{
  "slug": "var-parametric",
  "name": "Value at Risk — Parametric (Gaussian)",
  "category": "Risk Management",
  "description": "VaR computed under a normal-distribution assumption from mean and standard deviation.",
  "formula": "VaR_α = -(μ + Z_α × σ) × √T",
  "formula_latex": "\\text{VaR}_\\alpha = -(\\mu + Z_\\alpha \\sigma)\\sqrt{T}",
  "parameters": [
    {
      "name": "Mean return",
      "symbol": "μ",
      "type": "percent",
      "default": 0.0004
    },
    {
      "name": "Std deviation",
      "symbol": "σ",
      "type": "percent",
      "default": 0.012,
      "min": 0.0001
    },
    {
      "name": "Confidence level",
      "symbol": "α",
      "type": "percent",
      "default": 0.95,
      "min": 0.5,
      "max": 0.999
    },
    {
      "name": "Holding period (days)",
      "symbol": "T",
      "type": "integer",
      "default": 1
    }
  ],
  "outputs": [
    {
      "name": "VaR",
      "symbol": "VaR",
      "type": "percent"
    }
  ],
  "worked_example": {
    "narrative": "Portfolio with daily mean 0.04% and σ = 1.2%, 95% 1-day VaR.",
    "inputs": {
      "mu": 0.0004,
      "sigma": 0.012,
      "alpha": 0.95,
      "T": 1
    },
    "expected_outputs": {
      "var": 0.0193
    }
  },
  "limitations": [
    "Assumes normality; understates tail risk"
  ],
  "alternatives": [
    {
      "slug": "var-historical",
      "when_to_prefer": "Returns clearly non-normal"
    }
  ],
  "related_terms": [
    "var",
    "normal-distribution",
    "z-score"
  ]
}