{
  "meta": {
    "title": "Leverage Decay Study — computed results",
    "source": "Massive Market Data (daily adjusted closes). Author's calculations.",
    "window_standard": "2025-07-15 to 2026-07-17 (254 trading days)",
    "window_nbil": "2025-10-07 to 2026-07-17 (195 trading days; NBIL began trading Oct 2025)",
    "generated": "2026-07-18",
    "method": "For each pair: cumulative return = last_close / first_close - 1, measured on adjusted daily closes over the pair's common window. Target = stated daily leverage multiple x underlying cumulative return. Decay gap = ETF actual return - target, in percentage points. Underlying annualized volatility = stdev of daily log returns x sqrt(252). NBIL is measured over its own shorter window; its underlying NBIS is measured over the identical window.",
    "notes": "Positive decay gap means the ETF beat its leverage target (possible in strong, low-chop trends via positive compounding). Negative gap is volatility decay. This is not investment advice."
  },
  "pairs": [
    {"etf": "NBIL", "lev": 2, "underlying": "NBIS", "und_ret": 50.99, "target": 101.97, "etf_ret": -4.52, "decay_gap": -106.49, "und_vol": 100.5, "held_by_aea": true, "note": "GraniteShares 2x Long NBIS Daily ETF. Held in the AEA book; the reason this study is personal."},
    {"etf": "TSLL", "lev": 2, "underlying": "TSLA", "und_ret": 22.55, "target": 45.09, "etf_ret": 2.85, "decay_gap": -42.25, "und_vol": 44.6, "held_by_aea": false, "note": "2x TSLA daily."},
    {"etf": "NVDL", "lev": 2, "underlying": "NVDA", "und_ret": 18.81, "target": 37.62, "etf_ret": 11.36, "decay_gap": -26.26, "und_vol": 35.6, "held_by_aea": false, "note": "2x NVDA daily."},
    {"etf": "AAPU", "lev": 2, "underlying": "AAPL", "und_ret": 59.60, "target": 119.20, "etf_ret": 103.22, "decay_gap": -15.98, "und_vol": 24.3, "held_by_aea": false, "note": "2x AAPL daily."},
    {"etf": "MSFU", "lev": 2, "underlying": "MSFT", "und_ret": -22.15, "target": -44.29, "etf_ret": -52.27, "decay_gap": -7.98, "und_vol": 27.5, "held_by_aea": false, "note": "2x MSFT daily. Decay compounds the downside too: MSFT fell 22%, the 2x fund fell more than 2x that."},
    {"etf": "TQQQ", "lev": 3, "underlying": "QQQ", "und_ret": 24.90, "target": 74.69, "etf_ret": 59.21, "decay_gap": -15.48, "und_vol": 18.7, "held_by_aea": false, "note": "3x Nasdaq-100 daily. Low underlying vol keeps the gap modest even at 3x."},
    {"etf": "SOXL", "lev": 3, "underlying": "SOXX", "und_ret": 111.89, "target": 335.67, "etf_ret": 396.41, "decay_gap": 60.74, "und_vol": 42.4, "held_by_aea": false, "note": "3x semiconductors daily. The honest counterexample: in a strong, sustained uptrend, daily-reset leverage compounded in the holder's favor and BEAT 3x."}
  ],
  "flagship_series": {
    "pair": "NBIL vs NBIS",
    "note": "Indexed to 100 at 2025-10-07 (NBIL inception). Weekly samples of adjusted closes. The dashed reference line 2x-target = 100 + 2 x (NBIS index - 100) is computed in the page.",
    "day": [1,6,11,16,21,26,31,36,41,46,51,56,61,66,71,76,81,86,91,96,101,106,111,116,121,126,131,136,141,146,151,156,161,166,171,176,181,186,191,195],
    "nbil_idx": [100.0,116.3,75.9,101.0,81.3,68.7,52.6,49.3,60.3,53.4,34.0,48.5,46.8,55.0,66.5,46.7,42.3,44.6,48.6,52.8,36.8,44.4,60.9,59.3,46.8,67.1,117.0,102.6,82.7,151.5,166.1,140.1,189.8,244.8,174.1,285.0,197.4,145.8,139.5,95.5],
    "nbis_idx": [100.0,108.9,88.6,103.5,93.9,86.8,76.9,75.5,84.0,79.5,64.1,77.4,76.4,83.2,92.4,77.7,74.9,78.9,82.9,87.2,73.7,81.9,98.8,97.6,88.2,106.2,141.7,132.7,120.0,165.8,176.1,163.0,192.3,220.6,188.8,243.6,204.2,181.0,178.9,151.0]
  },
  "summary": {
    "avg_gap_2x_single_stock": -39.79,
    "avg_gap_all": -21.96,
    "worst_offender": "NBIL (-106.49 pp)",
    "best_tracker": "SOXL (+60.74 pp; the only fund that beat its target)"
  }
}