foxhunt/KELLY_CRITERION_QUICK_REF.md

Kelly Criterion Integration - Quick Reference Guide

TDD Test Suite Summary

Status: ✅ 16/16 Tests Passing File: ml/tests/kelly_criterion_integration_test.rs Coverage: Kelly sizing, position calculation, DQN integration, edge cases

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Kelly Formula at a Glance

f* = (b × p - q) / b

f*  = optimal Kelly fraction (% of capital to risk per trade)
b   = odds ratio = avg_win / avg_loss
p   = win_rate
q   = loss_rate = 1 - p

Example

Win Rate: 60%  (p = 0.6)
Avg Win: $150  (b = 150/100 = 1.5)
Avg Loss: $100

f* = (1.5 × 0.6 - 0.4) / 1.5 = 0.333
→ Risk 33.3% of capital per trade

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16 Tests at a Glance

Test	Scenario	Key Validation
1	Initialization	Config loading, empty history error
2	High edge (60% win)	Raw Kelly, max cap enforcement
3	Medium edge (55% win)	Half-Kelly safety multiplier
4	Losing strategy (40% win)	Zero Kelly, default fallback
5	Fractional Kelly (0.25x)	Ultra-conservative sizing
6	Position calculation	Capital × Kelly ÷ price
7	Min sample (10 trades)	Requirement validation
8	Confidence threshold	0.5 minimum enforcement
9	Multi-strategy (DQN vs PPO)	Separate Kelly per strategy
10	Multi-symbol (ES vs NQ)	Symbol-specific positioning
11	Kelly caps	Min/max limits (1%-25%)
12	Break-even (50% win)	Zero edge handling
13	Extreme rate (95% win)	Overfitting detection, cap
14	45-action scaling	Price-inverse position sizing
15	Action masking	Capital constraint compliance
16	Losing period	Rapid adaptation ≤ initial

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Default Configuration

KellyConfig {
    enabled: true,                          // Enable Kelly sizing
    confidence_threshold: 0.5,              // Min confidence required
    fractional_kelly: 1.0,                  // Full Kelly (use 0.5 for safety)
    min_kelly_fraction: 0.0,                // Minimum position
    max_kelly_fraction: 0.25,               // Maximum 25% per trade
    default_position_fraction: 0.05,        // Fallback: 5%
    lookback_periods: 100,                  // 100 trades for stats
}

Recommended for Production

KellyConfig {
    enabled: true,
    confidence_threshold: 0.5,
    fractional_kelly: 0.5,          // ← Use HALF-KELLY for HFT
    min_kelly_fraction: 0.01,       // ← 1% minimum
    max_kelly_fraction: 0.25,       // ← 25% maximum (prevent ruin)
    default_position_fraction: 0.05,
    lookback_periods: 100,
}

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Confidence Calculation

confidence = size_confidence × rate_confidence

size_confidence = min(trades / 100, 1.0)
  100 trades → 1.0
  50 trades → 0.5
  10 trades → 0.1

rate_confidence =
  1.0 if 0.3 ≤ win_rate ≤ 0.7  (reasonable)
  0.8 if 0.2 ≤ win_rate ≤ 0.8  (extreme)
  0.5 if win_rate < 0.2 or > 0.8  (likely overfitting)

Examples

100 trades, 55% win rate: 1.0 × 1.0 = 1.0 ✓ (use Kelly)
100 trades, 95% win rate: 1.0 × 0.5 = 0.5 ✓ (use Kelly, cap)
20 trades, 60% win rate:  0.2 × 1.0 = 0.2 ✗ (too low, default)

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Integration with 45-Action DQN

Action Space

45 Actions = 5 exposures × 3 order types × 3 urgencies

Exposures: Short100 (-100%), Short50 (-50%), Flat (0%), Long50 (+50%), Long100 (+100%)
Orders: Market, LimitMaker, IoC
Urgencies: Patient, Normal, Aggressive

Position Sizing

Kelly fraction: 0.15 (e.g., from test results)
Capital: $100,000
Entry price: $5,000

Position value: $100,000 × 0.15 = $15,000
Shares: $15,000 ÷ $5,000 = 3 contracts

With action masking (max_position = 2.0):
  Final position: min(3, 2.0) = 2.0 contracts

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When to Use Kelly Sizing

✅ USE KELLY

• ✓ 100+ historical trades collected
• ✓ Win rate between 45%-70% (reasonable)
• ✓ Avg win > avg loss (positive edge)
• ✓ Confidence ≥ 50%
• ✓ Market conditions stable

⚠️ CAUTION (Reduce Kelly)

• ⚠ 20-50 trades (use 0.25x Kelly)
• ⚠ Win rate 35-45% or 75-85% (use 0.5x Kelly)
• ⚠ Recent strategy changes
• ⚠ Market regime shift detected

❌ DON'T USE KELLY

• ✗ < 10 trades (insufficient data)
• ✗ Confidence < 50%
• ✗ Win rate < 30% (losing)
• ✗ Avg loss > avg win
• ✗ Extreme market conditions

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Test Coverage

By Category

• Basic: 1 test
• Calculations: 4 tests (raw Kelly, fractional, caps)
• Position Sizing: 3 tests (capital, multi-symbol, multi-strategy)
• Risk Management: 4 tests (confidence, caps, min/max)
• DQN Integration: 2 tests (45-action, masking)
• Edge Cases: 2 tests (break-even, extreme)

By Scenario

Scenarios tested:
├── Happy path (sufficient data, good win rate)
├── Risk management (caps, constraints)
├── Multi-dimensional (strategies, symbols)
├── Edge cases (break-even, extreme, adaptation)
├── DQN integration (45-action, masking)
└── Error handling (insufficient data, low confidence)

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Key Takeaways

1. Safety First

• Always cap Kelly: 25% maximum per trade
• Use fractional: 0.25x-0.5x Kelly recommended
• Require confidence: 50% minimum
• Small samples: Use defaults, not Kelly

2. Multi-Dimensional

Same strategy, different symbols?  → Separate Kelly per symbol
Same symbol, different strategies? → Separate Kelly per strategy
Symbol+Strategy combo?             → Individual Kelly calculation

3. Rapid Adaptation

• Kelly updates daily with new trade outcomes
• Losing periods reduce position size automatically
• Winning periods increase position size automatically
• No manual intervention needed

4. DQN Ready

• 45-action space fully supported
• Position scaling across all price levels
• Action masking constraints respected
• Capital constraints enforced

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Common Scenarios

Scenario A: New Strategy

Trades collected: 20
Win rate: 65%
Confidence: (20/100) × 1.0 = 0.2 < 0.5

Action: Use default position (5%), NOT Kelly
Wait until 100+ trades with stable 55-65% win rate

Scenario B: Established Strategy

Trades collected: 150
Win rate: 58%
Avg win: $120
Avg loss: $100
Confidence: (150/100) × 1.0 = 1.0 ≥ 0.5 ✓

Raw Kelly: (1.2 × 0.58 - 0.42) / 1.2 ≈ 0.24
Half-Kelly: 0.24 × 0.5 = 0.12 (12% of capital)

Position: $100k × 0.12 ÷ $5000 = 2.4 contracts
With action masking (max=2.0): 2.0 contracts

Scenario C: Market Downturn

Before: 100 trades, 60% win rate, position=2.0
After downturn: 150 trades, 40% win rate

New Kelly: 0 (losing strategy)
New position: default (5% of capital)
Action: Reduce position automatically, monitor

As market recovers:
- Win rate → 45%: Still below, maintain 5%
- Win rate → 55%: Back above 50%, resume Kelly

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Implementation Checklist

Before deploying Kelly sizing:

• Collect 100+ trade outcomes
• Validate win rate 45-70% (reasonable)
• Verify avg_win > avg_loss
• Set fractional_kelly = 0.5 (half-Kelly)
• Set max_kelly_fraction = 0.25
• Enable confidence threshold = 0.5
• Test with action masking constraints
• Monitor daily updates
• Alert on confidence < 0.5
• Verify position ≤ 25% of capital

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Troubleshooting

"Insufficient trade history" Error

• Cause: < 10 trades collected
• Fix: Wait for more trades or use default position

Low Confidence Warning

• Cause: Sample size < 100 or extreme win rate
• Fix: Collect more trades, review for overfitting

Position Exceeds Max

• Cause: Kelly cap enforcement
• Fix: Reduce fractional_kelly multiplier

Rapid Position Changes

• Cause: Normal Kelly adaptation
• Action: Expected behavior, monitor trends

Strategy Becoming Unprofitable

• Symptom: Win rate drops, Kelly → 0
• Action: Use default 5% position, investigate

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Files & APIs

Test File

/home/jgrusewski/Work/foxhunt/ml/tests/kelly_criterion_integration_test.rs

Implementation

/home/jgrusewski/Work/foxhunt/risk/src/kelly_sizing.rs
/home/jgrusewski/Work/foxhunt/ml/src/risk/kelly_optimizer.rs
/home/jgrusewski/Work/foxhunt/ml/src/risk/kelly_position_sizing_service.rs

DQN Integration

/home/jgrusewski/Work/foxhunt/ml/src/dqn/action_space.rs (45-action space)
/home/jgrusewski/Work/foxhunt/ml/src/trainers/dqn.rs (DQN trainer)

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References

• CLAUDE.md: System status and Wave 15 architecture
• KELLY_CRITERION_TDD_REPORT.md: Comprehensive test documentation
• Test Examples: All 16 tests in kelly_criterion_integration_test.rs

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Status: ✅ Ready for Production Test Pass Rate: 100% (16/16) Confidence Level: High (comprehensive coverage)