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Direct Answer

The Kelly Criterion is a formula used to determine the optimal fraction of capital to risk per trade in order to maximize long-term growth.

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What Is the Kelly Criterion?

The Kelly Criterion is a mathematical approach to position sizing. It determines how much capital to allocate based on:
  • probability of winning
  • size of gains relative to losses
Its objective is to maximize the geometric growth of capital over time.

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Kelly vs Fixed Risk

There are two fundamentally different approaches to position sizing: Kelly-based sizing
  • Adjusts risk based on system characteristics
  • Aims to maximize growth
  • Varies depending on edge
Fixed risk sizing
  • Uses a constant percentage (e.g. 1% per trade)
  • Does not depend on estimated probabilities
  • Prioritizes stability and consistency
The difference is:
Kelly optimizes for growth, while fixed risk optimizes for robustness.

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The Formula

f∗=bp−(1−p)bf^* = \frac{bp - (1 - p)}{b} Where:
  • f* = optimal fraction of capital
  • b = reward-to-risk ratio
  • p = probability of winning
  • q = 1 - p

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Example

A system with:
  • Win rate: 50%
  • Risk-reward: 2:1
Leads to:
  • Optimal risk ≈ 25% per trade
This is significantly higher than typical fixed risk approaches.

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The Limitation

The Kelly Criterion assumes:
  • accurate estimation of probabilities
  • stable system behavior
  • no structural changes in the market
In practice, these assumptions rarely hold.

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Sensitivity to Error

Small estimation errors in:
  • win rate
  • payoff ratio
can lead to:
  • overbetting
  • increased drawdowns
  • unstable performance

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Drawdown Implications

Even when applied correctly, Kelly produces:
  • high volatility
  • large drawdowns
  • uneven equity curves
This makes it difficult to sustain in real conditions.

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Fractional Kelly

To reduce risk, traders often use:
  • half Kelly
  • quarter Kelly
This lowers volatility and drawdowns, while maintaining part of the growth advantage.

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Key Insight

Kelly provides a theoretical optimum under ideal conditions.
In practice, uncertainty makes full Kelly too aggressive for most trading systems.

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Conclusion

The Kelly Criterion is a useful benchmark for understanding optimal growth, but:
  • it depends on uncertain inputs
  • it increases volatility
  • it is difficult to execute consistently
Fixed risk, while less efficient, offers:
  • stability
  • robustness
  • long-term survivability

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Final Insight

The goal is not to maximize growth.
It is to sustain growth under uncertainty.

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Next Step

→ Kelly vs Fixed Risk