{
  "run": "514-vix-predicts",
  "source": "Yahoo Finance via yfinance: ^VIX and ^GSPC daily closes, 1990-01-02 to 2026-08-20 (CBOE's own historical VIX back-calculation begins 1990).",
  "n_months_total": 439,
  "n_months_fit": 438,
  "date_range": [
    "1990-01-31",
    "2026-06-30"
  ],
  "spec_A_rv_on_vix": {
    "ols_hc3": {
      "n": 438,
      "slope": 0.009293,
      "intercept": -0.027182,
      "r2": 0.5119,
      "p": 5.16973699366995e-29,
      "slope_ci95": [
        0.007664,
        0.010922
      ]
    },
    "ols_hac3": {
      "n": 438,
      "slope": 0.009293,
      "r2": 0.5119,
      "p": 1.3866106268244598e-24,
      "slope_ci95": [
        0.007513,
        0.011073
      ]
    },
    "spearman_rho": 0.7241,
    "spearman_p": 2.44165666638916e-72
  },
  "spec_B_ret_on_vix": {
    "ols_hc3": {
      "n": 438,
      "slope": 0.02364,
      "intercept": 0.252935,
      "r2": 0.0017,
      "p": 0.6021978215547779,
      "slope_ci95": [
        -0.065252,
        0.112533
      ]
    },
    "ols_hac3": {
      "n": 438,
      "slope": 0.02364,
      "r2": 0.0017,
      "p": 0.6205828496078849,
      "slope_ci95": [
        -0.06996,
        0.117241
      ]
    },
    "spearman_rho": 0.0926,
    "spearman_p": 0.05269389422000127
  },
  "volatility_risk_premium": {
    "mean_vix_minus_rv_fwd": 0.04096,
    "ci95": [
      0.03466,
      0.04726
    ],
    "p": 5.500804945845531e-32,
    "n": 438,
    "pct_months_vix_above_realized": 83.3
  },
  "vix_terciles": {
    "low": {
      "n": 146,
      "mean_fwd_ret_pct": 0.5991,
      "sd": 2.5155
    },
    "mid": {
      "n": 147,
      "mean_fwd_ret_pct": 0.7356,
      "sd": 3.824
    },
    "high": {
      "n": 145,
      "mean_fwd_ret_pct": 0.8062,
      "sd": 5.8411
    }
  },
  "tercile_diff_high_minus_low": {
    "high_minus_low_mean_pct": 0.2071,
    "ci95": [
      -0.8339,
      1.2482
    ],
    "p": 0.695168484839958
  },
  "table": [
    {
      "ym": "1990-01",
      "date_end": "1990-01-31",
      "vix": 25.36000061035156,
      "rv_same_month": 0.16766325208168584,
      "rv_fwd": 0.11855828536733552,
      "ret_fwd_pct_next_month": 0.8502791354483286
    },
    {
      "ym": "1990-02",
      "date_end": "1990-02-28",
      "vix": 21.989999771118164,
      "rv_same_month": 0.11855828536733552,
      "rv_fwd": 0.10968249621402709,
      "ret_fwd_pct_next_month": 2.396550577972789
    },
    {
      "ym": "1990-03",
      "date_end": "1990-03-30",
      "vix": 19.729999542236328,
      "rv_same_month": 0.10968249621402709,
      "rv_fwd": 0.1112027065747979,
      "ret_fwd_pct_next_month": -2.7255212383089145
    },
    {
      "ym": "1990-04",
      "date_end": "1990-04-30",
      "vix": 19.520000457763672,
      "rv_same_month": 0.1112027065747979,
      "rv_fwd": 0.10898753117470614,
      "ret_fwd_pct_next_month": 8.800097873791124
    },
    {
      "ym": "1990-05",
      "date_end": "1990-05-31",
      "vix": 17.3700008392334,
      "rv_same_month": 0.10898753117470614,
      "rv_fwd": 0.13051672593620067,
      "ret_fwd_pct_next_month": -0.8926084910209298
    },
    {
      "ym": "1990-06",
      "date_end": "1990-06-29",
      "vix": 15.5,
      "rv_same_month": 0.13051672593620067,
      "rv_fwd": 0.12809781601435252,
      "ret_fwd_pct_next_month": -0.5236846788815086
    },
    {
      "ym": "1990-07",
      "date_end": "1990-07-31",
      "vix": 21.11000061035156,
      "rv_same_month": 0.12809781601435252,
      "rv_fwd": 0.2501041216158987,
      "ret_fwd_pct_next_month": -9.906281541277195
    },
    {
      "ym": "1990-08",
      "date_end": "1990-08-31",
      "vix": 29.899999618530277,
      "rv_same_month": 0.2501041216158987,
      "rv_fwd": 0.1611263541815602,
      "ret_fwd_pct_next_month": -5.254071046276909
    },
    {
      "ym": "1990-09",
      "date_end": "1990-09-28",
      "vix": 29.11000061035156,
      "rv_same_month": 0.1611263541815602,
      "rv_fwd": 0.22647648538797582,
      "ret_fwd_pct_next_month": -0.6720746005114187
    },
    {
      "ym": "1990-10",
      "date_end": "1990-10-31",
      "vix": 30.040000915527344,
      "rv_same_month": 0.22647648538797582,
      "rv_fwd": 0.16883051981034125,
      "ret_fwd_pct_next_month": 5.82068444450341
    },
    {
      "ym": "1990-11",
      "date_end": "1990-11-30",
      "vix": 22.15999984741211,
      "rv_same_month": 0.16883051981034125,
      "rv_fwd": 0.10044348681638736,
      "ret_fwd_pct_next_month": 2.4524556849066848
    },
    {
      "ym": "1990-12",
      "date_end": "1990-12-31",
      "vix": 26.3799991607666,
      "rv_same_month": 0.10044348681638736,
      "rv_fwd": 0.19192474662812709,
      "ret_fwd_pct_next_month": 4.067902429874781
    },
    {
      "ym": "1991-01",
      "date_end": "1991-01-31",
      "vix": 20.90999984741211,
      "rv_same_month": 0.19192474662812709,
      "rv_fwd": 0.17471031565588224,
      "ret_fwd_pct_next_month": 6.511445851577591
    },
    {
      "ym": "1991-02",
      "date_end": "1991-02-28",
      "vix": 21.229999542236328,
      "rv_same_month": 0.17471031565588224,
      "rv_fwd": 0.13326526712362882,
      "ret_fwd_pct_next_month": 2.1959938353917963
    },
    {
      "ym": "1991-03",
      "date_end": "1991-03-28",
      "vix": 16.8799991607666,
      "rv_same_month": 0.13326526712362882,
      "rv_fwd": 0.15741190844775063,
      "ret_fwd_pct_next_month": 0.031974823758318394
    },
    {
      "ym": "1991-04",
      "date_end": "1991-04-30",
      "vix": 18.239999771118164,
      "rv_same_month": 0.15741190844775063,
      "rv_fwd": 0.13518999714537167,
      "ret_fwd_pct_next_month": 3.787844010543928
    },
    {
      "ym": "1991-05",
      "date_end": "1991-05-31",
      "vix": 15.93000030517578,
      "rv_same_month": 0.13518999714537167,
      "rv_fwd": 0.1189969426897383,
      "ret_fwd_pct_next_month": -4.907746586014916
    },
    {
      "ym": "1991-06",
      "date_end": "1991-06-28",
      "vix": 19.549999237060547,
      "rv_same_month": 0.1189969426897383,
      "rv_fwd": 0.11007097361722558,
      "ret_fwd_pct_next_month": 4.388227631696129
    },
    {
      "ym": "1991-07",
      "date_end": "1991-07-31",
      "vix": 15.18000030517578,
      "rv_same_month": 0.11007097361722558,
      "rv_fwd": 0.1551428342807947,
      "ret_fwd_pct_next_month": 1.9458239201722627
    },
    {
      "ym": "1991-08",
      "date_end": "1991-08-30",
      "vix": 14.460000038146973,
      "rv_same_month": 0.1551428342807947,
      "rv_fwd": 0.07796303864250943,
      "ret_fwd_pct_next_month": -1.932934986955992
    },
    {
      "ym": "1991-09",
      "date_end": "1991-09-30",
      "vix": 15.850000381469728,
      "rv_same_month": 0.07796303864250943,
      "rv_fwd": 0.11302576835211395,
      "ret_fwd_pct_next_month": 1.1764759676739622
    },
    {
      "ym": "1991-10",
      "date_end": "1991-10-31",
      "vix": 15.479999542236328,
      "rv_same_month": 0.11302576835211395,
      "rv_fwd": 0.16291693159488937,
      "ret_fwd_pct_next_month": -4.489664780873692
    },
    {
      "ym": "1991-11",
      "date_end": "1991-11-29",
      "vix": 20.26000022888184,
      "rv_same_month": 0.16291693159488937,
      "rv_fwd": 0.13661069152382369,
      "ret_fwd_pct_next_month": 10.578949320065512
    },
    {
      "ym": "1991-12",
      "date_end": "1991-12-31",
      "vix": 19.309999465942383,
      "rv_same_month": 0.13661069152382369,
      "rv_fwd": 0.10110371183096586,
      "ret_fwd_pct_next_month": -2.0124906041997903
    },
    {
      "ym": "1992-01",
      "date_end": "1992-01-31",
      "vix": 17.399999618530273,
      "rv_same_month": 0.10110371183096586,
      "rv_fwd": 0.11265736677954927,
      "ret_fwd_pct_next_month": 0.954385530957591
    },
    {
      "ym": "1992-02",
      "date_end": "1992-02-28",
      "vix": 16.68000030517578,
      "rv_same_month": 0.11265736677954927,
      "rv_fwd": 0.07345537063126208,
      "ret_fwd_pct_next_month": -2.207370360663763
    },
    {
      "ym": "1992-03",
      "date_end": "1992-03-31",
      "vix": 16.18000030517578,
      "rv_same_month": 0.07345537063126208,
      "rv_fwd": 0.14301060448276495,
      "ret_fwd_pct_next_month": 2.751079773217402
    },
    {
      "ym": "1992-04",
      "date_end": "1992-04-30",
      "vix": 15.529999732971191,
      "rv_same_month": 0.14301060448276495,
      "rv_fwd": 0.09553535498313291,
      "ret_fwd_pct_next_month": 0.09634925174193398
    },
    {
      "ym": "1992-05",
      "date_end": "1992-05-29",
      "vix": 13.859999656677246,
      "rv_same_month": 0.09553535498313291,
      "rv_fwd": 0.09430572490275228,
      "ret_fwd_pct_next_month": -1.7511264288296857
    },
    {
      "ym": "1992-06",
      "date_end": "1992-06-30",
      "vix": 13.350000381469728,
      "rv_same_month": 0.09430572490275228,
      "rv_fwd": 0.09947853354698843,
      "ret_fwd_pct_next_month": 3.861830680387701
    },
    {
      "ym": "1992-07",
      "date_end": "1992-07-31",
      "vix": 13.170000076293944,
      "rv_same_month": 0.09947853354698843,
      "rv_fwd": 0.06574395713522006,
      "ret_fwd_pct_next_month": -2.4290163475820137
    },
    {
      "ym": "1992-08",
      "date_end": "1992-08-31",
      "vix": 13.579999923706056,
      "rv_same_month": 0.06574395713522006,
      "rv_fwd": 0.10466734230166519,
      "ret_fwd_pct_next_month": 0.9064387885348246
    },
    {
      "ym": "1992-09",
      "date_end": "1992-09-30",
      "vix": 14.279999732971191,
      "rv_same_month": 0.10466734230166519,
      "rv_fwd": 0.10652246429551268,
      "ret_fwd_pct_next_month": 0.21040675880250603
    },
    {
      "ym": "1992-10",
      "date_end": "1992-10-30",
      "vix": 16.149999618530273,
      "rv_same_month": 0.10652246429551268,
      "rv_fwd": 0.07824304193766249,
      "ret_fwd_pct_next_month": 2.981295217929958
    },
    {
      "ym": "1992-11",
      "date_end": "1992-11-30",
      "vix": 13.010000228881836,
      "rv_same_month": 0.07824304193766249,
      "rv_fwd": 0.0745947737599293,
      "ret_fwd_pct_next_month": 1.005702514832052
    },
    {
      "ym": "1992-12",
      "date_end": "1992-12-31",
      "vix": 12.56999969482422,
      "rv_same_month": 0.0745947737599293,
      "rv_fwd": 0.06774175069581073,
      "ret_fwd_pct_next_month": 0.702128090816867
    },
    {
      "ym": "1993-01",
      "date_end": "1993-01-29",
      "vix": 12.420000076293944,
      "rv_same_month": 0.06774175069581073,
      "rv_fwd": 0.1269679636618904,
      "ret_fwd_pct_next_month": 1.042905544963535
    },
    {
      "ym": "1993-02",
      "date_end": "1993-02-26",
      "vix": 13.15999984741211,
      "rv_same_month": 0.1269679636618904,
      "rv_fwd": 0.10599829796921496,
      "ret_fwd_pct_next_month": 1.8524653242830702
    },
    {
      "ym": "1993-03",
      "date_end": "1993-03-31",
      "vix": 12.529999732971191,
      "rv_same_month": 0.10599829796921496,
      "rv_fwd": 0.11103866956942116,
      "ret_fwd_pct_next_month": -2.57453969876007
    },
    {
      "ym": "1993-04",
      "date_end": "1993-04-30",
      "vix": 12.420000076293944,
      "rv_same_month": 0.11103866956942116,
      "rv_fwd": 0.10231557154836762,
      "ret_fwd_pct_next_month": 2.2463263865184047
    },
    {
      "ym": "1993-05",
      "date_end": "1993-05-28",
      "vix": 13.470000267028809,
      "rv_same_month": 0.10231557154836762,
      "rv_fwd": 0.08298445676998815,
      "ret_fwd_pct_next_month": 0.07549434975970826
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    {
      "ym": "1993-06",
      "date_end": "1993-06-30",
      "vix": 11.260000228881836,
      "rv_same_month": 0.08298445676998815,
      "rv_fwd": 0.08746026919919118,
      "ret_fwd_pct_next_month": -0.534128500779385
    },
    {
      "ym": "1993-07",
      "date_end": "1993-07-30",
      "vix": 11.729999542236328,
      "rv_same_month": 0.08746026919919118,
      "rv_fwd": 0.052294006833721644,
      "ret_fwd_pct_next_month": 3.385244141081678
    },
    {
      "ym": "1993-08",
      "date_end": "1993-08-31",
      "vix": 11.850000381469728,
      "rv_same_month": 0.052294006833721644,
      "rv_fwd": 0.07655766866099645,
      "ret_fwd_pct_next_month": -1.0038144175098296
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    {
      "ym": "1993-09",
      "date_end": "1993-09-30",
      "vix": 12.989999771118164,
      "rv_same_month": 0.07655766866099645,
      "rv_fwd": 0.06091744764020801,
      "ret_fwd_pct_next_month": 1.9207276337299461
    },
    {
      "ym": "1993-10",
      "date_end": "1993-10-29",
      "vix": 11.460000038146973,
      "rv_same_month": 0.06091744764020801,
      "rv_fwd": 0.08482929699429946,
      "ret_fwd_pct_next_month": -1.2994692567740884
    },
    {
      "ym": "1993-11",
      "date_end": "1993-11-30",
      "vix": 13.760000228881836,
      "rv_same_month": 0.08482929699429946,
      "rv_fwd": 0.056359762424538364,
      "ret_fwd_pct_next_month": 1.00405987830392
    },
    {
      "ym": "1993-12",
      "date_end": "1993-12-31",
      "vix": 11.65999984741211,
      "rv_same_month": 0.056359762424538364,
      "rv_fwd": 0.06849181481837487,
      "ret_fwd_pct_next_month": 3.1983767906036853
    },
    {
      "ym": "1994-01",
      "date_end": "1994-01-31",
      "vix": 10.630000114440918,
      "rv_same_month": 0.06849181481837487,
      "rv_fwd": 0.11783506739248568,
      "ret_fwd_pct_next_month": -3.0505597516047978
    },
    {
      "ym": "1994-02",
      "date_end": "1994-02-28",
      "vix": 14.869999885559082,
      "rv_same_month": 0.11783506739248568,
      "rv_fwd": 0.09610491959820953,
      "ret_fwd_pct_next_month": -4.682593067640006
    },
    {
      "ym": "1994-03",
      "date_end": "1994-03-31",
      "vix": 20.450000762939453,
      "rv_same_month": 0.09610491959820953,
      "rv_fwd": 0.1378299755985456,
      "ret_fwd_pct_next_month": 1.1464671878566257
    },
    {
      "ym": "1994-04",
      "date_end": "1994-04-29",
      "vix": 13.770000457763672,
      "rv_same_month": 0.1378299755985456,
      "rv_fwd": 0.09679388280978739,
      "ret_fwd_pct_next_month": 1.2320928865824143
    },
    {
      "ym": "1994-05",
      "date_end": "1994-05-31",
      "vix": 13.029999732971191,
      "rv_same_month": 0.09679388280978739,
      "rv_fwd": 0.09600079750483298,
      "ret_fwd_pct_next_month": -2.7156239046446373
    },
    {
      "ym": "1994-06",
      "date_end": "1994-06-30",
      "vix": 14.970000267028809,
      "rv_same_month": 0.09600079750483298,
      "rv_fwd": 0.06068584615437419,
      "ret_fwd_pct_next_month": 3.1004268952846914
    },
    {
      "ym": "1994-07",
      "date_end": "1994-07-29",
      "vix": 11.130000114440918,
      "rv_same_month": 0.06068584615437419,
      "rv_fwd": 0.07539658790711098,
      "ret_fwd_pct_next_month": 3.690910079063592
    },
    {
      "ym": "1994-08",
      "date_end": "1994-08-31",
      "vix": 11.970000267028809,
      "rv_same_month": 0.07539658790711098,
      "rv_fwd": 0.09858495142972087,
      "ret_fwd_pct_next_month": -2.7245341243997245
    },
    {
      "ym": "1994-09",
      "date_end": "1994-09-30",
      "vix": 14.279999732971191,
      "rv_same_month": 0.09858495142972087,
      "rv_fwd": 0.11950339390868343,
      "ret_fwd_pct_next_month": 2.061975964867635
    },
    {
      "ym": "1994-10",
      "date_end": "1994-10-31",
      "vix": 14.5600004196167,
      "rv_same_month": 0.11950339390868343,
      "rv_fwd": 0.098278636674226,
      "ret_fwd_pct_next_month": -4.030609832475918
    },
    {
      "ym": "1994-11",
      "date_end": "1994-11-30",
      "vix": 15.949999809265137,
      "rv_same_month": 0.098278636674226,
      "rv_fwd": 0.09381649024222702,
      "ret_fwd_pct_next_month": 1.2224097678835477
    },
    {
      "ym": "1994-12",
      "date_end": "1994-12-30",
      "vix": 13.199999809265137,
      "rv_same_month": 0.09381649024222702,
      "rv_fwd": 0.05733262886882521,
      "ret_fwd_pct_next_month": 2.3987692740721656
    },
    {
      "ym": "1995-01",
      "date_end": "1995-01-31",
      "vix": 11.960000038146973,
      "rv_same_month": 0.05733262886882521,
      "rv_fwd": 0.07458972517463726,
      "ret_fwd_pct_next_month": 3.543871277481525
    },
    {
      "ym": "1995-02",
      "date_end": "1995-02-28",
      "vix": 11.75,
      "rv_same_month": 0.07458972517463726,
      "rv_fwd": 0.0717298427496011,
      "ret_fwd_pct_next_month": 2.6962420103642692
    },
    {
      "ym": "1995-03",
      "date_end": "1995-03-31",
      "vix": 13.369999885559082,
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