Optimal f sizing and risk of ruin as exposure filters

Editorial frame

This editorial reads Optimal f sizing and Risk of ruin as pre-trade exposure filters that bound a loss you can survive. The paragraphs that follow restate the historical workflow. They are not treated here as equations that pick a growth-maximizing bet size.

How Optimal f sizing is defined

Optimal f sizing is defined from a system's historical results as the fixed fraction of trading capital allocated to a trade in order to maximize geometric account growth. That fraction is then divided by the largest loss to set contract count.

Under the common rationale, betting more than Optimal f sizing leads to ruin and betting less leaves the account undergrown.

When the win-to-loss dollar ratio is assumed to be 1, the simplified Optimal f sizing formula is f = 2P - 1. A 51% win rate implies a 2% fraction. A 75% win rate implies a 50% fraction.

What risk of ruin measures

Risk of ruin estimates the chance of going bust given a win percentage and the number of capital units risked per trade. There remains a positive chance of ruin whenever trading continues.

When profit and loss per trade are equal, ruin probability can be written R = ((1 - A) / (1 + A))^C or R = ((1 - W) / W)^C. The result depends only on win rate and capital units.

Why a growth-max fraction is a weak size rule

A stronger historical system raises the implied Optimal f sizing bet. That larger bet also raises eventual drawdown and can make a single later loss large enough to wipe out the account.

A high-percentage winning system paired with a high Optimal f sizing fraction can still show a high chance of going bust.

Writers who compute full Optimal f sizing often then cut it by an arbitrary divisor such as one-half or one-third. That step is little different from choosing an arbitrary percent of capital.

Bound the loss that can be tolerated

The historical workflow sets position size from the largest loss that can be tolerated rather than from an optimized fraction of capital. One worked example never risks more than a 15% drawdown, regardless of how many systems or open positions are held.