The mathematical principle that average outcomes across many investors differ from the time-average outcome for a single investor — explaining why positive expected-value strategies can still ruin individuals.
“The expected value of a strategy and the outcome for any individual who follows it are not the same thing — especially when the strategy can occasionally produce catastrophic losses. Survival is the prerequisite for compounding. — Daniel Kahneman”
— Daniel Kahneman
Deeper Explanation
Most investment theory is built on expected value — the probability-weighted average of all possible outcomes. But expected value assumes ergodicity: that the average across many investors in one period is the same as the average for one investor across many periods. This assumption fails whenever there is a possibility of total capital loss. A concrete example: a strategy that has a 50% chance of gaining 60% and a 50% chance of losing 50% has a positive expected value (+5%) but a negative geometric mean (the investor who plays this repeatedly ends up losing money over time, because the compounding mathematics of sequential gains and losses differs from the arithmetic average). This is why Kelly Criterion sizing exists — to maximise the geometric (time-average) growth rate rather than the arithmetic expected return. The practical implication for investors is profound: never risk ruin on any single position regardless of expected value, because ruin ends the game permanently and eliminates all future compounding. Diversification, position sizing limits, and stop-losses are not just risk management tools — they are ergodicity corrections that allow investors to capture the benefits of positive expected-value opportunities across many years.
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