Search system inputs together with Optimal f sizing

A larger unlevered profit can finish smaller

A five-trade sequence with 3100 unlevered net profit produced an optimal fraction of 43.3 percent. After that fraction was applied, the sequence showed a 40.87 percent compounded return.

A different five-trade sequence with 2800 unlevered net profit produced an optimal fraction of 46.3 percent and a 42.55 percent compounded return after that fraction was applied.

From the same 10000 starting equity, applying those optimal fractions turned the 3100-profit sequence into 4087 of profit and the 2800-profit sequence into 4255 of profit.

The sequence that earned about 10.71 percent more before any sizing rule produced about 1.7 percent less after Optimal f sizing, because the rival sequence had a smaller holding-period-return standard deviation and a higher Sharpe ratio.

The next stake comes from the trade series

Return-based sizing such as Optimal f sizing, martingale, and antimartingale sets the next stake from the historical profit-and-loss series. The fraction and the resulting account path depend on that series rather than on the unlevered net-profit ranking alone.

Optimal f sizing is the equity fraction that maximizes terminal wealth relative, the product of holding-period returns, when each trade is scaled by that fraction relative to the worst loss.

Search system inputs and money management together

A mechanical system with tunable inputs, illustrated as a two-input moving-average crossover, should have those inputs searched together with the money-management inputs rather than in a two-step sequence of system first and size second.

Changing a Stop-loss order level can raise profitability after a return-based sizing rule even when the same stop reduced unlevered system profit, because the stop reshapes the trade-return series that the fraction consumes.