Insights · Experience and assumptions

How much should you believe your own data?

Every experience investigation ends with the same decision, and it is almost never the one people spend their time on. The exposure has been built, the claims matched, the actual-versus-expected ratio calculated. It comes out at 0.91. The table says one thing and the portfolio says another. So: do you move the basis, or don't you?

Credibility theory exists to answer exactly this, and most actuaries can write down the limited fluctuation formula from memory. Yet in practice the answer often arrives before the theory does, through a rule of thumb, a previous year's decision, or the number that causes least argument with the pricing team. That is not a failure of technique. It is a failure to be explicit about what the technique is doing.

The formula is the easy part

Limited fluctuation credibility asks a narrow question: how likely is it that the observed result sits within a given tolerance of the true underlying rate? Under a Poisson claim count the credibility factor scales with the square root of expected claims against a full credibility standard, commonly 1 082 claims for a 90% probability of landing within 5%.

Two consequences are worth stating plainly. Credibility grows with the square root, not linearly, so quadrupling exposure only doubles confidence. And the standard is expressed in claims, not lives. A large book of young lives can carry enormous exposure and still generate a thin claim count, which is why block size is a poor proxy for how far to trust a result.

The credibility factor tells you how much weight to give your data. It says nothing about what receives the remaining weight, and that is the decision that actually moves the number.

The complement is where the judgement lives

If Z is 0.6, then 40% of the basis comes from somewhere else. Most reports leave that somewhere else unstated, and the default is the standard table at 100%. That default is a substantive assumption about the portfolio, and it is frequently wrong.

• The standard table unadjusted. Defensible where the book resembles the population the table was built on. Rarely true for a book sold through a single channel.
• The previous basis. Stable and easy to explain, but it compounds. Three years of blending toward last year's answer leaves you anchored to a decision nobody remembers making.
• A related segment in the same book. Often the strongest option and the most work, because it requires showing the segments genuinely share a rate.
• Industry experience. Useful, but the lag is real and mix differences are usually larger than assumed.

Whichever is chosen, the report should say which and why. A basis that documents Z but not the complement has documented the arithmetic and skipped the judgement.

Three ways this goes wrong

Chasing noise. A thin segment moves 15% and the basis follows. The next year it moves back and the basis follows again. Two years of movement, no information gained, and a reporting line that has to explain both.

Anchoring past the evidence. The opposite failure, more common in mature books. Experience moves consistently in one direction for four years, each year individually short of full credibility, and each year the basis holds. Credibility applied one period at a time will systematically miss a trend that is obvious across periods.

Band structures that destroy credibility. Fifteen age bands feels rigorous and often leaves every band with too few claims to say anything. Granularity is not precision. Where the underlying rate is smooth in age, a graduated fit across a coarser structure beats a fine one every time.

What to write down

An investigation that survives review states the exposure basis and period, the claim count as well as the ratio, the full credibility standard and why that standard, the complement of credibility and why that complement, and the resulting basis with the movement from the previous one explained.

That is five sentences. It is also the difference between a number that is correct and a number that is defensible, and only one of those is worth anything when somebody asks how it was arrived at eighteen months later.