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Objective

This case study compares how different position sizing methods affect growth, drawdown, and overall system stability when applied to the same trading strategy.

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Setup

We consider a system with:
  • Initial capital: $10,000
  • Win rate: 50%
  • Risk-reward: 2:1
  • 100 trades, executed consistently
Three position sizing methods are applied:
  • Full Kelly (~25% risk per trade)
  • Half Kelly (~12.5%)
  • Fixed risk (1%)
The strategy remains identical. Only the risk allocation changes.

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Equity Curve Comparison

Figure — Equity curve comparison: Full Kelly vs Half Kelly vs Fixed Risk

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Interpretation

The differences in behavior are entirely driven by position sizing. Full Kelly produces the highest theoretical growth, but this comes with extreme volatility. The equity curve expands rapidly during favorable sequences, but it also experiences sharp drawdowns and large fluctuations. Half Kelly reduces this effect, offering a more balanced profile. Growth remains strong, but variability is still significant and sensitive to the sequence of trades. In contrast, fixed risk leads to a much smoother equity curve. Growth is slower, but drawdowns remain controlled and the system behaves in a stable and predictable manner.

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Structural Implication

Although the underlying strategy is unchanged, the outcome varies dramatically depending on how capital is allocated. Kelly-based approaches amplify both returns and variance. This makes them highly dependent on accurate estimates of win rate and reward-to-risk ratio. In real trading, these parameters are uncertain and subject to change, which introduces additional risk. Fixed risk, while less efficient from a theoretical perspective, provides robustness. It limits drawdowns, reduces sensitivity to estimation error, and improves the ability to execute the system consistently over time.

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Key Insight

The method that maximizes growth is not the one that maximizes stability.

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Conclusion

Position sizing is a primary driver of performance. Even with a profitable system, aggressive allocation can lead to instability and large drawdowns, while conservative sizing enables sustained execution and long-term viability.

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Final Insight

The objective is not to maximize theoretical returns.
It is to maintain a system that can survive uncertainty and continue operating over time.

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Next Step

→ Why Consistency Beats Prediction