{
  "slug": "volatility-target",
  "title": "Capped volatility scaling",
  "topic": "risk",
  "summary": "Translate a stated volatility estimate and target into a capped proportional exposure reference.",
  "version": "1.0.0",
  "published": "2026-10-16",
  "status": "Educational reference",
  "formula": "exposure = min(target_volatility / estimated_volatility, leverage_cap)",
  "inputs": [
    [
      "target_volatility",
      "Decimal, 0 to 10",
      "Desired scale at the estimate frequency"
    ],
    [
      "estimated_volatility",
      "Decimal, 0.000001 to 10",
      "Positive risk estimate"
    ],
    [
      "leverage_cap",
      "Nonnegative multiplier, at most 10",
      "Maximum allowed model exposure"
    ]
  ],
  "method": [
    "The default 12% target divided by an 8% estimate requests 1.5 times exposure. The 1.25 cap binds, leaving a model-implied scaled volatility of 10%. The result is below target because the constraint is respected rather than silently relaxed.",
    "The estimate must precede the decision it informs. Replacing it retrospectively with realized volatility can make a historical scaling rule look implausibly precise. This static card has no observation clock, so timing and lag must be supplied by the surrounding study."
  ],
  "limits": [
    "Estimated scaled volatility is not realized risk. The formula omits financing, margin, transaction costs, gap risk and portfolio changes. Very small estimates can bind the cap; a zero estimate is rejected, not assigned unlimited exposure."
  ],
  "checks": [
    "Binding/nonbinding caps, zero target and zero cap checked.",
    "Invalid negative or zero estimate rejected."
  ],
  "related": [
    "volatility-targeting-limits",
    "out-of-sample-and-multiple-testing"
  ],
  "sources": [
    {
      "title": "RiskMetrics technical document, fourth edition",
      "url": "https://www.msci.com/documents/10199/5915b101-4206-4ba0-aee2-3449d5c7e95a"
    }
  ],
  "example": {
    "target_volatility": 0.12,
    "estimated_volatility": 0.08,
    "leverage_cap": 1.25
  },
  "frozen_result": {
    "schema_version": 1,
    "model_id": "volatility-target",
    "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": {
      "target_volatility": 0.12,
      "estimated_volatility": 0.08,
      "leverage_cap": 1.25
    },
    "outputs": {
      "uncapped_exposure": 1.5,
      "exposure": 1.25,
      "estimated_scaled_volatility": 0.1,
      "cap_binding": true
    },
    "notes": [
      "Same-frequency volatilities. This is a proportional exposure reference, not an order, realized-risk guarantee or borrowing-cost model."
    ]
  }
}