{
  "slug": "kelly-criterion",
  "name": "Kelly Criterion",
  "category": "Position Sizing",
  "description": "Optimal bet size to maximize the long-run growth rate of capital, given edge and odds.",
  "formula": "f* = p/a - q/b   (binary form)\nor   f* = (μ - r) / σ²  (continuous form)",
  "formula_latex": "f^* = \\dfrac{\\mu - r}{\\sigma^2}",
  "parameters": [
    {
      "name": "Excess return",
      "symbol": "μ - r",
      "type": "percent",
      "default": 0.06
    },
    {
      "name": "Variance",
      "symbol": "σ²",
      "type": "number",
      "default": 0.04,
      "min": 0.0001
    }
  ],
  "outputs": [
    {
      "name": "Optimal fraction",
      "symbol": "f*",
      "type": "percent",
      "description": "Fraction of capital to allocate",
      "interpretation": [
        {
          "range": "f* > 1",
          "label": "Leverage suggested",
          "meaning": "Mathematically optimal but practically aggressive"
        },
        {
          "range": "0 < f* ≤ 1",
          "label": "Allocate",
          "meaning": "Allocate this fraction of capital"
        },
        {
          "range": "f* ≤ 0",
          "label": "Avoid",
          "meaning": "No edge — do not bet"
        }
      ]
    }
  ],
  "worked_example": {
    "narrative": "Strategy with 6% excess return, 20% volatility (σ² = 0.04).",
    "inputs": {
      "edge": 0.06,
      "variance": 0.04
    },
    "expected_outputs": {
      "kelly_fraction": 1.5
    }
  },
  "limitations": [
    "Highly sensitive to estimation error in edge",
    "Practitioners typically use fractional Kelly (¼ to ½)",
    "Assumes log-utility and i.i.d. returns"
  ],
  "related_terms": [
    "kelly-criterion",
    "position-sizing",
    "fractional-kelly",
    "log-utility"
  ],
  "references": [
    {
      "title": "A New Interpretation of Information Rate",
      "author": "John L. Kelly Jr.",
      "year": 1956
    },
    {
      "title": "Fortune's Formula",
      "author": "William Poundstone",
      "year": 2005
    }
  ]
}