Nature's admonition

In 1738, at the Imperial Academy in St Petersburg, Daniel Bernoulli published a solution to a puzzle his cousin Nicolas had mailed him years earlier. The puzzle was a coin-toss game with infinite expected value that no sane person would pay more than a few ducats to enter. Bernoulli's answer was that the second ducat is worth less to you than the first, and the thousandth less still, so the value curve bends as it rises. He described that bend as nature's admonition to avoid the dice altogether.

Mark Spitznagel, who runs a fund built entirely around hedging catastrophic tails, keeps returning to that line. His reading is harsher than the textbook one. Even an absolutely fair game can be exceedingly unfair to the person playing it, because you do not experience the average outcome across a thousand parallel lives. You experience one path, in sequence, with your capital compounding multiplicatively along it. Lose 50 percent and the arithmetic mean does not care. Your path does.

The interesting part is that the mathematics was already there in 1738 and we still ignore it. Every quarter someone produces a table of expected returns and a Sharpe ratio and calls it risk management. The table has no column for the ordering of events. Ordering is the whole game.

And that is when the numbers apply at all. For the decisions that actually shape a life; whether to have children, whether to move countries, who to marry, the spreadsheet is theatre with a rounding error at the bottom. Russ Roberts works this out at length in Wild Problems: A Guide to the Decisions That Define Us, and the uncomfortable conclusion is that the calculation was never the hard part. Bernoulli's dice at least had known faces.

The questionnaire that ends careers

Down a corridor at the University of Pennsylvania, Jonathan Baron, a psychologist, has an office next to Philip Tetlock's. Baron built a short test for something he calls active open-mindedness. It is not clever. You are asked whether you agree with statements like: changing your mind is a sign of weakness. Intuition is the best guide to making decisions. It is important to persevere in your beliefs even when evidence is brought against them. It is more useful to listen to those who disagree with you than to those who agree.

Tetlock ran the world's largest forecasting tournament and then went looking for what separated the people who kept winning. Credentials did not do it. Access to classified material did not do it. The superforecasters, disproportionately, scored high on Baron's little questionnaire.

Which tells you the skill is not analytical. It is temperamental. The ability to hold a position loosely enough to drop it is a character trait wearing an intellectual costume.

Notice what the test is really measuring. Not intelligence — the cost of admitting you were wrong in front of people whose respect you want. That cost is denominated entirely in ego, which is why the pundit with the strongest convictions is usually the worst forecaster in the room and the most highly paid. He has optimised for the wrong currency. Ryan Holiday's Ego is The Enemy is essentially a long argument that the thing which got you here is metabolising you from the inside, and the tell is always the same: you start defending a position instead of examining it.

I have never met anyone who thinks he scores badly on Baron's test. But most of us do.

The tax farmer of 539

Picture a man in Constantinople in the year 539, buying the right to collect taxes in a province. The contract is straightforward. He pays the treasury a fixed sum upfront, keeps what he collects above it, and the yield on that arrangement was extraordinary. The province had farmers, harvests, families who paid every year as their parents had. The underwriting was sound. The demand was inelastic. Any analyst would have signed off.

Then grain ships from Egypt arrived at the harbour with rats aboard, and by 542 Constantinople was burying the dead faster than it could count them. By 555 most of those tax-farming positions had simply ceased to exist. Not defaulted. Ceased. There was nobody left in the province to collect from.

Arie van Gemeren, a real estate investor who spends a lot of time reading Roman history for the purpose of allocating capital, draws one line out of that: duration matters more than yield. A six percent return that survives a five-year disruption is worth dramatically more than a twelve percent return that requires uninterrupted operation to compound. The twelve percent is a bet on the world holding still. The six percent is not.

Here is the trap. Yield is visible. You can read it off a page, compare it against alternatives, defend it in a meeting. Duration is invisible until the moment it becomes the only thing that matters, and by then the position is already gone. So the entire apparatus of professional investing; the screens, the committees, the ranking tables — optimises relentlessly for the measurable variable and leaves the other one to chance. Not because anyone is stupid. Because nobody gets promoted for surviving a plague that hasn't happened yet.

The man in 539 was not wrong about the yield. He was wrong about how long the world would sit still for him.

My Ledger — notes on investing, books, and things I'm still figuring out. The Library is where I keep the books that shaped how I think. The Journal is where I work through ideas in public.

Mandelbrot — the private toolbox behind the thinking.

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