position-sizing Checked

This automatically reduces exposure in volatile markets and increases it in calm ones.

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3. Kelly Criterion

The mathematically optimal fraction of capital to risk, maximizing long-term growth rate. Derived from maximizing expected logarithmic utility.

### Formula

f* = (p * b - q) / b

Where:

• p = win rate (probability of winning trade)
• q = 1 - p (probability of losing trade)
• b = average win / average loss (payoff ratio)
• f* = optimal fraction of capital to risk

Equivalent form: f* = (p * (b + 1) - 1) / b

### Critical Rule: NEVER Use Full Kelly

Full Kelly assumes perfect knowledge of your edge. In practice, edge estimates are noisy. Always use fractional Kelly:

| Fraction | Use Case | Notes |

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

| 0.25x Kelly | Conservative, recommended default | Robust to edge estimation error |

| 0.50x Kelly | Moderate, for well-measured edges | Still significant drawdown risk |

| 1.0x Kelly | Never in practice | Theoretical maximum, catastrophic if edge is overestimated |

### Example

win_rate = 0.55       # 55% win rate
avg_win = 2.0         # Average win is 2x the average loss
avg_loss = 1.0
payoff_ratio = avg_win / avg_loss  # b = 2.0

kelly = (win_rate * payoff_ratio - (1 - win_rate)) / payoff_ratio
# kelly = (0.55 * 2.0 - 0.45) / 2.0 = 0.325 = 32.5%

quarter_kelly = kelly * 0.25  # 8.1% — use this
half_kelly = kelly * 0.50     # 16.25%

**If Kelly is negative, you have no edge. Do not trade.**

See references/sizing_formulas.md for the full mathematical derivation.

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4. Liquidity-Constrained Sizing

Critical for Solana tokens. Even if your risk model says you can take a large position, the pool may not support it without unacceptable slippage.

### Formula (Constant-Product AMM)

slippage ≈ trade_size / pool_liquidity
max_trade = pool_liquidity * max_slippage_pct

### Rules of Thumb

| Constraint | Guideline |

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

| Max single trade | 2% of pool liquidity |

| Max position | 5% of pool liquidity |

| Minimum pool depth | 10x your desired position size |

### Example

pool_sol = 500          # 500 SOL in pool
max_slippage = 0.02     # 2% max slippage

max_trade_sol = pool_sol * max_slippage  # 10 SOL
# For a $150 SOL price, that's $1,500 max per trade

**Always check all pools**, not just the largest. Aggregate liquidity across Raydium, Orca, and Meteora for the full picture. See the liquidity-analysis skill for pool depth assessment.

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5. Anti-Martingale Sizing

Increase size after wins, decrease after losses. This is the opposite of the gambler's fallacy (Martingale). The logic: winning streaks may indicate your strategy is in sync with the market; losing streaks may indicate regime change.

### Implementation

def anti_martingale_size(
    base_size: float,
    consecutive_wins: int,
    consecutive_losses: int,
    scale_factor: float = 0.25,
    max_multiplier: float = 2.0,
    min_multiplier: float = 0.5,
) -> float:
    if consecutive_losses > 0:
        multiplier = max(min_multiplier, 1.0 - consecutive_losses * scale_factor)
    elif consecutive_wins > 0:
        multiplier = min(max_multiplier, 1.0 + consecutive_wins * scale_factor)
    else:
        multiplier = 1.0
    return base_size * multiplier

Use conservatively. After 3+ consecutive losses, reducing size by 50% protects capital during drawdowns.

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Position Sizing Ladder

Combine all methods and take the most conservative result:

1. Calculate Kelly size          → theoretical max based on edge
2. Calculate fixed fractional    → risk-based size
3. Calculate volatility-adjusted → vol-normalized size
4. Calculate liquidity-constrained max → market-based ceiling
5. Final size = min(all four)    → binding constraint wins

The binding constraint tells you what is limiting your size:

• **Kelly-bound**: your edge is small, size accordingly
• **Risk-bound**: standard risk management is the limit
• **Volatility-bound**: market is too volatile for larger size
• **Liquidity-bound**: pool cannot absorb more without slippage

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Account-Level Limits

Individual position sizing is necessary but not sufficient. You also need portfolio-level constraints:

| Limit | Guideline | Rationale |

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

| Max single position | 10% of portfolio | Diversification floor |

| Max correlated exposure | 25% of portfolio | Correlated assets move together |

| Max total exposure | 50–80% of portfolio | Cash reserve for opportunities/margin |

| Max positions | 5–10 concurrent | Attention and management bandwidth |

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PumpFun / Meme Token Sizing

PumpFun and early-stage meme tokens require special sizing discipline:

• **Very small positions**: 0.1–1 SOL per trade due to extreme risk
• **Scale with bonding curve fill %**: smaller when early (high rug risk), slightly larger when proven (graduated to Raydium)
• **Never size based on expected return** — size based on acceptable total loss
• **Treat as lottery tickets**: expect most to go to zero
• **Position limit**: no more than 5–10% of portfolio across all meme positions comb