Experience Analysis: How Actuaries Compare Actual Results to Assumptions

In short: Experience analysis compares actual outcomes — deaths, lapses, claims — to the assumptions embedded in pricing and valuation models. The A/E ratio (Actual / Expected) is the core metric: above 100% is adverse for most insurance risks, below 100% is favourable. Where data volumes are too small to rely on own experience alone, credibility weighting blends the observed A/E with an industry benchmark to produce a more stable estimate. The findings feed directly into assumption updates, pricing reviews, and embedded value adjustments.

Every actuarial model is built on assumptions: about how many policyholders will die, how many will lapse, what expenses will cost, how many claims will be reported late. Those assumptions are calibrated at the point of pricing — using industry data, historical portfolio experience, and actuarial judgement — but the world does not stay still. Mortality rates improve over time. Lapse behavior changes with economic conditions. Expense inflation runs above or below target. Claims frequency in a particular liability class is affected by legislative changes.

Experience analysis is the actuarial discipline of systematically comparing actual experience to assumed experience, identifying where assumptions are drifting from reality, and feeding those findings back into models and pricing. Without it, a model that was correctly calibrated three years ago gradually becomes a model that systematically misprices risk — in either direction.

This post covers the A/E ratio, the mechanics of building an experience analysis in Excel, credibility theory, and the structured process for investigating adverse deviations.

The A/E Ratio: The Foundation of All Experience Analysis

The Actual to Expected ratio is defined as:

A/E Ratio = Actual events observed / Expected events (from model assumption)

An A/E ratio of 100% means experience exactly matched assumptions. Above 100% means more events occurred than expected; below 100% means fewer.

The interpretation of whether a deviation is adverse or favourable depends on the type of risk:

This asymmetry is worth emphasising because analysts sometimes assume that “more than expected” is always bad. For an annuity provider, higher-than-expected mortality is actually good news.

Calculating the Expected: Exposed to Risk

The denominator of the A/E ratio is the “Expected” — which requires calculating the central exposed to risk for the period under review.

For a mortality experience analysis, the exposed to risk for a specific age-band is the total number of life-years at risk during the observation period. If 1,000 policyholders were aged 50–54 throughout the year, the exposed to risk is 1,000 life-years. If 200 of them left mid-year (by lapsing or dying), they contribute half a life-year each on average — so their contribution is 100 life-years.

Expected Deaths (age band x) = Central Exposed to Risk (age band x) × qx (from standard table)

In Excel, the calculation requires a policy-level data extract with:

• Date of birth (to derive age band)
• Policy start date
• Policy end date or current date (whichever is earlier)
• Indicator for whether the exit was death, lapse, or maturity

Each policy’s contribution to the exposed to risk is the number of days it was in force during the observation year, divided by 365.

Building the Experience Analysis in Excel

A well-structured experience analysis has four core tables:

Table 1: Exposure and actual claims by age band and gender

The aggregate A/E of 115% means actual mortality across the book is 15% heavier than the standard table. This could reflect adverse selection (the book is attracting higher-risk lives), a change in the mix of smoker versus non-smoker policyholders, or simply statistical fluctuation.

Table 2: Trend analysis — A/E by calendar year

The spike in 2021–2022 followed by a return towards 110–115% in subsequent years is consistent with excess mortality from the COVID-19 pandemic. A trend analysis distinguishes pandemic-era anomalies from structural deterioration in the book — important for deciding whether the pricing basis needs a permanent adjustment or a one-off allowance.

Table 3: A/E by distribution channel

Segmenting by distribution channel is essential for understanding where adverse experience is concentrated. A 115% aggregate A/E might be driven entirely by direct-channel business (which may attract less well-underwritten lives) while IFA-distributed business runs at 96%.

Table 4: A/E by policy year (duration)

Mortality experience often varies by policy duration — very new policies (years 1–2) sometimes show lower mortality because underwriting excluded the highest-risk lives; policies in years 5–10 may show higher mortality as the underwriting selection effect wears off. This duration analysis informs both the underwriting process and the product design.

Credibility Theory: When Your Own Data Isn’t Enough

With small volumes of data, the A/E ratio is not reliable. If you have only 20 observed deaths in an age band and the expected was 18, the A/E of 111% could easily be statistical noise — you cannot distinguish genuine adverse experience from a random bad year.

Credibility theory provides a principled way to blend own experience with a benchmark:

Credibility-weighted rate = Z × Own A/E ratio + (1 − Z) × Benchmark A/E

Where Z is the credibility factor, ranging from 0 (no credibility — use the benchmark entirely) to 1 (full credibility — use own experience entirely).

The most common credibility formula (Bühlmann-Straub for Poisson-distributed claims):

Z = n / (n + k)

Where n is the observed claim count and k is a credibility parameter (often estimated at around 50 for mortality experience, though this varies by context).

For full credibility (Z = 1.00), you need a sufficiently large claim count. The classical actuarial standard for full credibility at a ±5% precision level with 90% confidence requires approximately 1,082 claims. For most individual insurer analyses, this threshold is reached only at the most aggregate level — at the age-band or channel level, credibility weighting is typically required.

A practical example: an insurer observes 85 deaths in the 40–49 age band against 78 expected (A/E = 109%). With k = 50:

Z = 85 / (85 + 50) = 85 / 135 = 0.63

Credibility-weighted A/E = 0.63 × 109% + 0.37 × 100% = 106.7%

Rather than accepting the raw 109% as the assumption update, the actuary would propose a 6.7% loading over standard mortality rates for this segment — a more stable, less reactive response to a single year’s data.

Investigating Adverse Experience

When an A/E ratio exceeds a trigger threshold — typically a 10–15 point adverse deviation or a statistically significant result — a formal experience investigation is required. A structured investigation follows four steps:

Step 1: Verify data quality. Before concluding that experience is genuinely adverse, confirm that the data feeding the analysis is complete and clean. Common errors include: late-reporting deaths that inflate a single year’s actual count (and will be absent the following year), data extract issues that misalign the observation period, or incorrect classification of exits (lapses coded as deaths or vice versa).

Step 2: Segment and isolate. Decompose the aggregate A/E into the smallest meaningful subgroups — age band, gender, channel, product, policy year, sum assured band. This identifies whether the adverse experience is broad-based (a systematic pricing error) or concentrated in a specific segment (a quality-of-business issue from one distribution partner or product variant).

Step 3: Benchmark externally. Compare the insurer’s A/E to available industry data from the CMI (for life and annuity business) or Lloyd’s market data (for general insurance). If the insurer’s A/E is running at 115% against the industry’s 105%, the residual 10-point excess is specific to this book and requires explanation. If both the insurer and the market are running at 115%, the standard table is simply out of date.

Step 4: Quantify the pricing impact and recommend an assumption change. The output of the investigation is an actuarial recommendation — either maintain the current basis with a monitoring plan, or update the pricing and valuation A/E factor. For a mortality A/E update from 100% to 110%: recalculate the premium rates that would have been charged, assess the impact on embedded value (an adverse mortality variance in the EV movement analysis), and set out the annual monitoring cadence.

Feeding Experience Back into the Model

The experience analysis cycle runs annually (or more frequently for large portfolios):

1. Observe actual experience → 2. Compare to expected → 3. Calculate A/E ratios
         ↑                                                           ↓
6. Monitor updated basis                             4. Credibility-weight with benchmark
         ↑                                                           ↓
5. Update pricing/valuation assumption           →  Formal investigation if A/E > trigger

The updated assumption feeds three places: the pricing model (new policies are rated using the revised qx or lapse basis), the valuation basis (the reserve calculation and embedded value use updated assumptions), and the experience variance line in the EV movement analysis (the current-year deviation from assumption is quantified explicitly for investor disclosure).

An insurer that performs rigorous experience analysis and updates its assumptions promptly is far less likely to face sudden large adverse assumption changes in one period — the kind of “reserve strengthening” announcement that tends to cause sharp share price reactions for life insurers. Consistent, incremental updates based on credible data are the hallmark of actuarial discipline.

Key Takeaways

• The A/E ratio (Actual / Expected) is the core metric of experience analysis. It measures whether observed events are above or below the model assumption. Whether above 100% is adverse or favourable depends on the risk type.
• The denominator “Expected” is calculated by multiplying the central exposed to risk (life-years at risk in the period) by the rate assumption from the standard table.
• Build the experience analysis as a four-table structure: aggregate A/E by segment, trend over time, A/E by distribution channel, and A/E by policy duration.
• Credibility weighting is essential when claim volumes are small: credibility-weighted A/E = Z × own experience + (1 − Z) × benchmark. Full credibility requires approximately 1,082 claims at the standard actuarial threshold.
• A formal experience investigation is triggered when A/E deviates by more than 10–15 points. The four steps are: data verification, segmentation, external benchmarking, and pricing impact quantification.
• Updated assumptions feed the pricing model, the valuation basis, and the experience variance line in the EV movement analysis.

Practice

A life insurer observes the following mortality experience over a one-year period for the age band 45–54 (male, non-smoker, term assurance): 35,000 life-years of exposure, 98 actual deaths. The standard AM92 table implies an A/E of 100% for this segment. Using the AM92 male qx rates (age 45 = 0.00280, 46 = 0.00315, 47 = 0.00354 — assume evenly spread exposure across ages), calculate: (1) expected deaths; (2) the raw A/E ratio; (3) the credibility-weighted A/E using Z = n/(n+50). Then, if the pricing basis currently uses 95% of AM92 (a 5% mortality improvement loading), calculate the revised A/E relative to the current pricing basis and comment on whether an assumption review is warranted.