How does longevity risk pooling through annuities work, and what are 'mortality credits'?

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AcadiFi · Accepted Answer

Longevity risk pooling is the mechanism by which annuity providers can offer higher guaranteed income than self-insurance because they pool the mortality experience of many individ...

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**Self-insurance vs. annuity:**

Suppose Robert Calloway, age 65, has $1M and needs $55,000/year in real terms. If he self-insures (manages his own portfolio), he must plan for the possibility of living to 100 — a 35-year horizon. At a 4% real return, he can safely withdraw only ~$51,000/year to avoid depletion.

With an annuity, the insurance company only needs to fund the average life expectancy of its pool (~20 years for a 65-year-old male), plus a reserve margin. The premiums of those who die at 72 fund the payments to those who live to 95. This pooling allows the annuity to pay ~$62,000/year — 21% more than self-insurance.

**Mortality credit calculation:**

The mortality credit is the additional return earned by annuity holders because they forfeit their remaining principal upon death. It can be approximated as:

*Mortality Credit ≈ q(x) / (1 - q(x))*

Where q(x) is the probability of death at age x. At age 65, q(65) ≈ 1.2%, yielding a mortality credit of ~1.2%. By age 85, q(85) ≈ 7.5%, producing a mortality credit of ~8.1% — a substantial return enhancement.

\`\`\`mermaid
flowchart TB
    A[1000 Annuitants Age 65] --> B[Year 1: ~988 Survive]
    B --> C[Deceased Members' Capital Redistributed]
    C --> D[Survivors Receive Enhanced Payments]
    D --> E[Year 2: ~975 Survive]
    E --> F[Mortality Credits Increase with Age]
    F --> G[At Age 85: Only ~550 Survivors]
    G --> H[Mortality Credit ~8% per Year]
\`\`\`

**Why portfolios cannot replicate mortality credits:**

Your study partner's argument fails because a self-managed portfolio must reserve capital for the maximum lifespan. An annuity pool releases capital from deceased members, creating a return source that no investment strategy can replicate. This is a pure insurance mechanism, not an investment return.

For CFA Level III, mortality credits are the key economic justification for annuitizing a portion of retirement wealth, particularly for essential spending. The optimal strategy typically combines partial annuitization (for the spending floor) with a managed portfolio (for discretionary spending and legacy goals).

How does longevity risk pooling through annuities work, and what are 'mortality credits'?

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