Optimal f (Ralph Vince)

Definition

Take the list of results per contract and its largest loss W, a negative number. For a candidate fraction f between 0 and 1, each trade becomes a holding period return 1 + f × (−tradeᵢ ÷ W): the largest loss becomes a loss of exactly f, and every other trade is scaled in proportion. The terminal wealth relative, TWR, is the product of all holding period returns. Optimal f is the value of f that makes the TWR largest. It is then turned into a size by allocating one contract per |W| ÷ f dollars of equity.

A worked example

Ten trades per contract: +400, −200, +300, −100, −200, +500, −150, +250, −200, +100. Net +700, largest loss −200. Scanning f gives an optimum near 0.24, with a TWR of about 1.49: equity would have grown 49% over the ten trades at one contract per 200 ÷ 0.24 ≈ 833 dollars. At f = 0.10 the TWR is about 1.31. At f = 0.50 it falls to about 0.94, a loss, although every trade list is identical. At f = 0.75 it is about 0.17, and at 0.90 about 0.01.

The shape is the lesson: growth rises slowly up to the optimum and collapses beyond it, so an estimation error on the high side costs far more than one on the low side.

Limits

• The largest historical loss is a sample statistic; a future loss larger than W costs more than f of equity.
• Optimal f is fitted to the past sequence and inherits all its sampling error.
• The drawdowns at optimal f are severe: at f = 0.24, two repeats of the worst loss in a row remove about 42% of equity.
• It ignores account rules such as daily loss limits and drawdown floors, which usually bind long before the optimum.

In Senzoukria

The desktop does not compute optimal f. The Performance panel shows a Kelly fraction derived from the win rate and the payoff ratio, with the hint that it is theoretical and assumes independent trades, which is rarely true within a session. Neither figure drives order size: quantities come from the order ticket, the script's decisions or the autopilot's capped settings.