Position sizing Kelly Criterion — optimal allocation

Kelly Criterion = optimal bet sizing dla compounding wealth long-term. Founder: John Kelly Jr. 1956 AT&T Bell Labs. Information theory paper. Applied gambling: Edward Thorp Beat the Dealer (1962) blackjack card counting. Applied finance: 1970s-1980s hedge funds (Renaissance Medallion famously uses Kelly variants). Formula: Kelly% = WR - (1-WR)/(avg win / avg loss). Where: WR = win rate decimal (0.55 = 55%). Avg win / avg loss = win-to-loss ratio. Example calculation: Strategy: WR 55%, avg win €150, avg loss €100, ratio 1.5. Kelly% = 0.55 - (1-0.55)/(150/100) = 0.55 - 0.45/1.5 = 0.55 - 0.30 = 0.25 = 25%. Interpretation: optimal risk per trade = 25% account balance. Multi-strategy Kelly: portfolio Kelly = sum individual Kellys. NIE exceed 100%. Negative Kelly: jeśli formula gives negative number = NIE edge, NIE trade strategy. Geometric vs arithmetic growth: Kelly maximizes geometric (compound) growth long-term. Arithmetic max bet = 100% (eventual ruin). Kelly balance growth vs ruin probability. Reality check: 25% per trade = massive volatility. 50%+ drawdowns possible. Psychologically devastating retail. Most traders use Half Kelly (12.5%) lub Quarter Kelly (6.25%) lub less.

Full Kelly = mathematical theory vs psychological reality. Theoretical optimum: Kelly maximizes geometric long-term growth. Anything less = suboptimal growth. Anything more = increased ruin risk. Reality drawdowns: Full Kelly 25% per trade: 50% drawdown probability w 1000 trade sample ~99%. 50% drawdown PER STRATEGY MAY OCCUR. Multiple times. Recovery math: -50% drawdown requires +100% gain dla recovery. Long path. Half Kelly 12.5%: drawdown probability 50% reduces to ~70%. Still aggressive. Quarter Kelly 6.25%: drawdown probability 50% reduces to ~25%. More palatable. 1% fixed: drawdown probability 50% near 0%. Safe but slower growth. Psychological reality: retail traders typically can't handle 25%+ drawdowns without panic-quitting. Statistically optimal NIE psychologically optimal. Monte Carlo simulation perspective: 1000 sims same strategy, Full Kelly: median final wealth highest. BUT distribution wide. 10% sims lose 80%+. 1% sims lose 95%+. Could be YOU. Half Kelly: median final wealth ~75% Full Kelly. Distribution narrower. Quarter Kelly: median ~50% Full Kelly. Distribution narrow. Safer. Krzysztof case: implemented Full Kelly. 6 mies. 50% drawdown. Panic-quit. Lost half capital + emotional damage. Switched 2% fixed. Year 2 +18% steady, no drawdown > 12%. Psychological sustainability matters > theoretical optimum.

Kelly Criterion ASSUMES accurate WR + R/R estimation. Errors = catastrophic. Common estimation errors: Survivorship bias: backtest WR 65% include only profitable mies. Live WR 55%. 10% overestimation. Sample size issues: 50 trades NIE enough dla statistical significance. 200+ minimum, 1000+ ideal. Regime changes: WR 65% w 2018 może być 45% w 2024 (different market regime). Random variation: same strategy może produce 50% WR over 50 trades, 60% WR next 50 — Monte Carlo demonstrated. Impact errors on Kelly: Example: assumed WR 60%, R/R 1.5 → Kelly 27%. Actual WR 50% → real Kelly 17%. Trading 27% instead 17% = overbetting 60%. Drawdown explosion. Asymmetric impact: Under-bet: smaller wealth, ale safe. Over-bet: catastrophic. NIE recoverable many cases. Asymmetric downside. Defense rules: (1) Discount estimated Kelly by 50% dla buffer. Kelly 25% → use 12.5%. (2) Minimum 200 trade history required. (3) Re-validate quarterly. Market regimes change. (4) NIE Full Kelly EVER. Half max realistic. (5) Quarter Kelly recommended retail. (6) Monte Carlo simulation overlay dla validation. Why Renaissance succeeded: 1000s strategies, billions data points, professional statisticians. Retail = small sample, biased estimation. Different game. Best practice retail: 1-2% fixed percentage. Conservative, sustainable, error-tolerant.

Practical position sizing dla retail: (1) Fixed percentage 1-2% (recommended majority retail): standard 1% per trade. Conservative, sustainable. NIE optimal mathematically ale optimal psychologically. Multi-decade career possible. (2) Quarter Kelly dla advanced retail z 200+ trade history: kalkulacja Kelly% × 0.25. Większy niż 1% ale safer Full Kelly. (3) Volatility-adjusted: position size adjust based ATR. High volatility = smaller size. Low volatility = larger. Adaptive. (4) Equity curve adaptive: po drawdown 10% reduce size 50%. Po recovery restore. Compound losses limiter. NIE recommended retail: Full Kelly: too aggressive, psychologically unsustainable. Half Kelly: borderline. Only z 1000+ trade history + statistical edge confirmed Monte Carlo. Anti-pattern: Increasing size na winning streak: feels good, statistically dangerous. Streaks reverse statistically. Decreasing na losing streak: actually GOOD (Quarter Kelly w drawdown adjust). Random size: emotional decisions. Statistical noise. Sample retail framework: Tier 1 beginner (year 1): 0.5% per trade fixed. Survive. Tier 2 intermediate (year 2-3): 1% per trade fixed. Standard. Tier 3 advanced (year 4+): 1-2% per trade + volatility adjustment. Tier 4 expert (1000+ trades history): Quarter Kelly max. Recalibrate quarterly. Anna case: started 5% per trade enthusiast. Blew account 6 mies. Restart 0.5%, then 1% steady. Year 5 +25% rocznie 1% sizing. Discipline > optimization.