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    {
      "year": 2024,
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    {
      "year": 2025,
      "method": "Buy & Hold",
      "start": "2024-12-31",
      "end": "2025-12-31",
      "days": 250,
      "final": 116.38780406111908,
      "return_pct": 16.387804061119084,
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      "floor_breached": true,
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      "risky_turnover": 0.0
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    {
      "year": 2025,
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      "days": 250,
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      "floor_breached": true,
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    {
      "year": 2025,
      "method": "CPPI",
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      "days": 250,
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      "floor_breached": false,
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    {
      "year": 2025,
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      "days": 250,
      "final": 103.63220836120767,
      "return_pct": 3.632208361207674,
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    {
      "year": 2025,
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      "days": 250,
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      "floor_breached": false,
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    {
      "year": 2025,
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  "summary": [
    {
      "method": "Buy & Hold",
      "mean_annual_return_pct": 13.784619754814404,
      "worst_within_year_drawdown_pct": 33.92495902426057,
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      "mean_rebalance_count": 250.375
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      "exit_years": 0,
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    },
    {
      "method": "Variable m",
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      "floor_breach_years": 0,
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      "mean_rebalance_count": 229.75
    },
    {
      "method": "OBPI (model)",
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      "worst_within_year_drawdown_pct": 28.61189116392273,
      "floor_breach_years": 0,
      "exit_years": 0,
      "mean_rebalance_count": 0
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  ],
  "obpi_sensitivity": [
    {
      "year": 2020,
      "method": "OBPI (model)",
      "return_pct": 17.158415299769246,
      "option_sigma": 0.15,
      "call_premium": 5.9866976090492585,
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    {
      "year": 2020,
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      "option_sigma": 0.2,
      "call_premium": 7.976435354518614,
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    {
      "year": 2020,
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      "option_sigma": 0.3,
      "call_premium": 11.939738615228464,
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    {
      "year": 2022,
      "method": "OBPI (model)",
      "return_pct": -10.0,
      "option_sigma": 0.15,
      "call_premium": 5.970348751257191,
      "call_units": 1.674944030345677
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    {
      "year": 2022,
      "method": "OBPI (model)",
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      "call_premium": 7.954684509454552,
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    {
      "year": 2022,
      "method": "OBPI (model)",
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      "option_sigma": 0.3,
      "call_premium": 11.907315625640898,
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    {
      "year": 2023,
      "method": "OBPI (model)",
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      "option_sigma": 0.15,
      "call_premium": 5.970348751257191,
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    {
      "year": 2023,
      "method": "OBPI (model)",
      "return_pct": 20.460665956092356,
      "option_sigma": 0.2,
      "call_premium": 7.954684509454552,
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    {
      "year": 2023,
      "method": "OBPI (model)",
      "return_pct": 10.349253790402969,
      "option_sigma": 0.3,
      "call_premium": 11.907315625640898,
      "call_units": 0.8398198480996225
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  ],
  "engine_sha256": "88f39d0eab2fb88d2c916a2a45a50f8c69d17931301ec32e2f833f8920e33d4d",
  "source": {
    "provider": "S&P Dow Jones Indices via FRED, SP500",
    "url": "https://fred.stlouisfed.org/series/SP500",
    "retrieved": "2026-09-19",
    "sha256": "dc701c49ac9deecbec444fd6e63a9bb9b77c3e4a49e48cf5eb9292a20d48ceee",
    "first": "2016-10-03",
    "last": "2025-12-31",
    "observations": 2325,
    "measure": "Daily close price index, no dividends; input kept local"
  },
  "assumptions": {
    "years": [
      2018,
      2019,
      2020,
      2021,
      2022,
      2023,
      2024,
      2025
    ],
    "initial": 100,
    "floor": 90,
    "reset": "Each calendar year independently; previous year final trading close to current year final close",
    "safe_rate": 0,
    "costs": 0,
    "dividends": false,
    "constant_m": 3,
    "variable_vol_window": 20,
    "signal_lag": "All volatility estimates end one trading close before execution",
    "variable_rule": "clamp(3*0.20/annualized_sample_log_return_volatility,1,6)",
    "execution": "Idealized observed closing prices; no intraday stop fills; fractional holdings",
    "obpi": "Reserve 90 + European ATM calls, r=q=0; start trailing 252-return volatility fixed through expiry; theoretical premiums and marks, not traded option history"
  }
}