Finance – Position Sizing
Overview
Position sizing is the most underrated skill in quantitative trading. A strategy with a mediocre edge and excellent position sizing will outperform a brilliant strategy with reckless sizing. This module covers four fundamental frameworks every trader and quant must understand before risking real capital.
Key Concepts
Why Position Sizing Matters
- Two traders with the same strategy and the same edge can have dramatically different outcomes based solely on how much they bet per trade.
- Over-betting leads to catastrophic drawdowns even with a positive expected value.
- Under-betting leaves profits on the table and may not cover transaction costs.
1. Fixed Fractional
Risk a constant percentage of your portfolio on every trade:
Example: Risk 1% of $100,000 with a 5% stop → buy $20,000 of stock.
Pros: Simple, scales with portfolio, well-understood. Cons: Doesn't adapt to strategy's actual edge or volatility conditions.
2. Kelly Criterion
The mathematically optimal bet fraction for maximum long-run compound growth:
| Term | Meaning |
|---|---|
| p | Win probability |
| q = 1-p | Loss probability |
| b | Net odds (avg win / avg loss) |
Practical rule: Always use Half-Kelly (
f*/2) or less. Full Kelly produces extreme drawdowns that most traders cannot tolerate psychologically.
3. Volatility Targeting
Scale positions so the portfolio hits a constant target volatility:
When a stock's volatility doubles, you halve your position size — keeping dollar risk constant. Used by Risk Parity funds and Managed Futures CTAs.
4. Risk of Ruin
The probability of losing enough capital to be unable to continue trading:
In practice, estimated via Monte Carlo over thousands of simulated trading careers.
Files
position_sizing_tutorial.py: Fixed fractional calculator, Kelly criterion with growth simulation, volatility targeting, and Monte Carlo Risk of Ruin.
How to Run
Financial Applications
1. Discretionary Trading
- Fixed fractional (1–2% risk per trade) is the standard rule taught in all professional trading courses.
- Most prop firms enforce maximum risk-per-trade rules contractually.
2. Systematic / Algorithmic Trading
- Kelly is used to size signals in multi-strategy systems (allocate more Kelly-fraction to higher-edge strategies).
- Volatility targeting is the default in Commodity Trading Advisors (CTAs) for futures positions.
3. Options Trading
- Greeks-based sizing: position size chosen to limit delta exposure to 1% of portfolio.
- Theta decay strategies (selling options) often use Kelly-like sizing based on edge estimates.
4. Portfolio Construction
- Risk Parity: every asset contributes equally to portfolio volatility via inverse-vol weighting.
- Maximum Sharpe portfolios from mean-variance optimisation often implicitly implement Kelly logic.
Best Practices
- Never use Full Kelly in practice: estimation error in win_prob and win_loss_ratio is significant, and Kelly's variance is unbounded near the optimum.
- Risk of Ruin > 5%? Don't trade: any strategy with meaningful ruin probability should be either improved or sized down.
- Re-calculate volatility targets frequently: asset volatility changes — update positions at least monthly (daily for liquid futures).
- Account for correlation: if trading multiple strategies, their combined Kelly fraction depends on their correlation structure (use portfolio-level Kelly).
- Transaction costs: include slippage and commissions when estimating win_prob and win_loss_ratio — overestimating edge is the #1 cause of over-sizing.