Drawdown and recovery mathematics

EN source master · P06-L04 · 30 minutes estimated · needs_review

Offline formative study. No wallet connection, real funds, private keys, signatures, live trade or personal portfolio inputs. Visuals are specifications. This source master remains needs_review; completing the formative exercise does not issue certification.

A 40% loss and 40% gain do not cancel because they use different starting values.

Keep a running peak

Drawdown at time t=(running peak−current value)/running peak. Maximum drawdown is the largest such ratio along the path. Values supplied as equity include modeled realized/unrealized effects and stipulated costs; no new cash flows occur. With deposits or withdrawals, an unadjusted equity comparison can mislead.

Recovery uses the trough

If a loss fraction is d, the remaining value is 1−d of the peak. Required gain from the trough to recover is d/(1−d). It increases nonlinearly: a 50% decline needs100% gain from the reduced base. At 100% loss, the no-new-capital recovery formula has no finite result.

Preserve path and horizon

Final value alone does not show the largest earlier drawdown. A path ending750 after a trough 600 differs from a smooth decline to 750. Sampling only endpoints can hide peaks and troughs. Percentages should be computed with unrounded values and labeled denominators.

Do not turn recovery into a target

This is original percentage arithmetic, not a market forecast or a reason to increase exposure. Sample statistics describe only supplied observations, with uncertainty in broader estimates [NIST]. The modeled recovery requirement says nothing about probability, time required or actual executable gains. Journal the path and assumptions; leave those facts UNKNOWN.

• Running peak: greatest previous supplied equity.
• Drawdown: decline relative to running peak.
• Recovery gain: required increase relative to reduced value.
• Cash-flow adjustment: separate contributions from performance.

ILLUSTRATIVE no-cash-flow equity path T0–T4:1000,800,900,600,750 fictional units. Values are already net under the fixture; no individual positions or actual portfolio are represented.

Drawdown/equity evidence panel: running peak1000, trough 600, endpoint750; show40% decline denominator 1000 and 66.6667% recovery denominator 600. No future trajectory.

Supplied path's drawdowns and mathematical recovery requirement.

Future recovery, time to regain peak, suitable risk or a maximum future drawdown.

• OBSERVED: FIX-P06-L04 supplies trough 600.
• INFERRED: maximum supplied drawdown40%.
• UNKNOWN: later equity path and recovery time.
• INSUFFICIENT EVIDENCE: the path guarantees eventual recovery.

• Using endpoint to define maximum drawdown.
• Adding equal loss/gain percentages.
• Including deposits as returns.

Compute drawdown at every point, maximum drawdown, recovery needed from600 to 1000, recovery achieved600→750 and still needed750→1000.

Deliver calculations or annotations, claim/source table and limitations. Suggested allocation: study 12 minutes, exercise 8, correction/quiz 10; estimate subject to calibration.

• Track running peak.
• Exclude cash-flow distortion.
• Label each denominator.
• Separate required arithmetic from forecast.

Drawdown uses the prior peak; recovery uses the reduced base. Neither percentage predicts whether recovery will occur.

• Compute peak-to-trough drawdown.
• Explain recovery percentages using the reduced denominator.

P06-L05 after correction review.

NONE in the authoritative catalog. The supplied offline fixture/package is sufficient; no paid feature or unverified Production capability is required. Lab/certification metadata denotes downstream associations, not access gates or live awards.

• [NIST] NIST — Confidence limits for mean — Sample-mean uncertainty depends on dispersion, size and assumptions. Checked 2026-10-01; locator turn11view4.