Annuity

An annuity converts a lump sum into an income that lasts as long as you do. Hand over the capital, receive a payment every month until death — whether that is next year or in forty years.

Almost every complaint about annuities comes from judging them as investments. They are not investments; they are insurance, and the risk they insure is genuinely uninsurable any other way:

• Longevity risk — the risk of living a long time and running out of money — cannot be diversified by one person. You only get one life.
• An insurer pools thousands of lives. Individual lifespans are wildly uncertain; the average across a large pool is predictable. That is the entire product.

The consequence is the mortality credit: those who die early subsidise those who live long. That cross-subsidy lets an annuity pay more than a portfolio drawn down safely could — and it is why no investment strategy replicates one.

The main variants

• Level — a fixed nominal payment forever. Highest starting income, and inflation eats it: at 3% inflation, half the purchasing power is gone in 24 years.
• Escalating / index-linked — payments rise with inflation or a fixed percentage. Starts materially lower and protects the thing that actually matters over a thirty-year retirement.
• Joint life — continues to a surviving spouse, usually at a reduced rate. Lower income, two lives covered.
• Guarantee period — pays for a minimum number of years even on early death. Reduces the "die early, lose everything" fear, at a cost.
• Deferred / longevity annuity — bought at 65, starts at 85. Very cheap because most buyers will not reach the start date, and it insures precisely the tail that ruins drawdown plans.
• Enhanced — a higher rate for health conditions or smoking that reduce life expectancy. Frequently unclaimed by people entitled to it.

What determines the rate

Pricing: mortality-weighted discounting

The fair value is the discounted stream of payments, each weighted by the probability of surviving to receive it:

• \({}_{t}p_x\) is the survival probability from a mortality table, projected forward for expected improvement — the assumption that has cost insurers the most over the past thirty years.
• \(y_t\) is the yield on the backing portfolio. Because \(a_x\) is a long-duration annuity factor, annuity rates track long bond yields almost mechanically. This is the same DV01 arithmetic as the swap calculator.

The risks the insurer runs — and hedges

• Longevity risk: everyone living longer than projected. Systematic, undiversifiable within the pool, and increasingly transferred through longevity swaps to reinsurers and capital markets.
• Reinvestment and duration risk: the liability runs decades beyond the available bond market. Matched with long government bonds, infrastructure and swaps — the same liability-driven machinery that broke down in the 2022 LDI crisis.
• Selection risk: voluntary annuity buyers live longer than the general population, because people who expect to live long buy them. Pricing must assume this, which makes annuities look poor value to anyone in average health — a genuine market failure driven by information, not by insurer margin.

Why the economics look bad and the decision may still be right

Judged as a bond, an annuity is unattractive: no liquidity, no residual, and often nothing for heirs. Judged as insurance, the comparison changes — an annuity removes the single risk that no drawdown strategy can remove, and it removes it from the tail rather than the average. Research on retirement income repeatedly finds partial annuitisation — covering essential spending, leaving the rest invested — dominates both extremes. That is an academic finding about structures, not a recommendation about anyone's circumstances.

The formulas above are standard textbook formulations, simplified for teaching. They explain the mechanism — they are not a valuation tool, and they will not reproduce a dealer’s price.