Kelly Position Sizing Perps

Rule: Compute full Kelly as the theoretical maximum. Apply a Kelly fraction of 0.25–0.50. Then enforce hard portfolio caps regardless of Kelly output. The Kelly formula is a ceiling, never a floor.

Kelly Formula for Perpetuals

Base Kelly Fraction

For a binary win/loss trade model (entry → TP or SL):

def kelly_fraction(
    win_rate: float,          # estimated probability of hitting TP before SL
    avg_win_pct: float,       # average win as % of notional (TP distance)
    avg_loss_pct: float,      # average loss as % of notional (SL distance)
) -> float:
    """
    Standard Kelly formula: f* = (p * b - q) / b
    where:
      p = win_rate
      q = 1 - win_rate
      b = avg_win_pct / avg_loss_pct  (reward-to-risk ratio)
    Returns fraction of bankroll to risk (0.0 to 1.0).
    Returns 0.0 if edge is zero or negative (do not trade).
    """
    if avg_loss_pct <= 0 or avg_win_pct <= 0:
        return 0.0
    b = avg_win_pct / avg_loss_pct
    q = 1.0 - win_rate
    f_star = (win_rate * b - q) / b
    return max(0.0, f_star)

# Example: 55% win rate, 2% TP, 1% SL (2:1 RR)
# b = 2.0
# f* = (0.55 * 2.0 - 0.45) / 2.0 = (1.10 - 0.45) / 2.0 = 0.325
# Full Kelly = 32.5% of bankroll at risk on this trade
# Quarter Kelly = 8.125% of bankroll at risk

Converting Kelly Fraction to Notional Size

def kelly_notional(
    portfolio_nav_usd: float,    # total account equity (totalRawUsd from marginSummary)
    kelly_f: float,              # full Kelly fraction from kelly_fraction()
    kelly_multiplier: float,     # fractional Kelly: 0.25 (conservative) to 0.50 (moderate)
    avg_loss_pct: float,         # SL distance as % of notional
    leverage: float,             # target leverage for the position
    carry_discount: float = 1.0, # from high-funding-carry-avoidance (0.0-1.0)
) -> dict:
    """
    Converts Kelly fraction to a notional position size in USD.
    Accounts for leverage (Kelly sizes the *risk*, not the notional),
    fractional Kelly multiplier, and carry cost discount.
    """
    # Kelly sizes the fraction of NAV to PUT AT RISK (i.e., the SL dollar amount)
    risk_usd = portfolio_nav_usd * kelly_f * kelly_multiplier

    # Apply carry discount (from high-funding-carry-avoidance skill)
    risk_usd_adjusted = risk_usd * carry_discount

    # Convert risk amount to notional via SL distance:
    # risk_usd = notional * avg_loss_pct  =>  notional = risk_usd / avg_loss_pct
    notional_usd = risk_usd_adjusted / avg_loss_pct

    # Margin required at target leverage:
    margin_required_usd = notional_usd / leverage

    return {
        "full_kelly_f": kelly_f,
        "applied_kelly_f": kelly_f * kelly_multiplier,
        "risk_usd": risk_usd_adjusted,
        "notional_usd": notional_usd,
        "margin_required_usd": margin_required_usd,
        "effective_leverage": leverage,
    }

# Example: $100k NAV, f*=0.325, quarter Kelly (0.25), 1% SL, 5x leverage, no carry discount
# risk_usd     = $100,000 * 0.325 * 0.25 = $8,125
# notional_usd = $8,125 / 0.01 = $812,500   <- notional exposure
# margin_req   = $812,500 / 5 = $162,500    <- but this exceeds NAV!
# -> Portfolio cap enforcement (below) will reduce this

Portfolio Cap Enforcement

Kelly output must pass through three hard caps in sequence. The final notional is the minimum of Kelly output and all three caps:

# Hard caps (configure per firm risk policy):
MAX_SINGLE_POSITION_PCT_NAV  = 0.20   # 20% of NAV as margin on any single position
MAX_SINGLE_NOTIONAL_PCT_NAV  = 2.00   # 200% of NAV as notional (2x gross leverage cap)
MAX_CORRELATED_EXPOSURE_PCT  = 0.35   # 35% of NAV in correlated assets (e.g. BTC+ETH)
MAX_TOTAL_MARGIN_UTILIZATION = 0.60   # 60% of NAV deployed as margin across all positions

def apply_portfolio_caps(
    kelly_result: dict,
    portfolio_nav_usd: float,
    current_margin_used_usd: float,
    correlated_exposure_usd: float,   # existing notional in correlated assets
    asset_correlation: float = 0.0,   # 0.0-1.0; BTC/ETH ~0.85, BTC/SOL ~0.70
) -> dict:
    notional  = kelly_result["notional_usd"]
    margin    = kelly_result["margin_required_usd"]
    leverage  = kelly_result["effective_leverage"]

    # Cap 1: single position margin
    max_margin = portfolio_nav_usd * MAX_SINGLE_POSITION_PCT_NAV
    if margin > max_margin:
        notional = max_margin * leverage
        margin   = max_margin

    # Cap 2: single position notional
    max_notional = portfolio_nav_usd * MAX_SINGLE_NOTIONAL_PCT_NAV
    if notional > max_notional:
        notional = max_notional
        margin   = notional / leverage

    # Cap 3: total margin utilization
    available_margin = portfolio_nav_usd * MAX_TOTAL_MARGIN_UTILIZATION - current_margin_used_usd
    if margin > available_margin:
        margin   = max(0.0, available_margin)
        notional = margin * leverage

    # Cap 4: correlated exposure
    # New notional adds to correlated bucket scaled by correlation coefficient
    correlated_addition = notional * asset_correlation
    if correlated_exposure_usd + correlated_addition > portfolio_nav_usd * MAX_CORRELATED_EXPOSURE_PCT:
        allowed_addition = max(0.0, portfolio_nav_usd * MAX_CORRELATED_EXPOSURE_PCT - correlated_exposure_usd)
        notional = allowed_addition / asset_correlation if asset_correlation > 0 else notional
        margin   = notional / leverage

    return {
        "final_notional_usd": max(0.0, notional),
        "final_margin_usd":   max(0.0, margin),
        "binding_cap": _identify_binding_cap(kelly_result["notional_usd"], notional),
    }

def _identify_binding_cap(original: float, final: float) -> str:
    if final >= original * 0.99: return "none"        # Kelly was binding
    if final < original * 0.30:  return "correlated"  # correlation cap cut deeply
    return "portfolio_margin"                          # margin/notional cap binding

Kelly Multiplier Selection Guide

The Kelly multiplier (fractional Kelly) is the most important practical decision in the sizing framework. Select based on strategy confidence:

Default to 0.25 when uncertain. Increase multiplier only after live performance confirms the win rate and RR ratio assumptions. The Kelly formula is only as good as the edge estimate — overestimated win rates produce oversized positions that ruin accounts.

Edge Estimation Best Practices

The Kelly formula amplifies errors in edge estimation. A 5% overestimate of win rate can double the recommended position size. Apply these checks before trusting any edge estimate:

def validate_edge_estimate(
    win_rate: float,
    avg_win_pct: float,
    avg_loss_pct: float,
    sample_size: int,
    confidence: str = "low",   # "low", "medium", "high"
) -> dict:
    # Minimum sample sizes for reliable Kelly estimation:
    MIN_SAMPLES = {"high": 200, "medium": 100, "low": 30}

    expectancy = win_rate * avg_win_pct - (1 - win_rate) * avg_loss_pct
    profit_factor = (win_rate * avg_win_pct) / ((1 - win_rate) * avg_loss_pct)

    # Wilson score interval 95% CI on win rate:
    import math
    z = 1.96
    n = sample_size
    p = win_rate
    centre = (p + z*z/(2*n)) / (1 + z*z/n)
    margin = (z * math.sqrt(p*(1-p)/n + z*z/(4*n*n))) / (1 + z*z/n)
    win_rate_lower_ci = max(0.0, centre - margin)

    # Conservative Kelly uses lower CI on win rate:
    kelly_conservative = kelly_fraction(win_rate_lower_ci, avg_win_pct, avg_loss_pct)

    return {
        "expectancy_pct": expectancy * 100,
        "profit_factor": profit_factor,
        "win_rate_lower_95ci": win_rate_lower_ci,
        "kelly_conservative": kelly_conservative,
        "sufficient_sample": sample_size >= MIN_SAMPLES[confidence],
        "recommendation": "use kelly_conservative" if sample_size < 200 else "use kelly_fraction",
    }

Always use kelly_conservative (lower CI on win rate) when sample size < 200 trades. This is the single most important practical adjustment to standard Kelly theory.

Regime Adjustments

Apply these multipliers to the Kelly output after the base calculation and before portfolio cap enforcement:

Worked Example — Full Sizing Pipeline

Inputs:
  Portfolio NAV:         $200,000
  Current margin used:   $20,000
  Asset:                 ETH perp
  Strategy:              Trending bull pullback (established, 120 live trades)
  Win rate (observed):   0.58  (58%)
  Sample size:           120 trades
  Avg TP distance:       1.8% of notional
  Avg SL distance:       0.9% of notional  (2:1 RR)
  Target leverage:       4x
  Funding 1h:            0.018% (carry_discount from carry-avoidance skill: 0.82)
  Cascade score:         2  (NORMAL, no multiplier)
  Correlated exposure
  (BTC position open):   $80,000 notional (ETH correlation to BTC: 0.85)
  Kelly multiplier:      0.33 (moderate; 120 validated trades)

Step 1 — Validate edge:
  win_rate_lower_95ci  = 0.494  (lower CI on 0.58 @ n=120)
  kelly_conservative   = kelly_fraction(0.494, 1.8%, 0.9%)
                       = (0.494 * 2.0 - 0.506) / 2.0 = 0.241

Step 2 — Base Kelly notional:
  risk_usd             = $200,000 * 0.241 * 0.33 * 0.82  (carry discount)
                       = $200,000 * 0.065 = $13,034
  notional_usd         = $13,034 / 0.009 = $1,448,222   <- very large; caps will bind
  margin_required      = $1,448,222 / 4 = $362,056

Step 3 — Apply portfolio caps:
  Cap 1 (20% NAV margin): max_margin = $40,000
    notional = $40,000 * 4 = $160,000  margin = $40,000
  Cap 3 (60% total margin): available = $200,000*0.60 - $20,000 = $100,000
    margin $40,000 < $100,000 ✔ passes
  Cap 4 (correlated 35% NAV = $70,000):
    new correlated addition = $160,000 * 0.85 = $136,000
    existing correlated     = $80,000 * 0.85 = $68,000
    total projected         = $68,000 + $136,000 = $204,000 > $70,000
    allowed addition        = $70,000 - $68,000 = $2,000
    max notional from corr  = $2,000 / 0.85 = $2,353

Final result:
  final_notional_usd  = $2,353  (correlated exposure cap is binding)
  final_margin_usd    = $2,353 / 4 = $588
  binding_cap         = "correlated"

Implication: the ETH position should not be sized until BTC is partially
closed, OR the Kelly multiplier is correct but the correlated cap policy
needs review if ETH is genuinely a separate signal.

Failure Modes to Avoid

• Using full Kelly (multiplier = 1.0): Full Kelly maximises long-run median wealth but the path includes drawdowns of 50%+ that are psychologically and operationally catastrophic. Quarter Kelly captures ~75% of the growth rate with ~25% of the drawdown. Never use full Kelly on live capital.
• Estimating win rate from too few trades: 20 trades can produce an apparent 70% win rate by chance alone. Always use the lower confidence interval on win rate for Kelly inputs. With < 30 trades, use 0.10 Kelly multiplier regardless of observed win rate.
• Using Kelly on correlated simultaneous positions as if independent: Two correlated positions (BTC + ETH) are not two independent Kelly bets. They share the same underlying risk factor. The correlated exposure cap and correlation multiplier in apply_portfolio_caps() handle this— but only if the correlation coefficient is set correctly.
• Ignoring leverage in Kelly notional conversion: Kelly sizes the amount at risk (SL distance × notional), not the notional directly. At 10× leverage, a 1% SL is 10% of margin. Confusing risk-on-notional with risk-on-margin produces positions 10× too large or too small.
• Not adjusting Kelly multiplier after drawdown: A 15% portfolio drawdown is a signal that edge estimates are wrong, market regime has changed, or both. After any 10%+ drawdown, reduce Kelly multiplier by 50% until live performance restores confidence in the edge estimate.
• Treating Kelly as a static calculation: Win rate and RR ratio drift as market regimes change. Recompute Kelly inputs from the most recent 50-trade rolling window, not from the all-time backtest average.

Integration with Other Skills

• high-funding-carry-avoidance (regime-detection/): Provides carry_discount multiplier applied to risk_usd before notional conversion. Always run funding check first; pass carry_discount into kelly_notional().
• liquidation-cascade-risk (regime-detection/): Provides cascade_score and book_fragility. Apply cascade regime multiplier to Kelly output before portfolio caps.
• trending-bull-entry-timing (regime-detection/): Provides regime classification (nascent/established/mature). Apply corresponding regime multiplier (0.40× / 1.0× / 0.50×) to Kelly output.
• slippage-budget-enforcement (execution/): Kelly output is the initial_size_usd input to max_size_within_budget(). If slippage enforcement reduces the size, the risk engine must be updated with the actual executed notional, not the Kelly target.
• drawdown-kill-switch-trigger (risk/): After any kill-switch fire, reset Kelly multiplier to 0.10 for the next session. Kelly assumes a stationary edge; a kill-switch fire signals the edge assumption has broken down.

Audit JSONL Schema

{
  "event": "kelly_position_sizing",
  "asset": "ETH",
  "timestamp_utc": "2026-04-07T22:00:00Z",
  "portfolio_nav_usd": 200000,
  "win_rate_observed": 0.58,
  "win_rate_lower_ci": 0.494,
  "sample_size": 120,
  "avg_win_pct": 0.018,
  "avg_loss_pct": 0.009,
  "kelly_full_f": 0.241,
  "kelly_multiplier": 0.33,
  "carry_discount": 0.82,
  "cascade_regime_multiplier": 1.0,
  "trend_regime_multiplier": 1.0,
  "risk_usd_adjusted": 13034,
  "kelly_notional_usd": 1448222,
  "binding_cap": "correlated",
  "final_notional_usd": 2353,
  "final_margin_usd": 588,
  "target_leverage": 4,
  "current_margin_used_usd": 20000,
  "correlated_exposure_usd": 68000
}

Quick Decision Tree

New position entry — compute Kelly size:
│
├── 1. Get regime inputs:
│     carry_discount      ← high-funding-carry-avoidance
│     cascade_multiplier  ← liquidation-cascade-risk (score ≥ 8? → 0.0x: no trade)
│     trend_multiplier    ← trending-bull-entry-timing (regime classification)
│
├── 2. Validate edge:
│     validate_edge_estimate(win_rate, avg_win, avg_loss, n_trades)
│     Use win_rate_lower_ci if n_trades < 200
│     kelly_f = kelly_fraction(win_rate, avg_win, avg_loss)
│     kelly_f == 0? → ABORT. No edge. Do not trade.
│
├── 3. Select Kelly multiplier from guide (default: 0.25)
│
├── 4. Compute notional:
│     result = kelly_notional(nav, kelly_f, multiplier, avg_loss,
│                             leverage, carry_discount)
│     Apply cascade_multiplier and trend_multiplier to result["notional_usd"]
│
├── 5. Apply portfolio caps:
│     final = apply_portfolio_caps(result, nav, margin_used,
│                                  correlated_exposure, correlation)
│     final["final_notional_usd"] == 0? → ABORT. Caps fully consumed.
│
├── 6. Pass final_notional_usd to slippage-budget-enforcement
│     as initial_size_usd → book walk may reduce further
│
└── 7. Log full kelly_position_sizing audit event.
         Execute at actual filled size.
         Update margin tracking with actual margin used.