{
  "slug": "maximum-drawdown",
  "title": "Observed-path maximum drawdown",
  "topic": "risk",
  "summary": "Find the deepest peak-to-observation decline in a finite nonnegative wealth path.",
  "version": "1.0.0",
  "published": "2026-10-16",
  "status": "Educational reference",
  "formula": "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)",
  "inputs": [
    [
      "returns",
      "1-250 decimals, -1 to 10",
      "Chronological period-end returns with no external flows"
    ]
  ],
  "method": [
    "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."
  ],
  "limits": [
    "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."
  ],
  "checks": [
    "Initial loss, recovery, all-positive path, complete loss and reordered paths.",
    "Observed maximum reconciled independently to peak tracking."
  ],
  "related": [
    "drawdown-path-and-sampling",
    "compound-return-and-cash-flows"
  ],
  "sources": [
    {
      "title": "PerformanceAnalytics: maximum drawdown",
      "url": "https://search.r-project.org/CRAN/refmans/PerformanceAnalytics/html/maxDrawdown.html"
    }
  ],
  "example": {
    "returns": [
      0.1,
      -0.2,
      0.15,
      -0.05
    ]
  },
  "frozen_result": {
    "schema_version": 1,
    "model_id": "maximum-drawdown",
    "model_version": "1.0.0",
    "engine_version": "1.0.0",
    "published_at": "2026-10-16",
    "scope": "Synthetic educational reference calculation. Not a fitted investment strategy, forecast, provider model or client return.",
    "inputs": {
      "returns": [
        0.1,
        -0.2,
        0.15,
        -0.05
      ]
    },
    "outputs": {
      "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
      ]
    },
    "notes": [
      "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."
    ]
  }
}