Position Sizing

Position sizing determines how much capital to allocate to each trade. Getting this right is arguably more important than the entry signal itself – even a mediocre strategy can survive if position sizes are managed well, and a great strategy can blow up if they are not.

The puffin.risk.position_sizing module provides three main approaches: fixed fractional, Kelly criterion, and volatility-based sizing.

Fixed Fractional

The fixed fractional method risks a fixed percentage of equity on each trade. It is the simplest and most widely used approach.

Formula:

Position Size = (Equity x Risk%) / Stop Distance

For example, risking 2% of a $100,000 account with a $5 stop distance gives a position of 400 shares.

from puffin.risk import fixed_fractional

# Risk 2% of $100,000 equity with a $5 stop
position_size = fixed_fractional(
    equity=100000,
    risk_pct=0.02,  # 2%
    stop_distance=5.0
)
print(f"Position size: {position_size} shares")  # 400 shares

The function raises ValueError if equity is non-positive, risk_pct is outside (0, 1], or stop_distance is non-positive.

Kelly Criterion

The Kelly Criterion calculates the theoretically optimal position size based on your win rate and the ratio of average win to average loss. It maximizes the long-run geometric growth rate of your equity.

Formula:

Kelly% = (Win Rate x Win/Loss Ratio - (1 - Win Rate)) / Win/Loss Ratio

from puffin.risk import kelly_criterion

# 55% win rate, 1.5 win/loss ratio
kelly_pct = kelly_criterion(
    win_rate=0.55,
    win_loss_ratio=1.5,
    fraction=0.5  # Half Kelly for conservatism
)
print(f"Optimal position size: {kelly_pct*100:.1f}% of equity")

Full Kelly can be aggressive. Full Kelly sizing maximizes long-run growth but can produce severe drawdowns along the way. In practice, most traders use half Kelly (fraction=0.5) or quarter Kelly (fraction=0.25) for more conservative sizing. The fraction parameter defaults to 0.5 for this reason.

Volatility-Based Sizing

Volatility-based sizing adjusts position size using ATR (Average True Range) so that each trade risks roughly the same dollar amount regardless of how volatile the instrument is.

from puffin.risk import volatility_based

# Adjust for volatility
position_size = volatility_based(
    equity=100000,
    atr=3.0,
    risk_pct=0.02,
    multiplier=2.0  # 2x ATR stop
)
print(f"Position size: {position_size} shares")

Benefits:

  • High volatility leads to smaller positions
  • Low volatility leads to larger positions
  • Automatically adapts to changing market conditions

Volatility-based sizing is especially useful when trading a diversified portfolio of instruments with different volatility profiles. It normalizes risk across positions so that a single high-volatility name does not dominate the portfolio’s P&L.

Exercises

  1. Compare sizing methods. Using a $50,000 account, calculate the position size for a stock at $120 with a $4 stop distance using both fixed fractional (2% risk) and volatility-based sizing (ATR = 2.5, multiplier = 2.0). Which gives a larger position? Why?

  2. Kelly sensitivity. Compute the full Kelly percentage for win rates of 0.45, 0.50, 0.55, and 0.60, all with a win/loss ratio of 1.5. At what win rate does Kelly first recommend a positive allocation? What happens at 0.45?

  3. Fractional Kelly. A strategy has a 60% win rate and a 2.0 win/loss ratio. Calculate the full Kelly, half Kelly, and quarter Kelly allocations. Plot a simulated equity curve for each over 200 trades (you can generate random win/loss outcomes using numpy.random).