Position Sizing¶
Difficulty advanced
Overview¶
Position sizing determines how much capital to allocate to each trade. It's arguably the most important aspect of risk management — it determines whether you survive long enough for your edge to play out.
Fixed Fractional¶
Position Size = (Account × Risk %) / (Entry - Stop Loss)
Example:
Account: $100,000
Risk per trade: 1% = $1,000
Entry: $50
Stop: $48
Risk per share: $2
Shares = $1,000 / $2 = 500 shares
where:
Accounttotal equity ·Risk %fixed fraction of equity risked per trade ·Entryentry price ·Stop Losspredetermined exit price for losses does: derives share count from a fixed-risk budget given a defined stop distance — used as the default sizing rule for discretionary and systematic traders alike because it caps per-trade loss to a known fraction of equity regardless of asset price.
Kelly Criterion¶
Formula¶
f* = (bp - q) / b
where:
b = Average Win / Average Loss (odds)
p = Win probability
q = 1 - p (loss probability)
where:
f*optimal fraction of equity per bet ·bnet win-to-loss ratio ·pwin probability ·q = 1 − pdoes: the discrete-outcome Kelly formula — used to anchor maximum-growth sizing for binary trades; in practice cut by 50–75% because parameter estimates are noisy and full Kelly produces unmanageable drawdowns.
Practical Kelly¶
Full Kelly is too aggressive for most traders. Use:
| Approach | Fraction | Risk Profile |
|---|---|---|
| Full Kelly | 100% | Aggressive, high drawdown |
| Half Kelly | 50% | Balanced, recommended |
| Quarter Kelly | 25% | Conservative |
| Tenth Kelly | 10% | Very conservative |
Volatility-Based Sizing¶
Position Size = (Account × Risk %) / (ATR × Multiplier × Price)
Normalizes risk across assets with different volatilities
where:
Accounttotal equity ·Risk %per-trade risk budget ·ATRaverage true range (volatility proxy) ·Multiplierstop distance in ATRs ·Pricecurrent asset price does: sizes positions inversely to volatility so each position contributes the same expected risk — used in CTA, futures, and multi-asset systematic books to equalize position contribution across assets with very different volatilities.
Risk Parity¶
where:
Weight_iportfolio weight of asseti·σ_ivolatility of asseti·Σ(1/σ_j)sum of inverse volatilities across all assets does: the inverse-vol weighting that gives each asset an equal marginal risk contribution — used as a robust allocation when expected returns can't be reliably estimated and as the building block inside multi-asset risk parity portfolios.
Optimal f (Ralph Vince)¶
Test different position sizes on historical trade sequence
Find f that maximizes Terminal Wealth Relative (TWR)
Portfolio-Level Sizing¶
Correlation-Adjusted¶
When positions are correlated, effective risk is higher
Adjusted Size = Base Size / √(1 + (n-1) × ρ)
where ρ = average correlation between positions
where:
Base Sizestandalone position size ·nnumber of correlated positions ·ρaverage pairwise correlation does: shrinks individual position sizes to keep portfolio variance constant as correlated positions accumulate — used so a basket of correlated trades doesn't quietly turn into a single oversized macro bet.
Maximum Portfolio Risk¶
Total Portfolio Risk ≤ 6% of capital
Individual Trade Risk ≤ 1-2% of capital
Maximum Correlated Risk ≤ 3% of capital
Position Sizing Decision Matrix¶
| Account Size | Risk/Trade | Max Positions | Notes |
|---|---|---|---|
| < $25,000 | 1% | 3-5 | Conservative |
| $25,000-100,000 | 1-2% | 5-10 | Standard |
| $100,000-1M | 0.5-1% | 10-20 | Diversified |
| > $1M | 0.25-0.5% | 20+ | Institutional |
Scaling In/Out¶
Scaling In¶
Initial entry: 50% of target size
Add on confirmation: 25%
Add on further confirmation: 25%
Or: Equal thirds at predefined levels
Scaling Out¶
Take partial profit at Target 1: 33%
Take partial profit at Target 2: 33%
Let remainder run with trailing stop: 34%
Practical Guidelines¶
- Never Risk More Than 2% — Survival is paramount
- Size Before Entry — Know your position size before you trade
- Adjust for Conviction — Higher conviction = larger size (within limits)
- Correlation Matters — Correlated positions amplify risk
- Reduce After Losses — Drawdown recovery requires smaller risk
- Increase After Wins — Compound profits, but gradually
- Document Everything — Track position sizes and outcomes
Drawdown and Position Sizing¶
After 10% drawdown → reduce risk by 25%
After 20% drawdown → reduce risk by 50%
After 30% drawdown → reduce risk by 75%
Recovery table:
10% loss needs 11% gain
20% loss needs 25% gain
30% loss needs 43% gain
50% loss needs 100% gain
q&a¶
Why is position sizing more important than entry timing?
Entry timing affects expected return per trade. Position sizing affects whether you survive long enough for expected return to play out. A great edge with terrible sizing still blows up. A mediocre edge with disciplined sizing compounds. The variance of your account growth is dominated by how much you risk per position, not when you click buy.
Should I risk a fixed dollar amount or a fixed percentage?
Fixed percentage. Risking $1,000 per trade is fine at $100K, ruinous at $10K. Percentage of equity scales naturally with account size, automatically reducing risk after losses and increasing it after wins — the mechanics of geometric growth.
How do I size around correlated positions?
Treat correlated positions as if they were one larger position. If you're long 5 tech names with average correlation 0.8, effective risk is much closer to 1 position × √(1 + 4×0.8) ≈ 2× the single-position risk, not 5× independent risk. See Correlation Analysis for the math.
What's wrong with full Kelly?
Kelly assumes you know your win rate and odds with certainty. In practice you estimate both with noise — and the second derivative of geometric growth around full Kelly is steep and asymmetric. Slight overestimation of edge plus full Kelly sizing produces catastrophic drawdowns. Half-Kelly cuts variance ~75% for ~25% expected-return reduction.
When should I reduce size?
After material drawdowns (rules-based, e.g. 10% / 20% / 30% triggers), when your strategy is statistically out-of-regime (rolling Sharpe below threshold), or when you're emotionally compromised by recent losses. Never increase size in revenge for losses.
Next Steps¶
- Kelly Criterion — Optimal growth theory
- VaR/CVaR — Portfolio risk measurement
- Portfolio Optimization — Allocating across positions