kelly-criterion Checked

### 3. Asymmetry of Over vs. Under Betting

Overbetting by 2x (betting at 2*f*) produces **zero** long-term growth — the same as not trading at all. Underbetting by 2x (betting at 0.5*f*) still captures ~75% of the optimal growth rate. The penalty for overbetting is catastrophically worse than for underbetting.

### Recommended Fractions

| Fraction | When to Use |

|----------|------------|

| 0.10x Kelly | Very uncertain edge, new strategy, < 30 trades in sample |

| 0.25x Kelly | Moderate confidence, 30-100 trades, reasonable Sharpe |

| 0.50x Kelly | High confidence, 100+ trades, consistent performance |

| 1.00x Kelly | Never recommended in practice |

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Estimating Your Edge

Kelly requires two inputs: win rate (p) and payoff ratio (b). Both must be estimated from data.

### Minimum Data Requirements

• **50 trades minimum** for any Kelly calculation. Below this, estimation error dominates.
• **100+ trades preferred** for half Kelly sizing.
• **200+ trades** before considering aggressive fractions.

### Calculation from Trade History

wins = [t for t in trades if t > 0]
losses = [t for t in trades if t < 0]

win_rate = len(wins) / len(trades)               # p
payoff_ratio = mean(wins) / abs(mean(losses))     # b
edge = win_rate * payoff_ratio - (1 - win_rate)   # should be > 0

kelly_full = (win_rate * payoff_ratio - (1 - win_rate)) / payoff_ratio

### Conservative Estimation

Use the **lower bound of a Wilson confidence interval** for win rate rather than the point estimate:

import math

def wilson_lower(wins: int, total: int, z: float = 1.96) -> float:
    """Lower bound of Wilson score interval (95% confidence)."""
    p = wins / total
    denominator = 1 + z**2 / total
    centre = p + z**2 / (2 * total)
    spread = z * math.sqrt((p * (1 - p) + z**2 / (4 * total)) / total)
    return (centre - spread) / denominator

Using the lower bound of the confidence interval for win rate automatically builds in conservatism, reducing the risk of overbetting due to sampling luck.

### Edge Strength Classification

| Edge Value | Classification | Notes |

|-----------|---------------|-------|

| < 0 | Negative edge | Do not trade this strategy |

| 0 - 0.02 | No meaningful edge | Transaction costs likely exceed edge |

| 0.02 - 0.10 | Marginal edge | Conservative fractions only |

| 0.10 - 0.20 | Good edge | Standard fractions appropriate |

| > 0.20 | Excellent edge | Rare; verify not overfitting or temporary |

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Multi-Bet Kelly (Simultaneous Positions)

When holding multiple positions simultaneously:

### Independent Bets

If bets are uncorrelated, each can be sized at its individual Kelly fraction. However, the **sum of all Kelly fractions** should not exceed 1.0 (total portfolio). If it does, scale each proportionally:

kelly_fractions = [0.15, 0.10, 0.12, 0.08]  # individual Kelly fractions
total = sum(kelly_fractions)  # 0.45
if total > 1.0:
    scale = 1.0 / total
    kelly_fractions = [f * scale for f in kelly_fractions]

### Correlated Bets

Correlated positions (e.g., multiple SOL memecoins) are effectively one larger bet. Reduce each position proportionally to the correlation:

# Simple correlation adjustment
def adjust_for_correlation(kelly_fractions: list, avg_correlation: float) -> list:
    """Reduce Kelly fractions based on average inter-position correlation."""
    n = len(kelly_fractions)
    # Effective number of independent bets
    n_eff = n / (1 + (n - 1) * avg_correlation)
    scale = n_eff / n
    return [f * scale for f in kelly_fractions]

In crypto, meme token positions often have correlations of 0.5-0.8 with each other (they all dump together in risk-off). Treat them as partially one bet.

### Portfolio Kelly Cap

Regardless of individual calculations, enforce a hard cap: **total Kelly allocation should never exceed 1.0** (100% of portfolio). A practical maximum is 0.6-0.8 to leave cash buffer for drawdowns and new opportunities.

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PumpFun / Meme Token Kelly

Meme token trading presents specific challenges for Kelly:

1. **Edge is hard to estimate**: Win rates and payoff ratios shift rapidly with market regime.

2. **Fat tails dominate**: A few large winners and many small losers. Standard Kelly assumes thin tails.

3. **Correlation spikes in drawdowns**: All meme tokens can dump simultaneously.

### Practical Adjustments

• Use **0.1x to 0.25x Kelly** maximum for meme tokens.
• Cap absolute position size at **2-5% of portfolio** regardless of Kelly output.
• Recalculate edge weekly — stale estimates are dangerous.
• If Kelly suggests > 30%, your edge estimate is almost certainly wrong. Use 5% maximum.

def meme_kelly(win_rate: float, payoff_ratio: float, account: float) -> float:
    """Conservative Kelly for high-uncertainty meme token trades."""
    kelly_full = (win_rate * payoff_ratio - (1 - win_rate)) / payoff_ratio
    kelly_conservative = kelly_full * 0.15  # 0.15x fractional
    max_fraction = 0.05                     # hard cap at 5%
    return min(max(kelly_conservative, 0), max_fraction) * account

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When Kelly Does Not