Experience study: significance, credibility and contaminated data
Korea Mutual Life is completing its 2024 experience study. The portfolio under review covers 45,000 life-years of exposure on five-year renewable term policies issued through the direct channel, with 210 expected deaths on the 2018 valuation table and 246 observed. Industry mortality has improved about 2% a year since that table was graduated. The pricing team wants to apply the full observed 17% excess to renewal premiums for the channel; the valuation actuary wants to keep the current table; the chief risk officer wants one credibility-weighted adjustment applied portfolio-wide. Splitting the data by smoking status gives 168 observed against 160 expected for non-smokers and 78 against 50 for smokers, but the sub-groups are small. A data audit found that 3% of policies had unknown smoking status coded as non-smoker and that 1,100 life-years from a broker channel were included in the direct-channel extract. The actuary must decide what adjustment, if any, to book.
1. Test whether the observed 246 deaths against 210 expected is statistically significant, and state the assumptions your test relies on.
Read the worked answer
A/E = 246/210 = 1.171, a 17.1% excess.
Treating deaths as Poisson with mean equal to the expected 210, the standard error of the observed count is sqrt(246) = 15.7 (using the observed count, which is the conventional variance-stabilised form). A 95% interval is 246 +/- 1.96 x 15.7 = (215.3, 276.7). Dividing by 210: (1.025, 1.318).
The interval excludes 1.0, so the excess is significant at the 5% level; a one-sided test against the alternative of a mortality excess is stronger still.
Assumptions worth stating explicitly, because they are where the test can fail:
- Poisson counts require independent lives. Term policies sold through one channel in one campaign are not obviously independent - regional or occupational clustering inflates the true variance and narrows the apparent significance.
- The expected 210 is treated as known. It is not: the table was graduated in 2018 and the company has seen about 2% a year improvement since. If exposure-weighted improvement of roughly 10% is applied to the expected, expected falls to about 189 and A/E rises to 1.30 - the excess is larger, not smaller, but the benchmark changes.
- This is one of many comparisons. Testing channels, products and smoking groups simultaneously at 5% will produce false positives by construction.
2. Compute a credibility-weighted adjustment using standard limited-fluctuation credibility, and show how the choice of standard changes the answer.
Read the worked answer
Full credibility standard (number of deaths needed for the observed A/E to be within +/-5% of the true value with 90% probability):
n_full = (1.645 / 0.05)^2 = 1,082 deaths.
Partial credibility: Z = sqrt(246 / 1,082) = sqrt(0.2274) = 0.477.
Credibility-weighted A/E = Z x (A/E observed) + (1 - Z) x 1.0 = 0.477 x 1.171 + 0.523 x 1.0 = 0.559 + 0.523 = 1.082.
So the indicated adjustment is about +8%, not +17%.
Sensitivity to the standard: using 95% probability and +/-5% gives n_full = (1.96/0.05)^2 = 1,537, Z = 0.400, and a weighted A/E of 1.068 - about +7%. The answer moves by roughly one percentage point, which is small relative to the data-quality issues below, so the choice of standard is not where the argument should be had. What matters is that the credibility weight reflects the volume of deaths, not the volume of policies: 45,000 life-years sounds large but produces only 246 deaths.
Both the full and the weighted figures should be shown to the pricing team, because the gap between +17% and +8% is exactly the difference between a repricing exercise and a routine assumption review.
3. Given the data audit findings, what adjustment would you actually book, and what would you require before the next review?
Read the worked answer
Book the credibility-weighted +8% as a prospective adjustment to the best-estimate assumption for the direct channel only, applied from the next valuation date, and disclose it as a change in estimate with the credibility calculation attached. Do not book +17%.
Why not the pricing team's figure:
- Contamination. 1,100 broker life-years sit inside a direct-channel extract. If broker business has different mortality - different occupations, different sum-assured bands - the channel A/E is measuring the wrong population. Recompute after removing them; if the direct-channel A/E falls materially, even +8% is too high for this channel.
- Smoking misclassification. Three percent of unknown status coded as non-smoker biases the split in a known direction: the non-smoker A/E (1.05) is overstated and the smoker A/E (1.56) is understated, or vice versa depending on who the unknowns really are. A 56% smoker excess on 50 expected deaths is 28 deaths above expected - within the noise of a small cell, and quite possibly an artefact.
- Trend. The 2018 table predates roughly 10-12% of cumulative improvement. Part of the observed excess is table staleness, which is a valuation-basis issue affecting all channels, not a direct-channel pricing issue. The two effects should be separated before either is booked.
Before the next review: require a reconciled policy-level extract with smoking status completeness above 98%, a documented treatment rule for unknowns (do not code them as non-smoker by default), separate exposure for each channel, and a test for clustering. Until then, keep the valuation table, add an explicit small provision for the identified deterioration, and do not reprice renewal premiums on a number the data cannot support.