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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

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