Rebuild the equity-path ratio before it ranks a designed system

A ranking score with its own construction

A published system-performance ratio that fits a line through successive equity readings was later rewritten after the original implementation misapplied the intended statistical formula. The restated procedure starts from equity observations and ends with an equity-path ratio.

An equity observation is closed-trade net profit plus open-position profit recorded at each sampling step. The full ratio is computed only after the last calculation date of the series.

How the equity-versus-time line is rebuilt

The equity-path slope is the ordinary least-squares coefficient of recorded equity on a one-based observation index. The restated slope uses the covariance form: the sum of index times equity, minus the product of the summed index and summed equity divided by the observation count, all divided by the similarly centered sum of squared index values.

The fitted intercept is mean equity minus the equity-path slope times the mean observation index.

Residual scale and slope standard error

Each equity observation is compared with the value projected from that fitted intercept and equity-path slope. The squared gaps are summed to form the residual total. Residual scale is the square root of the residual total divided by the observation count minus two.

The centered index weight is the sum of squared differences between each observation index and half of one plus the observation count. That weight is the slope standard-error denominator. Slope standard error is residual scale divided by the square root of the centered index weight.

End-of-sample evaluation of the ratio

The equity-path ratio is the equity-path slope divided by the product of the slope standard error and the square root of the observation count. End-of-sample evaluation means computing that ratio once on the completed equity series rather than as a running intra-sample score.