{
  "slug": "sortino-ratio",
  "name": "Sortino Ratio",
  "category": "Risk-Adjusted Performance",
  "description": "Like the Sharpe ratio, but penalizes only downside deviation. Better suited to asymmetric return distributions.",
  "formula": "Sortino = (R_p - MAR) / σ_d",
  "formula_latex": "\\text{Sortino} = \\dfrac{R_p - \\text{MAR}}{\\sigma_d}",
  "parameters": [
    {
      "name": "Portfolio return",
      "symbol": "R_p",
      "type": "percent",
      "default": 0.12
    },
    {
      "name": "Minimum Acceptable Return",
      "symbol": "MAR",
      "type": "percent",
      "default": 0.043,
      "description": "Often risk-free rate or 0%"
    },
    {
      "name": "Downside deviation",
      "symbol": "σ_d",
      "type": "percent",
      "default": 0.07,
      "min": 0.0001,
      "description": "Standard deviation computed only over returns below MAR"
    }
  ],
  "outputs": [
    {
      "name": "Sortino Ratio",
      "symbol": "Sortino",
      "type": "number",
      "description": "Excess return per unit of downside deviation"
    }
  ],
  "worked_example": {
    "narrative": "A fund with 12% return, 7% downside deviation, against 4.3% MAR.",
    "inputs": {
      "R_p": 0.12,
      "MAR": 0.043,
      "sigma_d": 0.07
    },
    "expected_outputs": {
      "sortino": 1.1
    }
  },
  "assumptions": [
    "Investor cares only about downside deviation"
  ],
  "limitations": [
    "Requires sufficient sample of below-MAR returns",
    "Sensitive to MAR choice"
  ],
  "alternatives": [
    {
      "slug": "sharpe-ratio",
      "when_to_prefer": "For symmetric distributions"
    }
  ],
  "related_terms": [
    "sortino-ratio",
    "downside-deviation",
    "minimum-acceptable-return"
  ],
  "references": [
    {
      "title": "Performance Measurement in a Downside Risk Framework",
      "author": "Sortino & Price",
      "year": 1994
    }
  ]
}