Kelly Criterion for Long-Run Bet Sizing and Capital Growth
Summary
The document introduces the Kelly criterion through repeated bets with known win probabilities and gain or loss sizes. It explains why a positive expected value alone does not justify risking all available capital: large bets expose a strategy to ruin and can produce poor long-run compounded growth. The proposed sizing rule chooses the fraction of capital that maximizes expected logarithmic growth, illustrated with examples where the optimal fraction is below full capital.
The article uses simulations and simplified repeated-bet examples to build intuition, including a case with a favorable but asymmetric payoff and an example applying the formula to a weekly stock system. It argues that the order of wins and losses does not change terminal wealth when the same outcomes and fixed fraction are used, though it affects the path. These demonstrations assume known, stable probabilities and payoffs. Real trading adds estimation error, financing costs, discrete position sizes, and more complex outcomes, so the examples do not establish that the stated sizing will be optimal in live markets.
Key ideas
- Kelly sizing selects a capital fraction to maximize long-run compounded growth under specified odds and payoffs.
- A positive expected return does not make full-capital bets prudent when losses can sharply reduce capital.
- The article uses repeated-bet simulations to illustrate the growth tradeoff across position fractions.
- Its examples assume known and stable outcome probabilities and payoff sizes.
- Practical use in markets must account for financing costs, estimation uncertainty, and non-simple payoffs.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.