Single-premium deferred annuity: basis change on a closed block
Hanbit Life wrote a single-premium deferred annuity for a 65-year-old male: premium 200,000,000 KRW, five-year deferral, lifetime income with a 10-year certain period, and 3,200 policies still in force. Pricing used a valuation rate of 2.75%, acquisition expenses of 3% of premium, a profit margin of 5% of premium, and a deferred annuity factor of 12.60 per 1 KRW of annual income. Two years later three things have happened: the company's own annuitant experience shows mortality 15% lighter than the pricing table, the supervisory valuation rate is being cut to 2.25%, and a competitor is offering roughly 5% more annual income on identical terms. The chief actuary's best-estimate assumption still contains no mortality improvement. The reserving team proposes strengthening with a 12% improvement scale applied from the valuation date; the pricing team argues no change is needed because the product is closed to new business and the reserves are 'already conservative'.
1. Reproduce the original annual income and test whether the competitor's 5% higher income is achievable on a comparable basis.
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Premium available for benefits = 200,000,000 x (1 - 0.03 - 0.05) = 184,000,000 KRW.
Annual income = 184,000,000 / 12.60 = 14,603,000 KRW.
The competitor at +5% pays 15,333,000 KRW, which implies the same 184m premium divided by a factor of 12.00 - about 4.8% below Hanbit's 12.60.
Is 4.8% plausible from basis alone? The duration of a lifetime annuity deferred five years and entered at 65, with a 10-year certain floor, is roughly 13-14. A 25 bp higher valuation rate is worth about 3.3-3.5%. Fifteen percent lighter annuitant mortality is worth roughly 5-8% on a life annuity factor, because the value is concentrated in the years where q is largest. Together that is 8-12%, comfortably more than the 4.8% required.
So the competitor is not necessarily buying market share at a loss; it may simply be pricing on a correct mortality basis and a higher discount rate. The useful conclusion for Hanbit is not 'match the price' but 'the 12.60 factor embeds two assumptions we now know are wrong'. If that same factor reserves the closed block, the block is under-reserved; if it only prices new business, Hanbit is quoting against firms with a lighter basis and will lose the healthy lives that make annuities profitable.
2. Quantify the direction and rough magnitude of the reserve strengthening from 15% lighter mortality and a 50 bp lower valuation rate, and advise whether and how it should be booked.
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Both changes raise the liability.
- Valuation rate: duration x yield change = about 14 x 0.50% = 7% (slightly less after convexity).
- Mortality: 15% lighter adds roughly 5-8% to the factor at these ages.
- Compounded: 12.60 x 1.07 x 1.065 is approximately 14.4, i.e. about +14%.
Per policy: 14.603m x (14.4 - 12.60) is approximately 26m KRW. On 3,200 policies that is roughly 84 billion KRW of additional reserve - material enough for board disclosure and for discussion with the FSS.
The pricing team's objections fail on their own terms. A supervisory valuation-rate cut is mandatory, not a matter of judgement. And 'closed to new business' is irrelevant to reserving: the reserves exist precisely for the policies still in force, which are the lives now surviving longer. A conservatism margin embedded at issue does not relieve the company of holding a current best-estimate assumption plus a separately identified risk adjustment.
Recommendation: recognise both changes as a change in estimate at the current valuation date, with no amortisation and no offset against future planned profits. Disclose the split between the rate effect (external, non-discretionary) and the mortality effect (experience-driven) so the board can see which part is a genuine deterioration in the block's economics.
3. The chief actuary adds that the shorter-term concern is anti-selection. Explain the mechanism in this product and what can and cannot be done about it.
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Annuities are bought by people who expect to live long. There is no medical underwriting on a single-premium deferred annuity of this size in the Korean retail market, so the people who decline cover are precisely those with impaired health, and the book's mortality converges to a light, self-selected population. Experience 15% lighter than a table graduated six years earlier is consistent with selection plus improvement, not with a table error.
The mitigation available is limited by contract. For in-force policies the income cannot be repriced and the guaranteed terms cannot be revisited - the 3,200 policies carry a contractual liability, which is exactly why the reserve strengthening is not optional. Levers that remain: reflect selection and improvement explicitly in the best-estimate assumption; review the deferral period and the certain-period design for future products; and adjust commission structures that reward volume in a product where volume itself worsens the mortality basis.
The important discipline is to avoid the two symmetrical errors - assuming the 15% gap is pure noise and leaving the basis unchanged, or extrapolating 15% into a permanent 2%-a-year improvement scale with no evidence. A 12% improvement scale applied once, with a review date, is defensible; the same scale applied indefinitely is not.