Trader Bot: Implement Kelly Criterion for optimal position sizing

[konard]

🎯 Summary

This PR implements the Kelly Criterion algorithm to maximize long-term profit through optimal position sizing in the TraderBot. The Kelly Criterion is a mathematical formula developed by John Kelly at Bell Labs in 1956, widely used by professional traders and investors for optimal capital allocation.

🔢 Mathematical Foundation

Formula: f = (bp - q) / b

• f = fraction of capital to invest
• b = profit/loss ratio (odds)
• p = probability of winning
• q = probability of losing (1-p)

🚀 Key Features

✅ Optimal Position Sizing

• Calculates optimal lot size based on Kelly Criterion formula
• Prevents over-betting and under-betting
• Maximizes long-term geometric growth rate

✅ Dynamic Learning

• Automatically calculates win probability and profit/loss ratio from completed trades (10+ minimum)
• Adapts position sizing based on actual performance
• Falls back to configured values when insufficient historical data

✅ Risk Management

• Configurable maximum fraction limit (default 25%) to prevent excessive risk
• Returns 0% allocation for negative expected value strategies
• Built-in safeguards against calculation errors

✅ Comprehensive Configuration

{
  "TradingSettings": {
    "UseKellyCriterion": true,
    "WinProbability": 0.55,
    "ProfitLossRatio": 1.2,
    "KellyFractionLimit": 0.25
  }
}

📊 Implementation Details

Core Components

• KellyCriterion.cs: Static calculation methods and historical analysis
• TradingSettings.cs: Added Kelly configuration parameters
• TradingService.cs: Integrated Kelly sizing into existing trading logic

Real-World Examples

Scenario	Win Rate	P/L Ratio	Max Risk	Kelly Result
Conservative	52%	1.1:1	10%	8.4% of capital
Aggressive	65%	1.5:1	50%	41.7% of capital
High Win Rate	80%	0.8:1	25%	25.0% (capped)
Breakeven	50%	1.0:1	25%	0.0% (negative EV)

Behavior Changes

• When Enabled: Uses Kelly formula for position sizing instead of "all available cash"
• When Disabled: Falls back to original behavior with no changes
• Learning Mode: Switches to historical metrics after 10+ completed trades

🧪 Testing

Created comprehensive test suite covering:

• Mathematical accuracy verification
• Edge case handling (negative probabilities, ratios)
• Maximum fraction limiting
• Historical metrics calculation
• Real-world scenario simulations

All tests pass ✅

📚 Documentation

Added detailed documentation in examples/KELLY_CRITERION_README.md including:

• Mathematical foundation and formulas
• Configuration parameters and examples
• Risk considerations and best practices
• Implementation details and testing instructions

⚠️ Risk Considerations

1. Accurate Probabilities Required: Kelly requires accurate win rate and profit/loss estimates
2. Volatility: Full Kelly can be volatile; fractional Kelly recommended (25% or less)
3. Market Conditions: Assumes consistent conditions; may vary during regime changes
4. Historical Data: Minimum 10 trades needed for dynamic learning

📈 Benefits

• Optimal Capital Allocation: Mathematically proven to maximize long-term growth
• Risk Management: Automatically reduces position size for poor-performing strategies
• Adaptability: Learns from actual performance and adjusts over time
• Professional Standard: Used by Warren Buffett and many hedge funds

🔗 References

• Kelly, J. L. (1956). "A New Interpretation of Information Rate"
• Thorp, E. O. (2006). "The Kelly Capital Growth Investment Criterion"
• Video reference: https://youtu.be/_FuuYSM7yOo

🛠️ Test Instructions

1. Build and run tests:

   cd examples
   dotnet build && dotnet run

2. Configure Kelly parameters in appsettings files
3. Enable with "UseKellyCriterion": true
4. Monitor logs for Kelly calculation details

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Closes #231

🤖 Generated with Claude Code