Term Reserve Release after Favorable Mortality
A life insurer has a closed block of 18,000 ten-year renewable term policies with an average face amount of 300,000. The current gross premium reserve is 54 million. Mortality experience over the last three years shows an actual-to-expected ratio of 0.58, based on 420 expected deaths. The block is reinsured under yearly renewable term; the current reinsurance rate is guaranteed for two more years, after which it resets to the reinsurer's then-current table. The reinsurer has signalled a 15% rate increase. Current lapse is 4%, but the insurer expects a 20% shock lapse at the reset because premiums will rise. The CFO wants to release 9 million of reserve, citing the favorable mortality. The appointed actuary must decide whether to support the release.
1. Evaluate the credibility of the 0.58 A/E ratio. What does the 420 expected deaths imply about the confidence you can place in the mortality result?
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The observed deaths are about $0.58 \times 420 \approx 244$, versus 420 expected. Under a Poisson approximation, the standard deviation of expected deaths is $\sqrt{420}\approx 20.5$, so the shortfall is roughly 8.6 standard deviations. That is statistically unusual, but statistical significance is not the same as full credibility for setting an ultimate assumption. The result is based on only three years and 420 expected deaths, which is a moderate exposure for a mortality study. It may reflect underwriting mix, claims lag, reinsurance effects, or temporary selection.
A credibility-weighted approach is appropriate. Give the experience partial credibility and combine it with the pricing table and any industry or reinsurer data. Do not extrapolate a 0.58 ratio directly into the valuation assumption without an explicit margin for estimation error and future deterioration.
2. Explain how the YRT reset and shock lapse interact with the proposed reserve release, including the direction of each effect.
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The YRT reset is an adverse development. A 15% increase in reinsurance cost raises future net premiums or reduces future margins, which generally increases the gross premium reserve if premiums cannot be raised enough. The favorable mortality result does not eliminate this contractual reset risk.
The 20% shock lapse has two effects. A lapse releases the insurer from future obligations and can release positive term reserves, which improves current reserves. But at a premium reset, healthier policyholders are more likely to lapse, leaving a worse mortality mix. That anti-selection raises future mortality and can offset the reserve release. The net effect on the reserve is therefore ambiguous and must be modeled, not assumed to be favorable.
The CFO's proposed 9 million release is 16.7% of the 54 million reserve. Supporting that full amount from a partial-credibility mortality result while ignoring the reset and anti-selection would be aggressive.
3. Recommend a reserve position and two conditions for any release.
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Do not support the full 9 million release. Recognize the credible portion of the favorable mortality, but hold an explicit margin for the YRT reset, anti-selection, and estimation error. A partial release may be defensible if it is based on a credibility-weighted mortality assumption and a gross premium valuation that reflects the 15% reinsurance increase.
Two conditions: first, model a stress scenario with a 15% YRT increase and a 20% shock lapse, with healthier lives lapsing at a higher rate, and confirm the reserve remains adequate. Second, document the release and obtain peer review or audit committee review before filing. If the CFO insists on the full release without that support, the appointed actuary should not sign the reserve opinion.