20K
Policies
261
Actual Deaths
98.8%
Overall A/E
49.1%
Credibility Z
Section 01
Why Mortality Needs Special Treatment
"You cannot measure mortality risk without first measuring the time each life was exposed to that risk."
— SOA Experience Study Calculations (2024) · Foundational Principle of Mortality Rate EstimationCore Formula
qx = Deaths (d) ÷ Exposed-to-Risk (E)
Numerator and denominator must be defined on the same basis · Full credibility: ~1,082 deaths (90% CI, ±5% margin)
1,082
Full Credibility Deaths
136K
TMI IV Deaths (22.7M records)
d ↔ E
Correspondence Principle
SOA Experience Study Calculations (2024) · TMI IV 2019 (AAJI) — 22.7 million exposure records across 52 companies
Section 02
What Is Exposed-to-Risk?
Exposed-to-Risk (ETR) is the total time — measured in policy-years — during which a group of policyholders was exposed to the risk of death within the observation period. It is the denominator in the mortality rate formula: qx = Deaths / ETR.
Master ETR Formula — Per Policy
ETRi = MAX(0, (MIN(study_end, exit_datei) − MAX(study_start, entry_datei)) / days_in_year)
days_in_year: 365 regular · 366 leap year (2024) · Exit priority: death → lapse → maturity → policy_end → study_end
✓ Initial ETR — for qx
Deaths contribute 1 full year
Deaths contribute 1 full year of exposure regardless of when in the year death occurred. Preferred for qx calculation — TMI IV & SOA standard.
Initial = Central + (1 − tdeath) per death
Central ETR — for μx
Deaths contribute time lived only
Deaths contribute only the time lived before death — a partial-year contribution. Used for force of mortality μx.
Ex(initial) ≈ Ex(central) + ½ · dx (UDD assumption)
Study Period: 1 Jan 2021 – 31 Dec 2025 · ANB = ROUND(|DOB − Entry| / days_in_year)
Section 03
4 Policy Scenarios
Step-by-step ETR calculation for four common policy scenarios — study period 1 Jan 2021 to 31 Dec 2025.
Scenario A · Inforce Throughout
Full Period Active
Entry: 1 Jan 2021 · Exit: 31 Dec 2025
(31 Dec 2025 − 1 Jan 2021) = 1,826 days (incl. 2024 leap)
(31 Dec 2025 − 1 Jan 2021) = 1,826 days (incl. 2024 leap)
ETR = 5.000 yrs — full exposure
Scenario B · New Business
Late Entry Policy
Entry: 1 Jul 2022 · Exit: 31 Dec 2025
(31 Dec 2025 − 1 Jul 2022) = 1,279 days (incl. 2024 leap)
(31 Dec 2025 − 1 Jul 2022) = 1,279 days (incl. 2024 leap)
ETR = 3.504 yrs — partial window
Scenario C · Lapsed
Early Lapse Exit
Entry: 1 Jan 2021 · Lapse: 30 Jun 2023
(30 Jun 2023 − 1 Jan 2021) = 911 days (no leap year)
(30 Jun 2023 − 1 Jan 2021) = 911 days (no leap year)
ETR = 2.496 yrs — lapse censors
Scenario D · Death Claim
Death Exit (Initial ETR)
Entry: 1 Jan 2021 · Death: 15 Mar 2024
Central ETR = 3.204 yrs · Initial ETR adjustment: +0.796
Central ETR = 3.204 yrs · Initial ETR adjustment: +0.796
Initial ETR = 4.000 yrs — death year = full year
Key rule: Only positive ETR contributes to exposure. Exit priority: death → lapse → maturity → policy_end → study_end
Section 04
6 Common ETR Mistakes
ANB vs ALB Confusion
✗ Using Age Last Birthday shifts policies into wrong age bands
✓ ANB = ROUND(|DOB − Entry| / days_in_year) per TMI IV
Death Year Zero Exposure
✗ Assigning zero exposure in death year understates ETR
✓ Initial ETR: death year = 1.000 yr (full year)
Study Boundary Error
✗ Including policies that lapsed before study start
✓ ETR > 0 within [Study Start, Study End] only
Reinstatement Double-Counting
✗ Counting reinstated policies as new entries
✓ Exclude: lapse date → reinstatement date gap
Partial First Year Overstatement
✗ Treating all new business as full-year exposure
✓ ETR = (Exit − Entry) / days_in_year (prorated)
Negative ETR — Missing Guard
✗ Omitting MAX(0,...) allows negative ETR values
✓ ETR = MAX(0, (Exit − Entry) / days_in_year)
Source: SOA Experience Study Calculations (2024) · TMI IV Methodology · Principle of Correspondence
Section 05
A/E Results: Male vs Female
Based on 20,000 policies, 261 deaths, 86,401 policy-year records. Study period 2021–2025. Reference: TMI IV 2019.
96.8%
Male A/E Overall
Within acceptable range (90–110%). However, 60+ M shows 142.4% — review needed for older age band.
102.3%
Female A/E Overall
Within range overall. 60+ F shows 154.6% — review needed. Most other bands within acceptable range.
98.8%
Combined A/E
Portfolio-level A/E within acceptable range. No immediate assumption revision required at aggregate level.
⚠️ Older Ages (60+) — Review Needed:
Male 60+: A/E = 142.4% (79 deaths, Z=27%) · Female 60+: A/E = 154.6% (55 deaths, Z=22.5%). Most credible band — adverse result warrants assumption review.
⚡ Young Ages (20–39) — Low Credibility:
20-29: M=83%, F=139%. 30-39: M=123%, F=86%. Small death counts (4–19 deaths/band) amplify random fluctuation — Z < 14%, results statistically unreliable.
Acceptable range: 90%–110% · A/E > 110%: review needed · A/E < 90%: potential release
Section 06
Credibility Weighting
Credibility Formula — Longley-Cook (1962)
Z = MIN(1, √(Actual Deaths / 1,082))
qx(final) = Z × qx(company) + (1 − Z) × qx(TMI IV)
When experience lacks full credibility, blend it — weight company data by Z, reference table by (1 − Z). The higher Z, the more the company's own experience dominates.
| Age Band | Deaths (M / F) | Z Factor (M) | Z Factor (F) | Recommendation |
|---|---|---|---|---|
| 20–29 | 4 / 4 | 6.1% | 6.1% | Use TMI IV entirely |
| 30–39 | 19 / 8 | 13.3% | 8.6% | Mostly TMI IV |
| 40–49 | 26 / 17 | 15.5% | 12.5% | Mostly TMI IV |
| 50–59 | 35 / 14 | 18.0% | 11.4% | Mostly TMI IV |
| 60+ | 79 / 55 | 27.0% | 22.5% | Blend starts to matter |
| Total Portfolio | 261 deaths | 49.1% | — | Meaningful blend at portfolio level |
Z Thresholds: Z < 10% → Use TMI IV (very low credibility) · Z 10–30% → Mostly TMI IV (partial blend) · Z > 30% → Blend starts to matter · Z = 49.1% at portfolio level — blend is meaningful, but individual bands still mostly TMI IV. Never update by band without credibility check.
Longley-Cook (1962): Full credibility n = 1,082 · SOA (2008): Credibility Methods Applied to Life, Health & Pensions · TMI IV 2019 (AAJI)
Section 07
Mortality Improvement: TMI IV vs TMI III
TMI IV 2019 shows significant improvement over TMI III at older ages — people are living longer. However, younger ages show slight adverse movement due to lifestyle factors.
5.33%
Male Improvement
5.06%
Female Improvement
−52%
Age 60 Rate Drop
+13%
Age 40 Rate Rise
PSAK 117 / IFRS 17 Implication: Current estimates must use up-to-date assumptions. Using TMI III when TMI IV is available may not satisfy the current estimates requirement — assumption update required.
TMI IV 2019 (AAJI) · Age 60 Male: TMI III 0.02100 → TMI IV 0.00999 (↓52%) · Age 40 Male: TMI III 0.00153 → TMI IV 0.00173 (↑slight)
Section 08
Assumption Update Decision
✅ Update Assumption — Act Now
- A/E ratio consistently outside 90–110% for 2+ consecutive years — not random fluctuation
- Credibility factor Z > 50% (~270+ actual deaths) — company experience is statistically dominant
- Financial impact exceeds materiality threshold — dual criteria: data volume AND financial tolerance
- Appointed actuary sign-off obtained — OJK POJK 8/2024 requires actuary accountability
⏳ Wait & Monitor — Observe Further
- Single-year deviation only — could be random volatility; SOA recommends 2–3 years of consistent deviation
- Credibility factor Z < 20% — insufficient data; industry table (TMI IV) should continue to dominate
- Financial impact below materiality threshold — deviation does not meet dual materiality criteria
PSAK 117 / IFRS 17 Routing: Future service assumption changes → adjust the CSM (deferred, released over coverage period) · Past/current service assumption changes → go directly to P&L (immediate impact) · Governance chain: Preparer → Reviewer → Appointed Actuary sign-off required.
OJK POJK 8/2024 · PSAK 117 / IFRS 17 · Nityasa Niscita (Dec 2024) · SOA Experience Study Calculations (2024)
Excel Worked Example — 20,000 Policies
Exact days ETR (365/366) · TMI IV VLOOKUP · A/E by age band × gender · Credibility Z · Blended assumption. Full step-by-step calculation ready to adapt for your own mortality study.
Download Excel File
Episode 2 — Key Takeaways
ETR is the foundation — qx = Deaths / ETR. Use Initial ETR for qx (deaths = 1 full year). Use MAX(0,...) guard. ANB not ALB. Exact days (365/366 for leap years).
A/E results: 98.8% overall — within acceptable range. But 60+ band shows 142–155% — most credible band (Z=22–27%), adverse result warrants assumption review.
Credibility Z = 49.1% at portfolio level — meaningful blend, but individual age bands still mostly TMI IV. Never update by band without credibility check. Full credibility requires 1,082 deaths.
TMI IV vs TMI III — significant improvement at older ages (Age 60: −52%). Using TMI III when TMI IV is available may not satisfy PSAK 117 current estimates requirement.
Update decision requires dual criteria — both statistical credibility (Z > 50%) AND financial materiality must be met. Single-year deviation alone is insufficient. Appointed actuary sign-off required.