Kelly Criterion Core Definition
Kelly Criterion is a mathematical formula proposed by John Kelly in 1956 for calculating the optimal capital allocation ratio for each bet to maximize long-term capital growth.
Basic Formula
Kelly% = (Win Rate × Win/Loss Ratio - Loss Rate) ÷ Win/Loss Ratio
Example: Win Rate = 55%, Win/Loss Ratio = 2:1 (average profit is 2x average loss)
- Kelly = (0.55 × 2 - 0.45) ÷ 2 = (1.10 - 0.45) ÷ 2 = 32.5%
This means theoretically you should allocate 32.5% of total capital to each trade.
Why Use Fractional Kelly in Practice?
| Kelly Ratio | Risk Level | Drawdown Range | Suitable For |
|---|---|---|---|
| Full Kelly | Extremely High | Potentially >50% | Not recommended |
| ½ Kelly | Medium | 20-30% | Experienced traders |
| ¼ Kelly | Low | 10-15% | Most traders |
| ⅛ Kelly | Very Low | <10% | Conservative |
Reason: Full Kelly assumes you know the exact win rate and win/loss ratio, but in practice these are estimates. Using fractional Kelly keeps you safe even with estimation errors.
Practical Calculation Steps
1. Determine Strategy Statistics
Extract from Trading Journal:
- Win rate: Average win rate from the last 50-100 trades
- Win/Loss ratio: Average profit amount ÷ Average loss amount
2. Calculate Kelly Ratio
Kelly = (Win Rate × Win/Loss Ratio - Loss Rate) ÷ Win/Loss Ratio
3. Choose Fractional Kelly
Recommend using ¼ Kelly:
Practical Ratio = Kelly% ÷ 4
Limitations of Kelly
Limitation 1: Requires Accurate Statistics
If win rate or win/loss ratio estimates are inaccurate, the Kelly result will also be off. It is recommended to use data from at least 50 trades.
Limitation 2: Does Not Account for Consecutive Losses
Kelly assumes independent win/loss distribution, but trading often involves consecutive losses. This is why fractional Kelly is safer in practice.
Limitation 3: Not Suitable for Correlated Trades
If your multiple trades are highly correlated (e.g., holding multiple tech stocks simultaneously), Kelly will underestimate risk.
Comparison with Other Position Sizing Methods
| Method | Pros | Cons |
|---|---|---|
| Fixed Percentage | Simple | Doesn't consider strategy characteristics |
| Kelly Criterion | Mathematically optimal | Requires accurate statistics |
| Volatility-Adjusted | Adapts to market | Requires ATR |
| Hybrid Approach | Most comprehensive | More complex |
Recommendation: Use fixed percentage as a base (1-2% risk per trade), use Kelly as an upper reference, and use volatility-adjusted method for final fine-tuning.
Summary
Key points of the Kelly Criterion:
- Formula: Kelly% = (Win Rate × Win/Loss Ratio - Loss Rate) ÷ Win/Loss Ratio
- Use ¼ Kelly in practice — Safety first
- Need at least 50 trades of data — Statistics must be meaningful
- Combine with fixed percentage method — Double safety protection
For more position sizing strategies, refer to the Strategy Center and Learning Center risk management courses.