{
  "title": "Five-product leverage comparison",
  "generatedAt": "2026-08-16T07:00:00+08:00",
  "dataThrough": "2026-08-14",
  "borrowRate": 0.0388,
  "definitions": {
    "pledged0050": "Daily rebalanced borrowing so that 0050 assets divided by investor equity remains 2.0x; 3.88% annual financing on the extra 1.0x notional; transaction costs, taxes, margin calls and forced liquidation excluded.",
    "annualVolatility": "Standard deviation of daily log returns annualized by sqrt(252)."
  },
  "taiwanLongSample": {
    "period": ["2016-01-04", "2026-08-14"],
    "0050": {"cagr": 0.2512, "annualVolatility": 0.2005, "maxDrawdown": -0.3383},
    "00631L": {"cagr": 0.4529, "annualVolatility": 0.3908, "maxDrawdown": -0.5514},
    "pledged0050Daily2x": {"cagr": 0.4460, "annualVolatility": 0.4020, "maxDrawdown": -0.5900}
  },
  "commonStartSample": {
    "note": "MUU-inception-era calendar interval; Taiwan and US trading calendars differ and this is a short bull-market sample.",
    "period": ["2024-10-10", "2026-08-14"],
    "0050": {"annualVolatility": 0.2733, "maxDrawdown": -0.2748},
    "00631L": {"annualVolatility": 0.5435, "maxDrawdown": -0.5026},
    "pledged0050Daily2x": {"annualVolatility": 0.5460, "maxDrawdown": -0.4920},
    "MU": {"annualVolatility": 0.7276, "maxDrawdown": -0.4278},
    "MUU": {"annualVolatility": 1.4585, "maxDrawdown": -0.7507}
  },
  "matchedDriftMonteCarlo": {
    "assumptions": {"geometricReturn": 0.12, "years": 3, "runs": 5000, "blockDays": 21},
    "taiwan50Distribution": {"historicalVolatility": 0.2099, "financedDaily2xMedianCagr": 0.1400, "financedDaily2xMedianMaxDrawdown": -0.4910},
    "muDistribution": {"historicalVolatility": 0.5812, "financedDaily2xMedianCagr": -0.1390, "financedDaily2xMedianMaxDrawdown": -0.9080}
  },
  "jointReview": {
    "reviewers": ["Codex", "Claude", "Grok"],
    "consensus": [
      "Product names do not create volatility drag; the underlying daily-return distribution, leverage reset rule and costs do.",
      "Pledged 0050 maintained at 2x and a daily-reset 2x ETF share the same gross leverage mathematics, but are not the same product.",
      "Pledged borrowing adds margin-call, forced-sale and debt-liability risks; 00631L investors are not personally margin-called.",
      "Without daily rebalancing, pledged 0050 becomes a drifting-leverage strategy and is no longer comparable with 00631L."
    ]
  }
}