Position Sizing Formulas: Risk-Adjusted Capital Allocation

Why Position Sizing Matters

Poor sizing = Blown accounts

Example:

• Put 50% of account in one trade
• Trade goes bad, down 80%
• Lost 40% of entire account
• Game over

Proper sizing = Consistent growth

Same scenario:

• Put 5% of account in one trade
• Trade goes bad, down 80%
• Lost 4% of entire account
• 95 more chances to get it right

The 5 Position Sizing Methods

Method	Best For	Complexity	Risk Level
Equal Dollar	Beginners	Low	Low-Medium
Fixed Fractional	Most traders	Medium	Medium
Kelly Criterion	Advanced	High	Medium-High
Volatility Adjusted	Experts	High	Medium
Tiered Allocation	All levels	Medium	Low-Medium

Method 1: Equal Dollar Allocation

How it works: Divide capital equally among all positions.

Formula:

Position Size = Total Capital / Target Number of Positions

Example - $150K account, 10 positions:

• Each position: $15,000
• Sell puts where margin ≈ $15K

Pros: ✅ Simple ✅ Automatic diversification ✅ Easy to track

Cons: ❌ Ignores individual trade risk ❌ Treats TSLA and AAPL the same (they're not)

Best for: Beginners, want simplicity

Method 2: Fixed Fractional Sizing

How it works: Risk a fixed percentage of capital per trade.

Formula:

Position Size = (Account Value × Risk %) / Max Loss Per Share

Example - $150K account, 2% risk per trade:

• Risk amount: $3,000
• Sell $200 put, max loss if stock goes to $0 = $200/share
• Position size: $3,000 / $200 = 0.15 contracts
• Round to 1 contract

Actual calculation (practical):

• Want to risk 2% per trade = $3,000
• Sell 1 put at $200 strike
• If assigned and stock drops 20% ($160), loss = $4,000
• Slightly over 2%, but acceptable

Pros: ✅ Limits losses ✅ Adapts as account grows ✅ Professional approach

Cons: ❌ Requires estimation of realistic max loss ❌ Can lead to small positions

Best for: Intermediate traders, conservative approach

Method 3: Kelly Criterion

How it works: Optimal bet sizing based on win rate and risk/reward.

Formula:

Kelly % = (Win Rate × Avg Win - Loss Rate × Avg Loss) / Avg Win

Example - Your wheel strategy stats:

• Win rate: 75%
• Loss rate: 25%
• Average win: +2.5%
• Average loss: -8%

Kelly = (0.75 × 2.5 - 0.25 × 8) / 2.5
Kelly = (1.875 - 2) / 2.5
Kelly = -0.125 / 2.5
Kelly = -5%

Wait, negative? This means risk/reward is unfavorable!

Correct example:

• Win rate: 85%
• Average win: +2%
• Average loss: -5%

Kelly = (0.85 × 2 - 0.15 × 5) / 2
Kelly = (1.7 - 0.75) / 2 = 0.475 = 47.5%

Kelly says bet 47.5% per trade, but that's aggressive!

Practical application: Use 1/4 Kelly

• 47.5% / 4 = 11.9%
• Use ~12% per position

Pros: ✅ Mathematically optimal ✅ Adapts to your edge ✅ Maximizes long-term growth

Cons: ❌ Requires accurate win rate data ❌ Full Kelly is too aggressive ❌ Complex calculation

Best for: Advanced traders with extensive track record

Method 4: Volatility-Adjusted Sizing

How it works: Size positions inversely to stock volatility.

Formula:

Position Size = Base Size × (Target Volatility / Stock Volatility)

Example - $150K account:

• Target position: $15,000 (base)
• Target volatility: 30% (moderate)

Stock A (AAPL) - 25% IV:

• Position size = $15,000 × (30 / 25) = $18,000
• Larger position (lower risk)

Stock B (TSLA) - 60% IV:

• Position size = $15,000 × (30 / 60) = $7,500
• Smaller position (higher risk)

Pros: ✅ Adjusts for volatility ✅ More consistent risk across positions ✅ Professional approach

Cons: ❌ Requires IV tracking ❌ Can lead to very small positions on high-vol stocks

Best for: Experienced traders, portfolio margin users

Method 5: Tiered Allocation

How it works: Group stocks by conviction/quality, allocate differently.

Tier structure:

Tier	Criteria	Allocation	Example Stocks
Core	Top quality, low vol	40%	AAPL, MSFT, GOOGL
Growth	Higher vol, growth story	35%	NVDA, META, AMD
Opportunistic	Situation-dependent	20%	Post-earnings, high IV
Speculative	High risk/reward	5%	Volatile, risky

$150K account allocation:

• Core: $60K across 3-4 positions
• Growth: $52.5K across 4-5 positions
• Opportunistic: $30K across 3-4 positions
• Speculative: $7.5K across 1-2 positions

Pros: ✅ Balances risk/reward ✅ Flexible framework ✅ Easy to implement

Cons: ❌ Subjective tier classification ❌ Requires ongoing adjustment

Best for: All experience levels

Comparing Methods: Real Example

$100,000 account, considering selling NVDA $850 put:

Method	Calculation	Position Size	# Contracts
Equal Dollar	$100K / 10 = $10K	$10K margin	1
Fixed Fractional (2%)	$100K × 2% = $2K risk, ~$10K margin	$10K	1
Kelly (1/4)	12% per trade	$12K	1
Volatility Adjusted	Base $10K × (30/55)	$5.5K	0
Tiered (Growth tier)	35% / 5 positions = 7% each	$7K	0

Recommendation: Use Fixed Fractional or Tiered for most traders.

Maximum Position Size Rules

Never violate these:

❌ Single position > 20% of account (unless core holding) ❌ Single sector > 40% of portfolio ❌ Total margin > 70% of account (portfolio margin) or 100% (Reg T) ❌ More than 15 simultaneous positions (hard to manage)

✅ Ideal: 8-12 positions, 50-70% margin utilization

Adjusting Size Based on Setup Quality

Grade your trade setup (A, B, C):

A+ Setup (Rare):

• Post-earnings dip
• High IV percentile (> 70)
• Quality stock you love
• Technical support nearby
• Size: 1.5x normal

A/B Setup (Common):

• Good IV (> 50)
• Decent stock
• Normal entry
• Size: 1.0x normal

C Setup (Marginal):

• Lower IV (< 50)
• Okay stock
• Opportunistic
• Size: 0.5x normal or skip

Real Trader Portfolios

Conservative - $100K Account

Stock	Tier	Allocation	Margin	Contracts
AAPL	Core	12%	$12K	2
MSFT	Core	12%	$12K	1
GOOGL	Core	10%	$10K	2
JPM	Core	8%	$8K	1
DIS	Growth	7%	$7K	2
Total	-	49%	$49K	8

Risk level: Low, comfortable, diversified

Aggressive - $100K Account

Stock	Tier	Allocation	Margin	Contracts
NVDA	Growth	15%	$15K	1
TSLA	Speculative	10%	$10K	1
AMD	Growth	12%	$12K	2
META	Growth	12%	$12K	1
AAPL	Core	10%	$10K	1
SHOP	Opportunistic	8%	$8K	1
Total	-	67%	$67K	7

Risk level: Higher, concentrated in tech, higher returns (and volatility)

Dynamic Sizing Based on Market Conditions

Bull Market (VIX < 15):

• Increase position sizes 10-20%
• Add more positions
• Take more aggressive strikes (0.30 delta)

Normal Market (VIX 15-25):

• Standard sizing
• Normal allocation
• Standard strikes (0.25 delta)

Volatile Market (VIX > 25):

• Decrease position sizes 20-30%
• Reduce total positions
• Move to safer strikes (0.20 delta)
• Keep extra cash (30%+)

Position Sizing Checklist

Before entering any trade:

☐ Calculated position size using chosen method ☐ Position < 15% of total account (or < 20% for core) ☐ Total margin utilization will stay < 70% ☐ No more than 3 positions in same sector ☐ Trade fits within tier allocation ☐ Have cash buffer (20%+ of account) ☐ Won't exceed total position limit (15 max)

Tracking and Optimization

Monthly review:

1. Calculate actual win rate
2. Calculate average win/loss
3. Adjust Kelly calculation if using
4. Review largest positions (any too big?)
5. Check sector concentration
6. Rebalance if needed

Quarterly deep dive:

• Compare intended vs actual sizing
• Analyze if larger/smaller positions performed better
• Adjust base allocation if needed
• Update tier classifications

Common Sizing Mistakes

❌ All-in on one trade - Recipe for disaster

❌ Equal sizing without regard to risk - TSLA ≠ AAPL risk

❌ Oversizing after wins - Euphoria leads to blow-up

❌ Undersizing after losses - Fear prevents recovery

✅ Consistent, systematic sizing - Boring but works

Case Study: Sizing Impact

Trader A: No system

• Sizes randomly
• Sometimes 5%, sometimes 30%
• Year return: 12%, volatility high
• Blew up once, had to restart

Trader B: Fixed 8% per position

• Consistent sizing
• 10-12 positions always
• Year return: 28%, volatility moderate
• No blow-ups, steady growth

Lesson: Consistency beats aggression.

Next lesson: Credit spreads for income and margin reduction.