Construct historical-optimum-leverage from one equity-path

A worksheet built from one equity-path

A return-versus-leverage spreadsheet is the layout used to inspect the reconstructed surface. Every tested exposure column can be seeded from a theoretical starting equity of 100. That series is the equity-path: a running account seeded at a fixed starting value and updated after each recorded return.

The same return sequence is then applied across a leverage-grid so ending equity can be compared across candidate sizes. The worksheet grows or shrinks each column's equity with each subsequent return.

Sample window and data grain

The construction expects at least 30 trades in the sample window. More trades and a longer relevant period are preferred. Daily closing values are presented as the preferred data grain for this leverage reconstruction.

How the leverage-grid is arranged

Candidate leverage levels can be laid across a header row beginning at 0 for no trading, then 0.5, then 1, then stepping by 1 out to 20. Those increments may be adjusted to the analyst's own range. The leverage-grid is that set of candidate exposure multiples applied to the same return sequence.

How each later cell is updated

Each later cell takes the period's fractional equity change, scales it by that column's leverage, applies the product to the pre-period leveraged equity, and adds the result back to that pre-period equity.

The return-versus-leverage-arch

An XY plot of leverage on the horizontal axis against each column's terminal equity on the vertical axis is expected to form an arch. That rise-then-fall shape is the return-versus-leverage-arch: ending equity typically rises, then falls as exposure increases past the useful range.

Historical-optimum-leverage is the tested multiple at which the reconstructed path reaches its highest ending equity on the grid. Optimal-f is that grid point used as a sizing filter, not as a forecast of future results.

Leverage-control after the peak is visible

Leverage-control keeps a loss or exposure decision bounded by choosing a multiple from the grid before entry and holding that bound while the position is open. Optimal-f remains the reconstructed peak used as a sizing filter, not as a forecast of future results.