II IntermediateWeek 4 • Lesson 10Duration: 60 min

PSZ Position Sizing

The thing that actually determines whether you survive

Learning Objectives

•Master fixed fractional sizing and Kelly criterion
•Understand the relationship between position size and drawdown
•See why ultra-conservative sizing is the smart play for funded accounts
•Learn drawdown-triggered risk scaling and why adaptive sizing matters
•Run Monte Carlo simulations to validate sizing choices

Explain Like I'm 5

Position sizing is deciding how much money to put on each trade. Too much and one bad trade kills you. Too little and winning doesn't matter. The goal is finding the spot where you grow steadily without risking blowup. It's the most important decision you make, and most people get it wrong.

Think of It This Way

Position sizing is a volume knob. Same song (strategy) plays at any volume. Too quiet (tiny size) — you can barely hear the gains. Too loud (oversized) — the distortion (drawdown) blows your speakers (account). You want it loud enough to feel but clean enough to last.

1Fixed Fractional — The Gold Standard

Fixed fractional means risking a fixed percentage of your current account on each trade. Production systems typically use 0.20-0.50%. Why this works: • As you win, sizes grow (compounding — winners get bigger) • As you lose, sizes shrink (protection — losers get smaller) • Mathematically impossible to reach zero (asymptotic approach) 0.30% feels tiny. Most retail traders hear that and think "that's not worth trading." That reaction is exactly why most retail traders blow up. Do the math: 0.30% risk × strong win rate × hundreds of trades per year = serious compounding. And keeping max drawdown small means you survive to take all those trades. Survival is the strategy. Most retail traders risk 2-5% per trade — roughly 7-17x what production systems use. Five losses at 3% each = 15% drawdown. Game over on any funded account.

Account Growth: 0.30% vs 1% vs 3% Risk (1000 Trades, 58% WR)

2Kelly Criterion — Optimal But Dangerous

Kelly criterion gives you the mathematically optimal position size for maximum long-run growth. Sounds great. Here's why it's terrifying in practice. f = p - q/b For a typical system with 59% win rate and 1.74 W/L ratio: f = 0.59 - 0.41/1.74 = 0.354 = 35.4% risk per trade 35.4%? That's insane. Full Kelly is far too aggressive because: 1. It assumes your edge estimate is perfect (it never is) 2. Drawdowns are brutal — 50%+ is normal with full Kelly 3. Any error in edge estimation becomes catastrophic 4. It ignores execution costs, slippage, and correlation That's why practitioners use fractional Kelly — typically 0.10x to 0.25x of the full number. Production systems go even lower, sometimes 0.01x Kelly or less. The math says go big. Survival instinct says go small. Always listen to survival.

Full Kelly vs Fractional Kelly — Expected Max Drawdown

3Position Size and Drawdown — The Tradeoff

There's a direct mathematical relationship between position size and expected max drawdown. Bigger positions = higher returns, but exponentially worse drawdowns. This relationship is not linear — it's much steeper than most people expect. Rough relationship: max DD ∝ risk_per_trade × √(number_of_trades) With real numbers over ~4,500 trades: • 0.20% risk: ~1.0% max DD • 0.30% risk: ~1.5% max DD • 0.50% risk: ~3.0% max DD • 1.00% risk: ~5-7% max DD (getting risky) • 2.00% risk: ~10-15% max DD (breach territory) • 5.00% risk: ~25%+ max DD (blown account) The jump from 0.30% to 2.00% risk is 6.7x in sizing but 7-10x in drawdown. The math punishes aggression more than it rewards it. Sizing isn't arbitrary — it comes from Monte Carlo simulations running thousands of scenarios. You pick the level that gives you a breach probability you can tolerate.

Risk Per Trade vs Expected Maximum Drawdown

4Drawdown-Triggered Risk Scaling

Your position size shouldn't be static. It should adapt to how things are going right now. If you're in a drawdown, continuing at the same risk is compounding losses. Smart systems scale down during drawdowns and back up during normal operation. Typical zones: NORMAL (0-4% DD) — full risk. Everything operating within expected range. CAUTION (4-6% DD) — reduce by ~15-20%. Something might be off — maybe a regime change, maybe a bad streak. Protect capital. DANGER (6-8% DD) — drop to survival mode. Reduce by ~35%. Getting close to limits that matter. CRITICAL (8-10% DD) — emergency mode. Minimum risk or stop entirely. Survival is the only priority. This sounds obvious when you read it, but almost nobody does it. Most traders keep the same size (bad) or revenge trade with bigger size after losses (catastrophic). The adaptive protocol is the difference between recovering from a bad streak and blowing the account.

DD-Triggered Risk Scaling Protocol

5Monte Carlo Validation

This is what separates guessing from engineering. Monte Carlo simulation takes your historical trades and resamples them thousands of times to answer: "across all possible orderings of these trades, how bad could it get?" The workflow: 1. Take your actual trade results (wins and losses) 2. Randomly resample with replacement to create a new equity curve 3. Measure the max drawdown 4. Repeat 5,000 times 5. Look at the distribution of max drawdowns You get a probability distribution: "95% chance max DD stays below X%," "99% chance it stays below Y%." For funded accounts, the key question is: "What's the probability max DD exceeds 10%?" That's your breach probability. You want it well below 5%, ideally below 1%. If Monte Carlo says breach probability is 3% at 0.50% risk but 0.08% at 0.30%, you take the 0.30%. The safety margin is worth more than the extra return. Because one breach = done. Start over.

Monte Carlo: Max Drawdown Distribution (5000 Simulations)

6Common Position Sizing Mistakes

Five mistakes I've seen destroy accounts: "I'll risk more on high-confidence trades." Sounds smart, isn't. Your confidence calibration is almost certainly wrong, and variable sizing adds massive variance. Fixed fractional is fixed for a reason. "I'll increase size after a winning streak." Gambler's fallacy in a suit. Winning streaks don't predict future wins. Your next trade has the same edge regardless of what just happened. Fixed fraction already handles this — account grew, so positions naturally got bigger. "I'll double down after losses." Martingale. 100% probability of eventual ruin given enough time. Don't. Ignoring execution costs. Your theoretical size assumes perfect fills. Reality has slippage, spread, commissions. A strategy profitable at 0.50% risk might be breakeven after costs. Not adjusting for correlation. Five open positions in USD pairs? Your real risk is 5x what you think. Individual trade sizing means nothing if you ignore portfolio-level exposure.

Key Formulas

Position Size (Fixed Fractional)

The formula for every trade. Calculates lot size based on account, risk percentage, and stop distance. Plug in the numbers, get the size. No guessing.

Kelly Criterion

Optimal fraction of capital per trade. p = win rate, q = 1-p, b = avg win / avg loss. Never use full Kelly in practice — use 0.25x or less.

Hands-On Code

Position Size Calculator

python

import numpy as np

def calculate_position_size(account_balance, risk_pct, 
                             stop_loss_pips, pip_value=10.0):
    """Calculate lot size for fixed fractional position sizing."""
    risk_amount = account_balance * risk_pct
    lot_size = risk_amount / (stop_loss_pips * pip_value)
    return round(lot_size, 2)

# Example: FTMO $100K account
account = 100_000
risk = 0.003  # 0.30%

# Different stop loss sizes
for sl in [30, 45, 60, 80]:
    lots = calculate_position_size(account, risk, sl)
    dollar_risk = account * risk
    print(f"SL: {sl} pips → {lots} lots (risking ${dollar_risk:.0f})")

# Kelly calculation for reference
win_rate = 0.592
avg_win = 1.65
avg_loss = 0.95
kelly = win_rate - (1 - win_rate) / (avg_win / avg_loss)
print(f"\nFull Kelly: {kelly:.1%}")
print(f"Quarter Kelly: {kelly/4:.1%}")
print(f"Production uses: 0.30% (≈ {0.003/kelly:.3f}x Kelly)")
print(f"→ Ultra conservative. Survival first.")

Compute position size before every trade. Never eyeball it. The code shows how different stop distances change lot size while keeping dollar risk constant.

Knowledge Check

Q1.Why use 0.30% risk instead of full Kelly (~35%)?

Q2.An account has $50K and uses 0.30% risk. What's the dollar risk per trade?

Assignment

Build a position size calculator that takes account balance, risk %, stop loss pips, and pip value. Test with a $100K FTMO account. What's the max position you'd ever take? Run a Monte Carlo sim comparing 0.30%, 1%, and 3% risk. Plot equity curves and max drawdown distributions side by side.

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