Position Sizing and Risk-Reward Ratios

Position sizing answers the question: "How many shares should I buy?" The answer isn't "as many as I can afford" or "whatever feels right." It's a function of your account size, the specific risk of each trade, and your tolerance for drawdowns. Combined with risk-reward analysis, proper position sizing can mean the difference between a 50% drawdown that destroys your trading capital and a 15% drawdown that's recoverable. The practical skill: using formulas that tie position size to defined risk levels before you enter any trade.

The Position Sizing Problem

Most traders size positions by dollars available or conviction level. Both approaches lead to ruin:

Dollar-based sizing failure:

• Account: $50,000
• Approach: Put $10,000 in each trade (20% per position)
• Five losing trades at 15% each: -$7,500 total (15% account loss)
• One position gaps down 40%: -$4,000 additional (23% total loss)

Conviction-based sizing failure:

• High conviction trade: 30% of account
• Medium conviction: 15% of account
• Low conviction: 5% of account
• Problem: Your "high conviction" trades aren't actually more accurate. Studies show trader conviction correlates weakly (r < 0.20) with outcome accuracy.

The point is: Position size should be determined by the dollar amount you're willing to lose, not by how much you want to invest or how confident you feel.

Fixed Fractional Position Sizing

The most practical approach for active traders: risk a fixed percentage of your account on each trade.

The formula:

Position Size (shares) = (Account Size x Risk %) / (Entry Price - Stop Loss Price)

Worked example:

• Account: $100,000
• Risk per trade: 1% ($1,000)
• Stock: XYZ trading at $50.00
• Stop loss: $47.00 (6% below entry)
• Risk per share: $50.00 - $47.00 = $3.00

Position size = $1,000 / $3.00 = 333 shares Position value = 333 x $50 = $16,650 (16.7% of account)

If stop triggers: 333 shares x $3.00 loss = $999 (1% of account, as intended)

Key insight: The position size (16.7% of account) is derived from the stop distance, not chosen arbitrarily. A tighter stop ($48.50) would allow a larger position; a wider stop ($45.00) would require a smaller position.

Risk percentage guidelines:

Consecutive loss survival:

The durable lesson: At 1% risk per trade, you can survive 22 consecutive losing trades before hitting a 20% drawdown. At 3% risk, only 7 losing trades puts you in recovery mode.

Kelly Criterion: Optimal Sizing Theory

The Kelly Criterion calculates the mathematically optimal bet size to maximize long-term growth. Developed by John Kelly at Bell Labs (1956).

The formula:

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

Or simplified: Kelly % = Win Rate - ((1 - Win Rate) / Reward:Risk Ratio)

Worked example:

Your trading system over 100 trades:

• Win rate: 55%
• Average winning trade: +$600
• Average losing trade: -$400
• Reward:Risk ratio: $600 / $400 = 1.5

Kelly % = 0.55 - (0.45 / 1.5) = 0.55 - 0.30 = 0.25 (25%)

Full Kelly interpretation: Bet 25% of your bankroll on each trade.

The problem with full Kelly:

• Requires precise knowledge of true win rate and average win/loss
• Assumes infinite time horizon and no psychological limits
• Drawdowns can exceed 50% even with accurate estimates
• Small errors in estimates produce large errors in optimal bet

Practical Kelly adjustments:

Most traders use quarter Kelly or less. This sacrifices some theoretical growth for dramatically smoother equity curves.

Kelly sensitivity example:

If your true win rate is 50% (not 55% as estimated):

• Estimated Kelly: 25%
• True optimal Kelly: 16.7%
• Overbetting by 8.3% leads to excessive drawdowns

The practical point: Kelly Criterion is useful for understanding optimal sizing theory, but real-world application requires conservative adjustments due to parameter uncertainty.

Volatility-Based Position Sizing

Adjusts position size based on the stock's volatility, ensuring consistent dollar risk across different instruments.

Average True Range (ATR) method:

Position Size = (Account x Risk %) / (ATR x ATR Multiple)

Worked example:

• Account: $100,000
• Risk per trade: 1% ($1,000)
• Stock: ABC trading at $75.00
• 14-day ATR: $2.50
• Stop: 2x ATR below entry ($75.00 - $5.00 = $70.00)

Position size = $1,000 / ($2.50 x 2) = $1,000 / $5.00 = 200 shares Position value = 200 x $75 = $15,000

Comparison across volatility:

Result: Lower volatility allows larger positions; higher volatility requires smaller positions. Dollar risk stays constant at $1,000.

Why volatility-based sizing works:

• A 2x ATR move is equally likely across stocks (roughly)
• Your stop distance (in ATR terms) has consistent probability of triggering
• You're not over-risking on volatile names or under-risking on stable ones

Risk-Reward Ratios

Risk-reward ratio compares potential profit to potential loss on a trade.

The formula:

Risk-Reward Ratio = (Target Price - Entry Price) / (Entry Price - Stop Loss Price)

Worked example:

• Entry: $50.00
• Stop loss: $47.00 (risk: $3.00 per share)
• Target: $59.00 (reward: $9.00 per share)

Risk-Reward = $9.00 / $3.00 = 3:1

Interpretation: You're risking $3 to make $9. If this trade works one-third of the time, you break even. Above 33% success rate, you're profitable.

Breakeven win rate by risk-reward:

The calculation shows: With a 3:1 reward-to-risk ratio, you only need to be right 25% of the time to break even (before commissions).

Expectancy formula:

Expectancy per trade = (Win Rate x Average Win) - (Loss Rate x Average Loss)

Example:

• Win rate: 45%
• Average win: $900 (3x risk)
• Average loss: $300 (1x risk)

Expectancy = (0.45 x $900) - (0.55 x $300) = $405 - $165 = $240 per trade

Positive expectancy: This system makes $240 on average per trade, despite winning less than half the time.

Combining Position Sizing and Risk-Reward

Complete trade setup example:

Account: $100,000 Risk per trade: 1.0% Stock: DEF Corp at $80.00 Technical analysis identifies:

• Support level (stop): $76.00
• Resistance target: $92.00

Step 1: Calculate risk-reward

• Risk: $80 - $76 = $4.00 per share
• Reward: $92 - $80 = $12.00 per share
• Risk-Reward: 3:1 (acceptable)

Step 2: Calculate position size

• Dollar risk: $100,000 x 1% = $1,000
• Shares: $1,000 / $4.00 = 250 shares
• Position value: 250 x $80 = $20,000 (20% of account)

Step 3: Evaluate maximum loss

• If stop triggers: 250 x $4 = $1,000 loss (1% of account) - acceptable
• If gap through stop (20% gap): 250 x $16 = $4,000 loss (4% of account) - understood

Step 4: Evaluate maximum gain

• If target hit: 250 x $12 = $3,000 gain (3% of account)

Trade parameters:

• Buy 250 shares at $80.00
• Stop loss at $76.00
• Target at $92.00
• Risk: $1,000 (1%)
• Potential reward: $3,000 (3%)

Position Sizing Rules for Portfolio Management

Single position limits:

Sector and correlation limits:

• No more than 25% in any single sector
• Correlated positions (similar stocks, same industry) count as one position for risk purposes
• If holding 3 tech stocks at 10% each, treat as 30% tech exposure

Portfolio heat:

Portfolio Heat = Sum of (Position Size x Distance to Stop)

Example:

• Position A: 15% of account, stop 5% below = 0.75% risk
• Position B: 10% of account, stop 8% below = 0.80% risk
• Position C: 12% of account, stop 4% below = 0.48% risk

Total portfolio heat: 2.03%

If all stops trigger simultaneously, account loses 2.03%. Keep portfolio heat under 5-6% to survive correlated drawdowns.

Common Position Sizing Mistakes

Mistake 1: Sizing up after wins (gambler's fallacy)

After three winning trades, you feel confident and double position size. The next trade loses 15%, wiping out previous gains.

Solution: Keep risk percentage constant regardless of recent results.

Mistake 2: Averaging down without plan

Stock drops 10% below entry. You double position size "at a better price." Now your effective risk is 2x the original plan.

Solution: Only add to positions at predetermined levels with predetermined size as part of the original plan.

Mistake 3: Ignoring slippage on stops

You calculate position size assuming stop at $47.00 fills at $47.00. In fast markets, stop triggers at $46.00 (2% slippage).

Solution: Assume 0.5-1.0% slippage on stops when calculating position size. Use slightly tighter stops or smaller positions.

Mistake 4: Too many positions

With 1% risk per trade, you take 15 positions (15% total risk). Market correction hits all positions; you lose 12% before stops trigger.

Solution: Track portfolio heat and limit total open risk to 5-6%.

Position Sizing Checklist

Before entering any trade:

• Define stop loss level based on technical levels, not arbitrary percentages
• Calculate risk-reward ratio and verify it exceeds 1.5:1 minimum (preferably 2:1+)
• Apply position sizing formula using fixed fractional (1% risk) or volatility-based method
• Check portfolio heat to ensure total open risk remains under 5-6%
• Account for slippage by assuming stops may fill 0.5-1.0% worse than intended

Position sizing summary:

The goal is survival first, growth second. A 50% drawdown requires a 100% gain to recover. A 20% drawdown requires only a 25% gain. Position sizing that limits individual trade losses to 1% of account and portfolio heat to 5% ensures you stay in the game long enough for positive expectancy to compound.