Monte Carlo shows the range of outcomes; sizing decides if you survive the bad ones.
What you will learn
Understand Monte Carlo simulation
Master position sizing
Appreciate the Kelly criterion
Fixed-fraction sizing
Fixed-fraction sizing
The drawdown risk
The drawdown risk
Monte Carlo simulation
Monte Carlo runs thousands of random scenarios — market returns, drawdowns, sequences — to show the distribution of possible outcomes, not one forecast. It answers: 'given my strategy and its variance, what's the probability I lose X%?' It's risk's crystal ball.
💡 Why sequence matters
Two retirees with the same average return can have wildly different outcomes depending on the order of returns. Withdrawing during an early crash devastates a portfolio (sequence-of-returns risk). Monte Carlo exposes this: it's not the average that kills you, it's the path.
Position sizing
Position size = (account × risk%) ÷ stop distance. Risk a fixed fraction (e.g., 1%) per trade, and no single trade — or even a bad streak — can cripple you. Sizing is the single most important risk decision, more than entry or exit.
The Kelly criterion
Kelly gives the mathematically optimal fraction to bet given your edge and odds: f* = (p·b − q) / b. It maximizes long-run growth but assumes you know your edge precisely — which you don't. So the practical rule: bet a fraction of Kelly (e.g., half or quarter).
💡 Half-Kelly in practice
If full Kelly says 20% and you're wrong about your edge, you overbet and can go broke. Half-Kelly (10%) sacrifices some growth for far less ruin risk. In the real world, under-betting your edge is how you stay alive long enough to let it compound.
The survival principle
Monte Carlo and Kelly converge on one truth: the goal is not to maximize return — it's to avoid ruin. Size positions so the worst plausible sequence of outcomes is a setback, not an ending. He who survives, compounds.
❓ Quick check
Position size = (account × risk%) ÷ ?
A) Leverage
B) Stop distance
C) Beta
D) Volatility
Size = risk ÷ stop distance.
(Knowledge check — full exam is next)
Key takeaways
Monte Carlo = the distribution of outcomes, not one forecast
Sequence-of-returns risk: the path matters, not just the average
Size for survival — fraction of Kelly; avoid ruin
📝 Weekly Exam — pass with 80% to unlock next week
10 questions. Review the Deep Dive and courses before attempting.
1. Monte Carlo simulation shows:
Thousands of scenarios.
2. Sequence-of-returns risk matters most when:
Order of returns matters in drawdown.
3. Position size = (account × risk%) ÷:
Risk ÷ stop distance.
4. The Kelly criterion computes:
Optimal growth fraction.
5. In practice, you should bet a ___ of Kelly:
Under-bet to avoid ruin.
6. The #1 goal of position sizing is:
Survival.
7. Risking 1% per trade means:
Fixed-fraction risk.
8. Over-betting your edge (full Kelly) risks:
Over-betting → ruin.
9. Monte Carlo is 'risk's crystal ball' because it:
Distribution of outcomes.
10. 'He who survives, compounds' means:
Survival enables compounding.
Your score: —
🛠 Weekly Project
Run a hand Monte Carlo.
1
Assume a 7% average annual return and 15% volatility.
2
Simulate 10 random 10-year paths (you can use a coin/random numbers for up/down years).
3
Note the spread between the best and worst path.
4
Write one sentence on how the path (sequence), not the average, drives the outcome.