The 'Fallacy' of Maximizing the Geometric Mean in Long Sequences of Investing or Gambling
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What they found
Samuelson's rebuttal to the claim that everyone should follow the Kelly criterion. He shows that although Kelly betting maximizes the long-run growth rate and almost surely beats any other strategy given enough time, that does not make it the right choice for an investor who cares about risk: a more risk-averse person would rationally prefer a smaller bet, accepting a lower growth rate to avoid Kelly's severe drawdowns. Maximizing expected log wealth is one utility function among many, not a law of nature.
What you can use
- Kelly is optimal only if your goal is maximum long-run growth and you can stomach 50%+ drawdowns; most traders should bet less.
- 'It wins in the long run' is not a sufficient argument when the long run may be longer than your career or your tolerance.
- Choose position size based on how much drawdown you can survive, financially and psychologically, then compare it with Kelly.
Caveats
A short, dense theoretical note. Samuelson does not argue against Kelly as a ceiling, only against it as a universal rule.
Tags: risk, position-sizing, kelly, utility
Summaries are our own reading of the paper, not the authors' words. Educational only, not advice. Discuss it in Book Club.