{
  "slug": "bond-duration",
  "name": "Modified Duration",
  "category": "Fixed Income",
  "description": "First-order sensitivity of a bond price to a parallel shift in yield.",
  "formula": "MD = MacD / (1 + y/n)\nΔP/P ≈ -MD × Δy",
  "formula_latex": "\\text{MD} = \\dfrac{\\text{MacD}}{1 + y/n},\\quad \\dfrac{\\Delta P}{P} \\approx -\\text{MD}\\cdot \\Delta y",
  "parameters": [
    {
      "name": "Macaulay Duration (years)",
      "symbol": "MacD",
      "type": "number",
      "default": 7.5
    },
    {
      "name": "Yield",
      "symbol": "y",
      "type": "percent",
      "default": 0.05
    },
    {
      "name": "Coupon frequency per year",
      "symbol": "n",
      "type": "integer",
      "default": 2
    }
  ],
  "outputs": [
    {
      "name": "Modified Duration",
      "symbol": "MD",
      "type": "number"
    },
    {
      "name": "Approx % price change for 1bp move",
      "symbol": "DV01%",
      "type": "number"
    }
  ],
  "worked_example": {
    "inputs": {
      "MacD": 7.5,
      "y": 0.05,
      "n": 2
    },
    "expected_outputs": {
      "MD": 7.317,
      "dv01_pct_per_bp": 0.000732
    }
  },
  "related_terms": [
    "macaulay-duration",
    "modified-duration",
    "convexity",
    "dv01"
  ]
}