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The Risk-Constrained Kelly Criterion: From the foundations to trading

Optimal bet sizing using Kelly Criterion

AdvancedPosition Management

Kelly Criterion Overview

The Kelly Criterion is a well-known formula for allocating resources into a portfolio, ensuring maximum long-term return for trading strategies. However, traditional Kelly Criterion can lead to significant drawdowns that are unacceptable in real trading scenarios.

To overcome these limitations, Busseti et al. (2016) introduced the risk-constrained Kelly Criterion that maximizes long-term log-growth rate while incorporating drawdown constraints, resulting in smoother equity curves with reduced risk exposure.

This approach balances optimal capital allocation with risk management, making it more practical for real-world trading applications where drawdown control is essential for sustained performance.

Key Points

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Kelly Criterion maximizes long-term growth but can produce unacceptable drawdowns in practice
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Risk-constrained Kelly adds probability constraints to limit wealth dropping below thresholds
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Standard formula: K% = W - (1-W)/R where W is win rate and R is win/loss ratio
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Risk constraint: Prob(Minimum wealth < α) < β limits downside risk exposure
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Constrained approach typically reduces position sizes by 50-75% versus standard Kelly
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Maximum drawdowns reduced from 40-50% to 15-25% with risk constraints
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Solution requires bisection algorithm when standard Kelly violates risk constraints
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Alpha parameter (0.6-0.8) sets minimum acceptable wealth as fraction of capital
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Beta parameter (0.05-0.1) limits probability of hitting minimum wealth threshold
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Trade-off: Lower absolute returns but significantly improved risk-adjusted performance
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Suitable for systematic trading where consistent performance is prioritized over maximum growth
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Can be enhanced with stop-loss, take-profit, and trend-following filters