Observed-path maximum drawdown

Calculation contract

W_0 = 1; W_t = W_(t-1)*(1+r_t); DD_t = W_t/max(W_0...W_t)-1; MDD = min(DD_t)

Method and interpretation

The initial wealth point is included. An immediate negative first return therefore creates a drawdown rather than being treated as a new starting baseline. The default path 1, 1.1, 0.88, 1.012, 0.9614 has maximum drawdown -0.2.

The full wealth and drawdown arrays expose the path behind the summary. Unlike terminal compounding, drawdown depends on order. Reordering a series for a stress illustration must be disclosed as a constructed scenario, not described as the historical experience of an actual investor.

Where the reference stops

The output is a nonpositive fraction. It records only supplied observation endpoints, so an intraperiod low can be missing. It is not a forecast of worst future loss and does not model intraday liquidation, cash flows or margin.

Published synthetic inputs

{
  "returns": [
    0.1,
    -0.2,
    0.15,
    -0.05
  ]
}

Frozen calculation output

{
  "maximum_drawdown": -0.2,
  "ending_wealth": 0.9614,
  "wealth_path": [
    1,
    1.1,
    0.88,
    1.012,
    0.9614
  ],
  "drawdown_path": [
    0,
    0,
    -0.2,
    -0.08000000000000002,
    -0.12600000000000003
  ]
}

Initial wealth 1 is included as a peak. End-of-period observations only; intraperiod losses and external flows are not reconstructed. Drawdown is a nonpositive fraction.

Verification coverage

• Initial loss, recovery, all-positive path, complete loss and reordered paths.
• Observed maximum reconciled independently to peak tracking.

Unit and independent-reference checks test arithmetic and rejection rules, not future investment performance.

Method references

• PerformanceAnalytics: maximum drawdown

Read the assumptions in context