Filter leverage by sequence-loss odds

Contract count before the sequence

After a closed sequence of long or short trades with no external cash flows, ending equity equals starting equity multiplied by the product of one plus leverage times each trade return.

Editorial reading: treat contract count as a before-the-sequence filter under Leverage control, Risk of ruin, and Margin management. Keep a leverage setting only if your own closed-trade history still leaves the chance of finishing underwater, and the chance of a 40 percent draw, inside the loss the live account can absorb.

Raising leverage on a fixed history

When historical trade returns are held fixed and leverage is raised as a decision variable, the compounded equity path typically rises then falls through zero, so leverage past the peak can exhaust the account.

The leverage that maximizes that historical compounding curve is not identified as optimal because the curve does not incorporate risk.

Loss odds from resampled returns

Resampling historical trade returns in random order and compounding them at a chosen leverage produces frequency diagrams of later equity outcomes without assuming a named return distribution.

About 100 forward trades and at least 100 resampled paths are treated as enough to estimate mean outcome, variance, and the chance of finishing below starting equity.

For a long enough sequence the log of the equity multiplier is treated as approximately normal, so outcome probabilities can be read from a lognormal model of the multiplier. Estimating the return standard deviation used there is described as requiring at least 30 completed trades.

At leverage 3 and a 100-trade horizon, simulated frequencies moved toward the theoretical curve as the number of paths rose from 100 to 500 to 2,000.

When mean trade return and its dispersion are positive, the chance the equity multiplier finishes below 1 is a strictly increasing function of leverage. Defining a severe loss as 40 percent or more of starting capital, that chance also rises with leverage and approaches the simple chance of any loss.

A revisable capital-protection setting

Because a live account can be forced out by the order of losses even when the full-sequence product is positive, the modeled full-path results are described as generous.

Leverage is framed as a revisable capital-protection policy that can be re-estimated after results change and, if capital is thin, examined over a shorter horizon of 10 or 20 trades.

Editorial reading: use the chance of finishing underwater and the chance of a 40 percent or larger draw as the filter on the setting. If either chance sits outside the loss the live account can absorb, do not keep that leverage.