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7. Advanced risk management
Average result and sample size
Expectancy in R units: E[R] = p × W - (1 - p) × L, where p is the win proportion, W the average win and L the average absolute loss. If costs are excluded from W/L, subtract their average separately. Do not subtract the same fee twice.
With p = 0.4, W = 2R and L = 1R, expectancy before costs is 0.2R. Average costs of 0.1R leave 0.1R. This is arithmetic for a hypothetical model, not a forecast of future income. Estimates of p and W/L from a small successful sample may be unstable.
Win Rate measures the share of positive outcomes under the chosen definition. Profit Factor = the sum of positive net results / the absolute sum of negative results. Without negative results, a finite PF estimate is undefined; this is not proof of an infinite edge.
Drawdowns and streaks
Maximum drawdown is measured from each previous peak in the chosen capital curve. State whether you use closed trades only or equity including open positions. The second can reveal danger hidden by the first.
Ten consecutive losses of 1% of current capital leave 0.99^10 ≈ 90.44% of the original account: a drawdown of approximately 9.56%, excluding costs and gaps. Fixed money losses require a different calculation. Do not mix those models in one table.
The rough probability of K consecutive losses in one specific preselected block of independent trades is (1 - p)^K. The probability of encountering at least one such streak somewhere in a long history is a different problem. Trade dependence and regime changes violate the independence assumption.
Combined risk and correlation
Five altcoin longs may effectively depend on the same BTC and broad-market move. Summing stop risks is useful as an initial control, but does not capture correlation jumps, price gaps or simultaneous deterioration in execution.
Set limits before the session begins: permitted risk for one idea, a group of related assets, total open risk and a stopping rule after departing from the plan. Choose actual values from your circumstances and evidence, not a supposedly universal textbook percentage.
Example. Three positions have planned losses of $4, $3 and $5: total $12. With a practice combined-risk ceiling of $10, the third position at full size is not acceptable. Unrealised profit in the first position is not a guaranteed source of cover for the others' future losses.
Exercise. For [2R, -1R, -1R, 3R, -1R], the sum is 2R, the mean 0.4R, win rate 40%, PF = 5/3 ≈ 1.67, if the figures are already net. Five observations cannot establish reliable future returns. Calculate the same metrics after adding five ordinary losses.