{
  "slug": "sharpe-ratio",
  "name": "Sharpe Ratio",
  "category": "Risk-Adjusted Performance",
  "description": "Excess return per unit of total volatility. The most widely used risk-adjusted performance metric.",
  "use_cases": [
    "Manager selection",
    "Portfolio comparison",
    "Strategy benchmarking"
  ],
  "formula": "Sharpe = (R_p - R_f) / σ_p",
  "formula_latex": "\\text{Sharpe} = \\dfrac{R_p - R_f}{\\sigma_p}",
  "parameters": [
    {
      "name": "Portfolio return",
      "symbol": "R_p",
      "type": "percent",
      "description": "Annualized portfolio return",
      "default": 0.12,
      "unit": "decimal"
    },
    {
      "name": "Risk-free rate",
      "symbol": "R_f",
      "type": "percent",
      "description": "Annualized risk-free rate (typically 3-month T-bill)",
      "default": 0.043,
      "unit": "decimal"
    },
    {
      "name": "Portfolio volatility",
      "symbol": "σ_p",
      "type": "percent",
      "description": "Annualized standard deviation of returns",
      "default": 0.1,
      "unit": "decimal",
      "min": 0.0001
    }
  ],
  "outputs": [
    {
      "name": "Sharpe Ratio",
      "symbol": "S",
      "type": "number",
      "description": "Risk-adjusted return per unit of volatility",
      "interpretation": [
        {
          "range": "< 0",
          "label": "Underperforming",
          "meaning": "Returns worse than risk-free; do not invest."
        },
        {
          "range": "0 - 0.5",
          "label": "Sub-par",
          "meaning": "Risk-free outperforms, marginally."
        },
        {
          "range": "0.5 - 1.0",
          "label": "Adequate",
          "meaning": "Modest risk-adjusted returns."
        },
        {
          "range": "1.0 - 2.0",
          "label": "Good",
          "meaning": "Healthy risk-adjusted return; typical for diversified equity portfolios."
        },
        {
          "range": "2.0 - 3.0",
          "label": "Excellent",
          "meaning": "Strong manager skill or favorable regime."
        },
        {
          "range": "> 3.0",
          "label": "Exceptional",
          "meaning": "Often indicative of specialized strategies (HFT, high-frequency stat arb, or unsustainable alpha)."
        }
      ]
    }
  ],
  "worked_example": {
    "narrative": "A fund with 12% annual return, 10% annual volatility, against a 4.3% T-bill.",
    "inputs": {
      "R_p": 0.12,
      "R_f": 0.043,
      "sigma_p": 0.1
    },
    "expected_outputs": {
      "sharpe": 0.77
    }
  },
  "assumptions": [
    "Returns are normally distributed",
    "Volatility is a complete measure of risk",
    "Returns are independent and identically distributed (i.i.d.)"
  ],
  "limitations": [
    "Penalizes upside and downside volatility symmetrically",
    "Inappropriate for strategies with negatively-skewed return distributions (option-writing, merger arb)",
    "Sensitive to choice of risk-free benchmark and observation frequency",
    "Annualized Sharpe via √T scaling assumes i.i.d. returns; serial correlation inflates Sharpe"
  ],
  "alternatives": [
    {
      "slug": "sortino-ratio",
      "when_to_prefer": "When you want to penalize only downside volatility"
    },
    {
      "slug": "calmar-ratio",
      "when_to_prefer": "When max drawdown matters more than volatility"
    },
    {
      "slug": "information-ratio",
      "when_to_prefer": "When measuring active manager vs benchmark"
    }
  ],
  "related_terms": [
    "sharpe-ratio",
    "sortino-ratio",
    "information-ratio",
    "risk-free-rate",
    "volatility"
  ],
  "implementation_notes": "Server compute: returns Sharpe directly. For Sharpe from a return series, use /api/v1/compute/sharpe-ratio-series.",
  "references": [
    {
      "title": "Mutual Fund Performance",
      "author": "William F. Sharpe",
      "year": 1966,
      "publisher": "Journal of Business"
    },
    {
      "title": "The Sharpe Ratio",
      "author": "William F. Sharpe",
      "year": 1994,
      "publisher": "Journal of Portfolio Management"
    }
  ]
}