Milevsky Ch. 2: The Gompertz Insight — Why Mortality Risk Compounds and Intuition Fails

"Mortality is not linear. It is exponential, and human beings have never been good at exponential." — the practical consequence of Benjamin Gompertz's 1825 observation

Investment Background

In 1825 a British actuary named Benjamin Gompertz noticed something about death that has held up for two centuries across almost every human population ever measured: after early adulthood, the rate at which people die does not rise steadily. It rises by a roughly constant percentage each year, which means it compounds.

The practical version of that observation is a rule of thumb: adult mortality risk roughly doubles every eight years. At 55 the chance of dying within the year is well under 1%. At 65 it is around 1.3%. At 75 it is near 3%. At 85 it is around 8%. At 95 it is above 20%.

Investors understand compounding perfectly well when it applies to money. Everyone nods at the story of a penny doubling for thirty days. But the identical structure applied to mortality produces almost no intuition at all, and the reason matters: the doubling is happening to a number that starts very small. For twenty years it feels like nothing is happening. Then it stops feeling like nothing very abruptly.

Milevsky's insight is not the biology. It is what the compounding does to decisions. Because mortality is exponential rather than linear, the same financial choice — how much to withdraw, whether to buy guaranteed income, how much equity to hold, whether to keep a long-term care policy — has an entirely different answer at 85 than at 65, and the change between them is not gradual. The industry's habit of writing one plan at retirement and reviewing it annually against markets, rather than against age, is a direct casualty of this.

The Wall Street Translation

The Decision: Which Risk Dominates Right Now?

At every moment in retirement you are exposed to two competing hazards, and they move in opposite directions with age:

Age	Annual mortality risk	Which risk dominates	What that implies
60–70	~1%	Longevity and sequence risk	Long horizon, inflation is the enemy, keep growth assets, delay guaranteed income
70–80	~2–4%	Balanced	Sequence risk fading, mortality credits becoming meaningful
80–90	~5–10%	Mortality risk	Horizon short, pooled income cheap, complexity is the enemy
90+	15%+	Mortality dominates completely	Simplify ruthlessly, spend, guaranteed income is highly efficient

The mistake in each direction is symmetric and both are common.

The young-retiree mistake: acting old. A 63-year-old with a possible 35-year horizon moves to 30% equities because "I'm retired now, I should be conservative." But at 63 mortality risk is around 1% a year — essentially zero — while inflation risk over 35 years is enormous. At 3% inflation, a dollar of spending power becomes 35 cents in 35 years. The dominant hazard at 63 is not dying; it is living a long time with a portfolio that cannot outrun prices. De-risking early is the expensive error.

The old-retiree mistake: acting young. An 87-year-old maintaining a 60/40 portfolio, a rebalancing schedule, a tax-loss-harvesting routine and a "legacy horizon of 20 years" is running a plan calibrated to a hazard rate one-eighth of the one they actually face. At 87 the odds of dying within five years are close to one in three. Holding equities to fund a spending stream that has a one-in-three chance of ending within five years is not growth investing; it is unnecessary variance in the years when a loss can no longer be recovered. Worse, it is variance being managed by someone whose capacity to manage it is statistically declining.

The Counterintuitive Consequence: Guaranteed Income Gets Cheaper With Age

Here is the result that most reliably surprises people. Because mortality compounds, the amount of capital required to buy a dollar of lifetime income falls sharply as you age — and it falls much faster than most retirees expect.

A rough sense of the shape: to buy $10,000 a year of nominal lifetime income, a 65-year-old might commit somewhere around $150,000–$165,000 at recent rate levels. A 75-year-old needs closer to $110,000–$125,000. An 80-year-old, closer to $95,000–$105,000. The exact figures depend entirely on interest rates, the insurer, the state and the product features, but the direction is structural, not a quote artifact.

The practical implication runs against the sales pitch. The annuity industry pushes products at 60 and 65 because that is when people have the largest liquid balance and the most anxiety. But the mortality credit — the extra return that comes from pooling with people who die before you — is small at 65 and large at 80. Buying pooled income too early means paying for decades of insurance company fees and giving up flexibility during exactly the years when your health, your spouse's health, and your spending pattern are still uncertain.

Why Intuition Fails Specifically Here

Three cognitive failures stack up. First, people anchor on life expectancy — a single number — and never form a picture of the hazard rate rising underneath it. Second, exponential growth from a small base is invisible for a long time and then sudden; the same reason people misjudge epidemics. Third, and most human: nobody wants to sit down and think carefully about their own conditional probability of death within twelve months. The topic is genuinely unpleasant, so the plan gets built on the one number that lets you avoid thinking about it.

Nothing in this changes the portfolio core. Through all of it, the growth engine remains a broad, low-cost, globally diversified index portfolio. What changes with age is not the quality of the core but its job description: at 65 it is funding thirty-plus years of inflation-exposed spending, and at 88 it is funding a much shorter and much more uncertain claim, alongside income that does not depend on markets at all.

Execution Rules

1. Put an age-based review on the calendar, not just a market-based one. Formally revisit asset allocation and income structure at 70, 75, 80 and 85. Markets are what most reviews discuss; age is what actually changed the problem. A plan untouched since 65 is running on assumptions that expired.

2. Do not de-risk at retirement date. De-risk at hazard-rate milestones. Retiring at 62 with a 35-year joint horizon is not a reason to cut equities to 30%. If you are covering essential spending from Social Security and other lifetime income, a 60/40 or even 65/35 core is defensible well into the seventies. The real de-risking trigger is a shortening horizon, not a birthday party with a cake.

3. Delay pooled income purchases into the seventies unless the floor is unsafe now. Because mortality credits are small at 65 and material at 78, the efficient window for buying guaranteed income for most healthy retirees is the mid-seventies to early eighties, not the mid-sixties. The exception is a household whose essential spending is uncovered today — that gap is an emergency and should be fixed immediately regardless of pricing efficiency.

4. Simplify one layer at a time, on a schedule. Consolidate accounts at 75. Eliminate any strategy requiring quarterly decisions at 80. Put remaining assets in two or three broad funds by 85. Sign a durable power of attorney and give a trusted person visibility long before you think you need it. This is not defeatism; it is the same logic as reducing single-stock risk — you are removing a failure mode you cannot personally underwrite.

5. Underwrite your own hazard rate honestly, in both directions. Smoking, uncontrolled diabetes, advanced cardiac disease and obesity move you meaningfully up the mortality curve; non-smoking, normal weight, exercise and higher income and education move you down. Get an actual number from a reputable longevity calculator rather than an impression from family anecdotes, and revisit it after any major diagnosis.

Retirement Application

Consider two retirees with identical $1.1 million portfolios and identical $45,000 of Social Security.

Ellen, 64, non-smoker, good health. Her annual mortality risk is roughly 0.9%. Her joint horizon with her husband runs into the mid-nineties. Her dominant enemy is inflation over three decades. The correct posture is a growth-oriented, low-cost indexed core — perhaps 60–65% global equity — a two-year cash buffer to survive a bad sequence without selling into it, no annuity purchase yet, and a plan to delay Social Security to 70 to buy the cheapest inflation-linked lifetime income available. She should be spending more than she thinks, not less.

Robert, 86, widower, mild cardiac history. His annual mortality risk is close to 9% and his median remaining horizon is around five to six years. His dominant enemy is not inflation; it is complexity, cognitive risk and the possibility that a bad market year forces an ugly decision he is no longer well positioned to make. The correct posture is a much simpler portfolio, a larger cash and short-bond sleeve covering three to four years of spending, a consolidated account structure, and permission to spend meaningfully more than 4%. If he still had a gap in essential spending, this is the age at which pooled lifetime income is genuinely efficient — mortality credits are large and the capital required is far lower than it would have been at 65.

The two are not different because of risk tolerance, wealth, or personality. They are different because one has a hazard rate ten times the other's.

Risk Management

• The compounding runs both ways and the middle is where it bites. Between 70 and 80 the hazard rate roughly doubles, which is exactly the decade most people leave their plan untouched. Set an explicit review at 75.
• Do not treat a low hazard rate as permission for concentration. Being 63 with a long horizon justifies equity exposure; it does not justify a single stock, a leveraged fund, or an unindexed active manager charging 90 basis points. The long horizon argument only works for the diversified core.
• Cognitive risk rises with the same curve. Financial decision-making quality peaks around the mid-fifties and declines measurably after 75; confidence does not decline with it. Build the simplification into the plan while you are the one making the decision.
• A health shock resets everything at once. A serious diagnosis moves you far up the mortality curve overnight and changes the correct answer on Social Security timing, annuity purchase, Roth conversions and spending rate simultaneously. Treat it as a trigger for a full plan review, not just a medical event.

What This Chapter Cannot Do

This chapter cannot give you your personal mortality curve. Population tables and online calculators produce a reasonable estimate, but individual variation is enormous and no model captures the diagnosis you have not received yet.

It also cannot resolve the bequest question. Everything above is framed around funding your consumption. A retiree who genuinely intends to leave a substantial estate has a longer effective horizon than their own mortality curve implies, and should weight growth assets accordingly. That is a legitimate objective, not an error — but it must be stated explicitly and funded deliberately, rather than arrived at by accident through chronic underspending.

Finally, none of this displaces the index core. Age changes the mix between market-dependent and market-independent money. It never argues for replacing broad, low-cost, diversified holdings with expensive complexity.

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Key Takeaway: Mortality risk doubles roughly every eight years, so the plan you wrote at 65 is calibrated to a hazard rate one-eighth the size of the one you face at 89. De-risk by hazard-rate milestone rather than by retirement date, delay pooled lifetime income into the seventies when the mortality credit is actually large, and simplify deliberately while you are still the person making the decision.