Risk management & position sizing

Define 1R as the amount you risk on a trade — entry to stop, in money. Every outcome then becomes a multiple: a win that makes twice your risk is +2R, a stopped-out loss is −1R. Suddenly trades of any size, in any market, are comparable — and your system becomes a distribution of R.

Expectancy is that distribution's average: `winRate × avgWin − lossRate × avgLoss` (all in R). Positive expectancy is the *only* thing that makes a system worth sizing. A 40% win rate with 2.5R winners is a good business (+0.4R/trade); a 90% win rate that risks 10R to make 1R is a blowup on a timer (−0.1R/trade). Win rate alone tells you nothing.

The professional default is fixed-fractional sizing: risk the same small percentage of the account on every trade — commonly 0.5–2%. The size follows mechanically from where your stop is: risk amount divided by stop distance. Wide stop → small position; tight stop → larger position. Same R either way.

This solves the problem beginners have backwards. They pick a position size that feels exciting, then place a stop they can 'afford' — usually too tight, guaranteeing noise stops them out. The formula runs the other way: thesis sets the stop, stop sets the size.

Percentages lie to your intuition: a −50% loss needs +100% to recover. The recovery requirement grows non-linearly — small drawdowns are a toll, deep drawdowns are a trap. This asymmetry is the single strongest argument for risking small.

It also reframes what risk management is *for*: not avoiding losses (impossible) but keeping every loss in the shallow zone of the curve, where recovery is routine arithmetic instead of a heroic comeback.

A 45%-win-rate system will hit 8+ consecutive losses somewhere in its first few hundred trades with near-certainty. That's not a malfunction — it's what the probability distribution *is*. The question is only whether your sizing survives the streak that is definitely coming.

Risk of ruin is the probability that drawdowns force you to stop — blown account, broken confidence, or pulled capital — before the edge can play out. It compounds from three inputs: expectancy, variance, and risk per trade. You control the third completely. At 1% risk, an 8-loss streak is −7.7%; at 5% risk, it's −33.7% and your decision-making is no longer the same person's.