IntermediateOptions, Derivatives & FinancePython

Run this module

cd "Finance - Position Sizing"
python "position_sizing_tutorial.py"

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:

dollar_risk = portfolio × risk_pct
position_size = dollar_risk / stop_loss_pct

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:

f* = p – q/b = p – (1 – p) / (avg_win / avg_loss)

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:

notional = portfolio × (target_vol / asset_vol)

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:

Risk of Ruin ≈ ((1 – edge) / (1 + edge))^(capital / risk_per_trade)

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¶

python position_sizing_tutorial.py

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.

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