Optimal f is an advanced position sizing method developed by Ralph Vince in his book "Portfolio Management Formulas." It calculates the exact fraction of your capital to risk on each trade to maximize geometric growth. While powerful, it comes with significant caveats that every trader must understand.
What is Optimal f?
Optimal f answers a specific question: "What percentage of my capital should I risk to grow my account as fast as possible?" It is related to the Kelly Criterion but uses your actual trade history rather than simple win rate calculations.
Key concept: Optimal f is the fixed fraction of your capital that, if wagered on every trade with the same characteristics as your past trades, would produce the maximum terminal wealth.
How Optimal f Differs from Kelly
While Kelly Criterion uses win rate and average win/loss ratio, Optimal f uses your entire distribution of trade outcomes. This makes it more accurate but also more data-intensive.
- Kelly: Uses two parameters (win rate, win/loss ratio)
- Optimal f: Uses all historical trade P&L values
The Optimal f Calculation
Optimal f is found by testing different f values (from 0.01 to 1.0) and finding which produces the highest Terminal Wealth Relative (TWR).
TWR Formula
TWR = Product of (1 + f x Trade Return / Largest Loss)
Where f is the fraction being tested, and you multiply across all trades.
Step-by-Step Process
- Collect all trade P&L results
- Identify the largest loss
- Test f = 0.01 and calculate TWR
- Test f = 0.02 and calculate TWR
- Continue testing until f = 1.0
- The f with highest TWR is optimal f
Practical Example
Let us work through a simplified example with five trades:
Trade History
- Trade 1: +$500
- Trade 2: -$200
- Trade 3: +$300
- Trade 4: -$400 (largest loss)
- Trade 5: +$200
Testing f = 0.25
Largest loss = $400
- Trade 1: 1 + (0.25 x 500/400) = 1.3125
- Trade 2: 1 + (0.25 x -200/400) = 0.875
- Trade 3: 1 + (0.25 x 300/400) = 1.1875
- Trade 4: 1 + (0.25 x -400/400) = 0.75
- Trade 5: 1 + (0.25 x 200/400) = 1.125
TWR = 1.3125 x 0.875 x 1.1875 x 0.75 x 1.125 = 1.15
You would test many f values and find which gives the highest TWR.
Converting Optimal f to Position Size
Once you find optimal f, convert it to a position size:
Position Size Formula
Position Size = (Account x Optimal f) / Largest Historical Loss Per Share
- Account: $50,000
- Optimal f: 0.20 (20%)
- Largest loss per share: $8
- Position Size: ($50,000 x 0.20) / $8 = 1,250 shares
The Danger of Optimal f
Here is the critical warning: trading at optimal f produces maximum growth but also maximum drawdowns. Ralph Vince himself warns against using full optimal f.
Drawdown Reality
- Optimal f often suggests risking 20-40% of capital per trade
- This can result in 50-80% drawdowns during losing streaks
- Most traders psychologically cannot handle this
- One bad trade can devastate your account
Warning: Trading at full optimal f is like driving at maximum speed - technically fastest, but any mistake is catastrophic. Most professionals use a fraction of optimal f.
Fractional Optimal f
Like fractional Kelly, you can use a fraction of optimal f:
- Half optimal f: 50% of calculated value
- Quarter optimal f: 25% of calculated value
Quarter optimal f still achieves about 75% of the growth rate with dramatically reduced drawdowns.
When to Use Optimal f
Optimal f is appropriate when:
- You have at least 100+ trade samples for accuracy
- Your strategy has remained consistent over those trades
- You understand and accept severe drawdowns
- You are optimizing for long-term geometric growth, not comfort
When NOT to Use Optimal f
- You have fewer than 30-50 trades
- Your strategy is still evolving
- You trade money you cannot afford to lose 50% of
- You have not backtested extensively
- You need consistent income from trading
Optimal f vs Fixed Fractional
For most traders, fixed fractional (1-2% risk) is more practical than optimal f because:
- It does not require extensive historical data
- Drawdowns are more manageable
- It is psychologically sustainable
- It works across different market conditions
Advanced Concept: Secure f
Ralph Vince later introduced "Secure f" which considers maximum acceptable drawdown:
Secure f Concept
Instead of maximizing growth, Secure f finds the optimal f that stays within your drawdown tolerance.
If you can only tolerate 25% drawdown, Secure f finds the highest f that historically would not have exceeded that.
Track Your Trade History
Pro Trader Dashboard records all your trades with detailed P&L history. Build the dataset you need for optimal f calculations or simpler statistics for other position sizing methods.
Implementing Optimal f in Practice
- Export your trade history with all P&L values
- Use a spreadsheet or program to test f values from 0.01 to 1.0
- Find the f with highest TWR
- Apply fractional optimal f (quarter or half) for actual trading
- Recalculate monthly or quarterly as your trade history grows
- Never exceed your optimal f even when confident
Summary
Optimal f is the mathematically precise way to maximize long-term growth. However, the severe drawdowns it produces make it impractical for most traders. Use fractional optimal f (quarter to half) or stick with simpler fixed fractional methods unless you fully understand and accept the risks.
Want to learn simpler approaches? Check out fixed fractional sizing or explore Kelly Criterion for a balance between simplicity and optimization.