R-multiple expectancy, drawdown, and volatility position sizing

R as a common risk unit

R is the dollar amount at risk on a trade, computed from entry, stop, and position size. Keeping R a constant dollar amount or a constant fraction of equity makes later performance comparable in risk units.

An r-multiple is a closed trade's profit or loss expressed as a multiple of the dollars placed at risk on that trade.

Expectancy from a set of r-multiples

From a set of historical r-multiples a trader can compute mean R (expectancy) and the standard deviation of R, then use those two statistics as the inputs for a minimum acceptable performance curve. Expectancy is the mean r-multiple of a strategy's historical trade set: the average return in risk units per trade.

A worked r-multiple sample has mean 0.370, median -1.000, win ratio 0.397, and standard deviation 2.806. The sample shows positive expectancy with a losing-trade majority and a fat right tail.

A straw-broom of cumulative R

Resampling the r-multiple set into many long Monte Carlo paths produces a straw-broom of cumulative R. A straw-broom is a family of those resampled equity paths, used to sketch the likely spread of future cumulative R. The center of the broom tracks mean R times trade count, and the width is governed by the R standard deviation.

Lower and upper confidence bounds on cumulative R after n trades are given by LL = [μ − (z · σ / √n)] · n and UL = [μ + (z · σ / √n)] · n. A live equity path that falls through the lower bound can be treated as a broken-system filter.

Drawdown limit before entry and in an open book

The same lower-bound construction also supplies a worst-case drawdown envelope and a maximum breakeven trade count. Together they act as a drawdown limit that can be checked before entry and during an open book of trades.

A drawdown limit is a pre-agreed floor on cumulative R or equity. Below that floor the strategy is treated as broken and risk is reduced or trading stops.

Volatility position sizing from equity and stop distance

Once a risk fraction is chosen, position size is scaled from current equity so that a one-R stop loss stays inside that fraction. Volatility position sizing sizes each position from account equity, current volatility, and the stop distance so the loss if the stop is hit stays inside a planned fraction of equity.

Using market-money as a separate risk pool changes how aggressively the next trade is sized. Market-money is the surplus of current equity over starting equity, treated as a pool that can be risked more aggressively than original capital.

A 50 percent compression factor on the downside and a matching expansion factor on the upside means the next trade risks more than simple proportional sizing after a rise and less after a decline. Compression-expansion shrinks risk after a drawdown and enlarges risk after an equity rise, typically by a fixed fraction of the gap from a reference equity. This is a volatility-and-equity position-sizing rule rather than a signal rule.