Constructing equity versus leverage with resampled trades

Bound exposure before any size is taken

Leverage-control is a pre-trade and in-trade filter. It recomputes the equity path at successive gearing levels so a loss or exposure decision stays bounded before size is increased.

The leverage-grid is the row of those gearing settings. It begins at 0.00 and rises by 0.05 until it reaches 1, and ending equity is read at each of those settings.

When no beginning equity is supplied, the first cell of a leverage sweep is seeded with 1. That unit-equity-seed lets later periods compound from a defined base.

Turn the stated margin rate into a daily charge

Margin-management converts a stated financing or margin rate into a daily charge. The charge is applied for the days a position is open and deducted from the leveraged return.

A stated annual margin rate in decimal form is converted to a daily-margin-rate by dividing by 365 before it is applied to the equity path. The daily figure can then be scaled by the number of days in the trade.

Express return against committed capital

Net-return-after-leverage is formed from marked position profit and costs relative to the capital committed at the chosen gearing. After margin and residual charges, the return is expressed against that committed capital.

Feed the same filter a discrete resample

Monte-carlo-simulation is a discrete resample of observed holding periods and net returns, drawn with replacement from the historical trade book. The rebuilt equity-versus-leverage path sits out of sample of the original sequence.

In the simulated book, each of the 35 historical trades is treated as equally likely. Equal-trade-probability is 1/35, which is one divided by the number of observed trades.

The Monte Carlo test expands the 35-trade book to 70 draws by independently sampling holding days and returns from those empirical discrete pairs.

Rebuild the return series before the draws

Rebuilding the return series with a commission of 30 instead of 106 changes the returns that enter the simulation even when the same trade list is reused.

Each resampled trade updates equity with the selected leverage, a daily margin charge scaled by days in the trade, and a residual cost factor. The last row of that sweep is ending equity at each leverage.