompt to look more closely at the data before selecting a factor.
Choosing the Lookback Period#
The number of periods to average, the lookback period, is as much a judgment call as the choice between simple and medial. The central question is how much weight to give to recent months.
- Use a shorter lookback (e.g. 3 months) when the payment pattern is changing and you want the selected factors to reflect the most recent experience. Provider network changes, claim system migrations, or processing improvements can all speed up or slow down completion. A shorter window responds to those shifts more quickly.
- Use a longer lookback (e.g. 12 months) when the monthly factors for a given lag are variable but not trending. A longer window averages over more observations, producing a more stable factor and reducing the influence of any single month.
There is a genuine trade-off here. A short lookback is responsive but noisy; a long lookback is stable but slow to react to real changes in the runoff pattern. The right balance depends on what is actually driving the variability in your data.
When the Method No Longer Applies#
If the factors for a given lag are not merely variable but extremely volatile, no averaging method will rescue the estimate. In that situation the completion factor method may not be appropriate for the population at all, and an alternative reserving method may be needed, either alongside the completion factor method or in place of it. Persistent volatility, or later lags that fail to converge toward 1.0, are signs that the historical data may not support a reliable completion factor projection.
Judgment, Documentation, and the Standards#
As with most actuarial analyses, setting reserves is part art and part science. Actuarial Standards of Practice No. 5, No. 23, No. 41, and No. 56 provide guidance on reserving methodologies, data quality, communications, and modeling, respectively. Importantly, none of them dictate the use of any specific averaging method.
This affords the actuary flexibility in determining an appropriate averaging method, so long as the choice is reasonable, appropriate, and properly documented. It is entirely possible for two qualified actuaries to review the same data set and reach different, defensible conclusions about which averaging method to use. An individual's judgment, external context, and reserving experience all shape the method and parameters ultimately selected.
Because the choice is discretionary, documentation carries real weight. Recording why a particular method and lookback period were selected, and what alternatives were considered, is what turns a discretionary choice into a well-supported actuarial position.
How IBNR Health Helps#
IBNR Health provides an easy-to-use dashboard for testing different averaging methods, so you can spend more time assessing results than building formulas by hand in Excel. Switch between simple and medial averages, adjust the lookback period, and see the impact on age-to-ultimate factors, completion factors, and the final reserve immediately.
The platform also offers full transparency into the math, so you always know exactly what goes into your reserve calculations, which makes documenting your selection straightforward when it comes time to support your work.
Disclaimer: This article reflects the opinions of the IBNR Health Team. It is intended for educational purposes only and should not be relied upon as the sole basis for professional decisions. Readers should exercise independent judgment when making actuarial or financial decisions. Please contact support@ibnrhealth.com if you have feedback or identify any mistakes on this page.