Return-path volatility and the recovery burden

Sequential compounding and the recovery burden

Each completed trade rescales the capital available for the next trade. Under sequential compounding, the ending equity of one trade becomes the starting capital of the next, so the size and order of returns change ending wealth even when the list of percentage outcomes looks similar.

Restoring a 20 percent advance after a 20 percent decline requires a 50 percent gain on the remaining equity. That extra lift is the recovery burden: the larger percentage gain required to restore a prior equity level after a decline.

Return volatility of the equity path

In this evaluation, return volatility is the period-to-period variability of those percentage equity changes, not the variability of an entry signal alone. It is the spread of period-to-period percentage changes in account equity produced by a trade sequence.

Monte Carlo campaigns that isolate swing size

Monte Carlo simulation here means repeated random or matched-seed return sequences used to compare how two volatility settings finish after many paths. Across 100 independent random campaigns started from the same equity, the half-range return path finished ahead in about 60 to 70 trials.

Holding the random seed fixed isolates swing size as the variable under test, so a better finish cannot be blamed on a luckier set of trades. A matched-seed comparison feeds two equity series the same random returns while shrinking the period gains and losses of one series.

When both paths reused the same random draws and only the lower-volatility path took half of each gain or loss, that path finished ahead in about 80 of 100 trials. A practical system check prefers smaller losses even when wins shrink with them, because less ground then has to be recovered after a decline.

Bounds that keep swings recoverable

A drawdown limit is a precommitted bound on loss or exposure, set from equity, volatility, and stop distance, so one sequence cannot force an outsized recovery. Volatility position sizing scales exposure so the allowed gain-and-loss range stays inside a chosen bound before entry and while the position is open.

Exposure can be judged before entry and during a position by whether the allowed return range keeps equity swings inside a bound the account can recover from.