Optimal F

What is Optimal F?

Optimal f is Ralph Vince's position-sizing construction: the fixed fraction of capital that, applied to every trade in a strategy's historical trade list, would have maximized the geometric growth of the account over that history. Vince developed it in his books on money management beginning around 1990, as an empirical, trade-list-driven relative of the Kelly criterion. Where Kelly needs a probability model of outcomes, optimal f needs only the recorded trades: it searches over candidate fractions and keeps the one with the highest terminal wealth relative, with each trade's risk keyed to the largest loss in the sample.

Traders care about it for the same reason they care about Kelly: it marks the growth-maximizing ceiling on size. Any fraction above optimal f produced both more volatility and less final wealth on the strategy's own history, so it defines the boundary between aggressive and self-defeating. The expectancy of a system tells you whether to trade it; optimal f claims to tell you how hard it could have been pressed.

The construction's honesty problem is well documented, including by Vince himself: trading at full optimal f is brutal. Drawdowns at the optimum routinely exceed levels most traders and allocators would abandon, frequently more than half the account, and the estimate is hostage to the sample. The largest loss seen so far anchors the whole calculation, and the next largest loss is by definition not in the data yet. In practice optimal f functions as a diagnostic ceiling, with live sizing set far below it.

How it's calculated

Optimal f maximizes the terminal wealth relative (TWR) over the trade history:

The search is done numerically since TWR(f) has no closed form for arbitrary trade lists.

Because largest_loss scales every term, one new outlier loss changes f_opt and every position size derived from it.

How traders use it

• As a ceiling diagnostic: traders compute f_opt from a backtest and treat any live sizing approaching it as an error, since the historical optimum already assumes the future repeats the sample exactly.
• As a fractional base: like fractional Kelly, some practitioners trade a small fraction of f_opt, accepting slower growth for drawdowns that a human or an allocator can actually sit through.
• As a comparison metric across systems: a strategy whose f_opt is tiny cannot support meaningful size no matter how attractive its win rate looks, which makes f_opt a useful complement to drawdown statistics.
• As a stress-testing input: recomputing f_opt with the largest loss inflated (for example doubled) shows how fragile the sizing conclusion is to the tail event that has not happened yet.
• With honest limits: optimal f assumes independent, identically distributed trades and a known worst loss. Real strategies drift, trades correlate, and the true worst loss lies ahead, so full-f trading carries serious risk of ruin in practice even though the idealized math avoids it.

Optimal f vs other sizing frameworks