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The Kelly criterion estimates the fraction of capital that maximizes long-run logarithmic growth when the outcome probabilities and payoffs are known and stable. Fixed-fraction risk uses a chosen percentage of current equity without claiming that it is growth-optimal.

Example assumptions

  • Win probability: 50%
  • Win payoff: +2R
  • Loss payoff: −1R
  • Independent outcomes
  • Stable probabilities and payoffs
  • No costs, slippage, gaps, or external drawdown limits
For a binary payoff, the Kelly fraction is: Kelly fraction = (b × p − q) ÷ b where (b) is the net win multiple, (p) is win probability, and (q = 1 − p). Under these assumptions, full Kelly is 25% of capital per trade.

Comparison

A 25% risk fraction is not a practical recommendation. Two consecutive full losses would reduce equity by 43.75%; five would reduce it by more than 76%.

Estimation risk

The Kelly result changes sharply when the estimated win probability or payoff changes. Live trading adds costs, serial dependence, regime shifts, changing liquidity, and imperfect execution. A strategy that appears to justify a large Kelly fraction can be overfit or temporarily favorable. Fractional Kelly reduces but does not eliminate that problem. A conservative fixed fraction may be less efficient in the model while being more robust to uncertainty and external constraints.

Prop-account constraint

Kelly optimizes growth relative to capital. A prop account introduces a separate failure boundary. A theoretically optimal fraction can be operationally impossible if one or two losses would breach the daily or maximum-loss rule. The governing size is the smallest allowed by the strategy, the account buffer, and the external rules.

Kelly criterion explained

Review the formula, assumptions, and fractional Kelly.

Position sizing models

Compare sizing methods across practical constraints.

Risk of ruin

Connect sizing with failure probability.

Prop firm risk management

Size from the usable loss buffer.
Kelly calculations are only as reliable as their probability and payoff estimates. This example is educational, not a position-sizing recommendation.