/position-sizer

Position Sizing Methodologies

Overview

Position sizing determines how many shares to buy on each trade. Correct sizing is the single most important factor in long-term portfolio survival. A great stock pick with bad sizing can destroy an account; a mediocre pick with proper sizing preserves capital for the next opportunity.

This reference covers three primary methods: Fixed Fractional, ATR-based, and Kelly Criterion. Each has distinct strengths and ideal use cases.

Fixed Fractional Method (Percentage Risk)

Concept

Risk a fixed percentage of the account on every trade. The most widely used method among professional traders, popularized by Van Tharp and applied rigorously by Mark Minervini and William O'Neil.

Formula

risk_per_share = entry_price - stop_price
dollar_risk    = account_size * risk_pct / 100
shares         = int(dollar_risk / risk_per_share)

In the CLI, whole-share mode remains the default and floors to an integer. When the broker supports fractional shares, --fractional --share-precision N floors to the requested decimal precision instead of rounding up.

Standard Risk Levels

Example

• Account: $100,000
• Entry: $155.00, Stop: $148.50
• Risk per share: $6.50
• At 1% risk: $1,000 / $6.50 = 153 shares
• Position value: $23,715 (23.7% of account)

When to Use

• Default method for most swing and position trades
• When you have a clear technical stop level (support, moving average, prior low)
• When trading a system with established risk parameters
• When a small account or high-priced stock would otherwise round the position to zero shares, provided the broker supports fractional trading for that security and order type

Fractional-Share Mode

Fractional shares can make the risk budget usable for small accounts, high-priced stocks, or very tight risk budgets:

python3 skills/position-sizer/scripts/position_sizer.py \
  --account-size 1000 \
  --entry 155 \
  --stop 148.50 \
  --risk-pct 1.0 \
  --fractional \
  --share-precision 4 \
  --output-dir reports/

With the inputs above, the risk budget is $10 and risk per share is $6.50. Whole-share mode returns 1 share. Fractional mode floors to 1.5384 shares, keeping risk at or below the $10 budget while using more of the account's intended risk allocation.

Use fractional mode as a sizing calculation, not as broker permission. Brokers can impose minimum order sizes, limited fractional support by security or order type, wider effective spreads for small notional orders, margin restrictions, and different tax-lot behavior.

Minervini / O'Neil Integration

Mark Minervini recommends:

• Risk no more than 1% per trade during the early stages of a rally
• Tighten to 0.5% after consecutive losses
• Use a "progressive exposure" model: start with half position, add on confirmation
• Maximum portfolio heat (total open risk): 6-8%

William O'Neil recommends:

• Cut losses at 7-8% below purchase price (hard maximum)
• Preferred loss cut: 3-5% for experienced traders
• Use a "follow-through day" to confirm market direction before increasing exposure

ATR-Based Method (Volatility Sizing)

Concept

Use the Average True Range (ATR) to set stop distance, automatically adjusting position size to a stock's volatility. Originated with the Turtle Traders (Richard Dennis, 1983).

Formula

stop_distance  = atr * atr_multiplier
stop_price     = entry_price - stop_distance
risk_per_share = stop_distance
dollar_risk    = account_size * risk_pct / 100
shares         = int(dollar_risk / risk_per_share)

ATR Multiplier Guidance

Example

• Account: $100,000, Risk: 1%
• Entry: $155.00, ATR(14) = $3.20, Multiplier = 2.0x
• Stop distance: $6.40, Stop: $148.60
• Dollar risk: $1,000
• Shares: int($1,000 / $6.40) = 156 shares

When to Use

• When you want volatility-adjusted sizing across different stocks
• When a stock lacks clear support/resistance for a discrete stop
• For systematic/mechanical trading systems
• When comparing positions across stocks with different price ranges and volatilities

Advantages Over Fixed Stop

1. Low-volatility stocks get larger positions (tighter stop relative to price)
2. High-volatility stocks get smaller positions (wider stop protects against noise)
3. Normalizes risk across the portfolio regardless of stock price

Kelly Criterion

Concept

The Kelly Criterion calculates the mathematically optimal fraction of capital to risk, given known win rate and payoff ratio. Developed by John L. Kelly Jr. (1956) at Bell Labs.

Formula

R         = avg_win / avg_loss       (payoff ratio)
kelly_pct = W - (1 - W) / R          (full Kelly percentage)
half_kelly = kelly_pct / 2            (practical recommendation)

Where W = historical win rate (0 to 1).

Full Kelly vs. Half Kelly

Full Kelly maximizes long-term geometric growth but produces extreme volatility. Drawdowns of 50%+ are common. No professional fund uses full Kelly.

Half Kelly achieves approximately 75% of the theoretical growth rate with dramatically lower drawdowns. This is the standard recommendation for real trading.

Example

• Win rate: 55%, Avg win: $2.50, Avg loss: $1.00
• R = 2.5 / 1.0 = 2.5
• Kelly = 0.55 - 0.45 / 2.5 = 0.55 - 0.18 = 0.37 = 37%
• Half Kelly = 18.5%
• On $100,000 account: risk budget = $18,500

Negative Expectancy

When the Kelly formula produces a negative value, the system has negative expected value. The Kelly percentage is floored at 0%, meaning "do not trade this system."

Example:

• Win rate: 30%, Avg win: $1.00, Avg loss: $1.50
• R = 1.0 / 1.5 = 0.667
• Kelly = 0.30 - 0.70 / 0.667 = 0.30 - 1.05 = -0.75 -> floored to 0%

Two Modes of Use

1. Budget Mode (no entry price): Returns a recommended risk budget as a percentage of account. Useful for capital allocation planning before identifying specific entries.

2. Shares Mode (with entry and stop): Converts the half-Kelly budget into a specific share count using the entry/stop distance.

When to Use

• When you have reliable historical win rate and payoff statistics (100+ trades minimum)
• For portfolio-level capital allocation across multiple strategies
• As a ceiling check: "Am I risking more than Kelly suggests?"
• Not suitable for discretionary traders without track records

Portfolio Constraints

Maximum Position Size

Limit any single position to a percentage of account value:

max_shares = int(account_size * max_position_pct / 100 / entry_price)

Guidelines:

• 5-10%: Conservative (diversified portfolio, 10-20 positions)
• 10-15%: Moderate (concentrated portfolio, 7-10 positions)
• 15-25%: Aggressive (high-conviction portfolio, 4-7 positions)

• 25%: Speculative (not recommended for most traders)

Sector Concentration

Limit total exposure to any single sector:

remaining_pct = max_sector_pct - current_sector_exposure
remaining_dollars = remaining_pct / 100 * account_size
max_shares = int(remaining_dollars / entry_price)

Guidelines:

• Individual stock: 5-10% of portfolio
• Single sector: 25-30% maximum
• Correlated positions: Treat as a single exposure

Position Count and Diversification

Research shows that beyond 20 uncorrelated positions, additional diversification benefit is minimal. For active traders, 5-10 positions with proper sizing often produces better risk-adjusted returns than 20+ positions with diluted conviction.

Binding Constraint Logic

When multiple constraints apply, the strictest (minimum share count) wins. The position sizer identifies which constraint is "binding" so the trader understands what limits the position.

Priority order:

1. Risk-based shares (from Fixed Fractional, ATR, or Kelly)
2. Max position % limit
3. Max sector % limit
4. Final = minimum of all candidates

Method Comparison

Recommended Workflow

1. Start with Fixed Fractional at 1% risk for new strategies or market conditions
2. Switch to ATR-based when comparing opportunities across different volatility profiles
3. Use Kelly as a ceiling after accumulating 100+ trade records
4. Always apply constraints (position limit, sector limit) as a final filter
5. Reduce risk after consecutive losses (Minervini's "progressive exposure" in reverse)

Risk Management Principles

The 1% Rule

Never risk more than 1% of account equity on a single trade. This ensures survival through inevitable losing streaks:

• 10 consecutive losses at 1% = 9.6% drawdown (recoverable)
• 10 consecutive losses at 5% = 40.1% drawdown (devastating)
• 10 consecutive losses at 10% = 65.1% drawdown (account-threatening)

Portfolio Heat

Total open risk across all positions should not exceed 6-8% of account:

portfolio_heat = sum(shares_i * risk_per_share_i) / account_size * 100

If portfolio heat exceeds 8%, do not add new positions until existing trades are moved to breakeven or closed.

Small-Account Friction

For small accounts, the calculated risk budget can be smaller than the practical cost of trading. Before accepting a position size, check:

• Bid/ask spread as a percentage of notional value
• Commission, regulatory, platform, or currency-conversion fees
• Slippage on marketable orders
• Broker minimum order value and fractional-share support
• Margin eligibility, borrow availability for shorts, and settlement rules

If these costs consume a meaningful share of planned risk, reduce frequency, raise the setup-quality bar, use wider time frames, or skip the trade.

Intraday Margin and Day-Trading Controls

Do not treat the legacy "$25,000 pattern day trader" rule as the only current constraint. FINRA Notice 26-10 replaced the old day-trading margin requirements, including the pattern-day-trader day-count and $25,000 minimum-equity requirements, with new intraday margin standards effective 2026-06-04. FINRA allows firms to phase in implementation through 2027-10-20, so the practical rule a trader experiences can still vary by broker during the transition.

Source: https://www.finra.org/rules-guidance/notices/26-10

Asymmetry of Losses

Losses require disproportionately larger gains to recover:

This asymmetry is why position sizing and loss cutting are more important than stock selection.