{
  "slug": "expected-shortfall",
  "name": "Expected Shortfall (CVaR)",
  "category": "Risk Management",
  "description": "Average loss conditional on losses exceeding VaR. A coherent risk measure unlike VaR.",
  "formula": "ES_α = E[L | L > VaR_α]",
  "formula_latex": "\\text{ES}_\\alpha = \\mathbb{E}\\left[L \\mid L > \\text{VaR}_\\alpha\\right]",
  "parameters": [
    {
      "name": "Returns",
      "symbol": "R",
      "type": "vector",
      "default": []
    },
    {
      "name": "Confidence level",
      "symbol": "α",
      "type": "percent",
      "default": 0.975
    }
  ],
  "outputs": [
    {
      "name": "Expected Shortfall",
      "symbol": "ES",
      "type": "percent"
    }
  ],
  "worked_example": {
    "narrative": "Same series, 97.5% ES.",
    "inputs": {
      "alpha": 0.975
    },
    "expected_outputs": {
      "es": 0.027
    }
  },
  "related_terms": [
    "expected-shortfall",
    "cvar",
    "coherent-risk-measure"
  ],
  "references": [
    {
      "title": "Coherent Measures of Risk",
      "author": "Artzner, Delbaen, Eber, Heath",
      "year": 1999
    }
  ]
}