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One Path
Ergodicity, Explained: Why the Average Outcome Is Not Your Outcome
A process is ergodic when the average over time equals the average across people. Wealth is not ergodic, and that changes how you should bet, invest and size risk.
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One Path
Why Insurance Makes Both Sides Richer
In expected wealth, insurance is zero-sum: the buyer pays more than the expected loss and the insurer pockets the difference. In the growth rate each side lives through, there is a range of fees where both come out ahead.
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One Path
The Kelly Criterion: How Much to Bet When You Have an Edge
The Kelly criterion says how much of your wealth to put on a bet you expect to win: the fraction that maximizes the growth rate you live through over time. Why overbetting is worse than underbetting, and what it means for investors.
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One Path
Volatility Drag: Why Your Average Return Overstates Your Wealth
Volatility drag is the gap between an investment's average return and the rate it actually compounds at: roughly half the variance. Where it comes from and what to do about it.
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When Rules Repeat: The Fixed Point Ladder
Markets as Reflexive Fixed Points
Markets are more than noisy aggregators of information: beliefs about prices help determine prices, which makes reflexivity a fixed-point problem with fat tails, non-ergodicity, and hysteresis.