Optimal F Calculator
Find the fraction of capital (Optimal F) that maximizes geometric growth from your trade history. Based on Ralph Vince's method for position sizing.
Enter wins as positive and losses as negative (e.g. 100, -50, 200). At least one loss is required.
Used to show recommended risk per trade in dollars.
Risk this fraction of capital per trade to maximize geometric growth (Ralph Vince).
Terminal Wealth Relative
Largest single loss
How to Use the Optimal F Calculator
Optimal F (Ralph Vince) is the fraction of your capital to risk per trade that maximizes long-term geometric growth. This calculator finds it from your actual trade history.
- Enter Trade P&L: Paste or type your trade results as comma- or newline-separated numbers. Wins are positive (e.g. 100), losses negative (e.g. -50).
- Optional: Account Balance: Enter your account size to see the recommended risk per trade in dollars.
- Read Optimal F: The result is the fraction (as a percentage) of capital you would risk per trade to maximize geometric growth on that sequence of trades.
- Use With Caution: Optimal F can be aggressive. Many traders use half or quarter Optimal F (Half-Kelly style) for safety.
What is Optimal F (Ralph Vince)?
Ralph Vince's Optimal F is a position-sizing method that finds the fixed fraction of capital to bet on each trade so that the Terminal Wealth Relative (TWR) is maximized. TWR is the product of per-trade growth factors: each trade multiplies your stake by 1 + f × (trade outcome / |worst loss|).
- Worst loss: The most negative trade in your list. It is used to normalize outcomes so that the same fraction "f" applies across trades.
- TWR: Terminal Wealth Relative. If TWR = 2.5, your capital would have grown 2.5× over the sequence at that fraction.
- Optimal F: The "f" (between 0 and 1) that maximizes TWR for your given trade sequence.
Why Optimal F Matters for Traders
Optimal F tells you the theoretically optimal risk per trade forthat specific set of outcomes. It is sequence-dependent: the same win/loss stats in a different order can yield a different Optimal F.
- Maximize growth: Under the assumption that future trades resemble your sample, betting Optimal F maximizes geometric growth.
- Risk of ruin: Betting full Optimal F can be very aggressive and may lead to large drawdowns. Using a fraction of Optimal F (e.g. 25–50%) is common.
- Compare with Kelly: Kelly Criterion uses win rate and payoff ratio; Optimal F uses the actual distribution of trade outcomes. Both are tools for position sizing.
Frequently Asked Questions
What is Optimal F (Ralph Vince)?
Optimal F is the fraction of your capital to risk per trade that maximizes geometric growth over a given sequence of trade outcomes. Ralph Vince derived it from the Terminal Wealth Relative (TWR) formula. It uses your actual trade P&L history, not just win rate and payoff.
How do you calculate Optimal F?
Optimal F is found by maximizing the Terminal Wealth Relative: TWR(f) = ∏ [1 + f × (trade outcome / |worst loss|)] over all trades. The calculator searches for the fraction f (between 0 and 1) that gives the highest TWR for your entered trade list.
Should I use full Optimal F?
Full Optimal F can be very aggressive and may cause large drawdowns. Many traders use a fraction of Optimal F (e.g. 25% or 50%)—similar to Half-Kelly—to reduce volatility and risk of ruin while still benefiting from the sizing logic.
Optimal F vs Kelly Criterion?
Kelly uses win rate and average win/loss ratio to suggest a single fraction. Optimal F uses your actual sequence of trade P&L and maximizes geometric growth for that exact sequence. Optimal F is sequence-dependent; Kelly is distribution-based. Both are tools for position sizing.
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