{
  "title": "S&P 500 Fundamental vs. Market-Cap Concentration",
  "path": "/research/sp500-fundamental-vs-market-cap-concentration",
  "publishedAt": "2026-09-22",
  "updatedAt": null,
  "dataAsOf": "2026-09-21",
  "version": "1.0",
  "universe": {
    "frozenSecurityRows": 503,
    "frozenIssuerCompanies": 500,
    "matchedSecurityRows": 503,
    "matchedIssuerCompanies": 500
  },
  "market": {
    "top1IssuerWeightPct": 8.2245,
    "top5IssuerWeightPct": 30.5839,
    "top10IssuerWeightPct": 40.4509,
    "top20IssuerWeightPct": 50.5307,
    "issuerWeightHhi": 242.1964,
    "sectors": [
      {
        "sector": "Information Technology",
        "issuerCount": 74,
        "marketWeightPct": 39.0369
      },
      {
        "sector": "Financials",
        "issuerCount": 76,
        "marketWeightPct": 11.7649
      },
      {
        "sector": "Communication Services",
        "issuerCount": 20,
        "marketWeightPct": 10.1006
      },
      {
        "sector": "Health Care",
        "issuerCount": 60,
        "marketWeightPct": 9.1602
      },
      {
        "sector": "Consumer Discretionary",
        "issuerCount": 47,
        "marketWeightPct": 8.7717
      },
      {
        "sector": "Industrials",
        "issuerCount": 83,
        "marketWeightPct": 8.0738
      },
      {
        "sector": "Consumer Staples",
        "issuerCount": 33,
        "marketWeightPct": 4.3572
      },
      {
        "sector": "Energy",
        "issuerCount": 21,
        "marketWeightPct": 3.3846
      },
      {
        "sector": "Utilities",
        "issuerCount": 31,
        "marketWeightPct": 1.9081
      },
      {
        "sector": "Real Estate",
        "issuerCount": 30,
        "marketWeightPct": 1.7404
      },
      {
        "sector": "Materials",
        "issuerCount": 25,
        "marketWeightPct": 1.7017
      }
    ],
    "topIssuers": [
      {
        "name": "Nvidia",
        "symbols": [
          "NVDA"
        ],
        "sector": "Information Technology",
        "marketWeightPct": 8.224537
      },
      {
        "name": "Apple Inc.",
        "symbols": [
          "AAPL"
        ],
        "sector": "Information Technology",
        "marketWeightPct": 7.394309
      },
      {
        "name": "Alphabet Inc.",
        "symbols": [
          "GOOG",
          "GOOGL"
        ],
        "sector": "Communication Services",
        "marketWeightPct": 5.606115
      },
      {
        "name": "Microsoft",
        "symbols": [
          "MSFT"
        ],
        "sector": "Information Technology",
        "marketWeightPct": 5.56722
      },
      {
        "name": "Amazon",
        "symbols": [
          "AMZN"
        ],
        "sector": "Consumer Discretionary",
        "marketWeightPct": 3.79171
      },
      {
        "name": "Broadcom",
        "symbols": [
          "AVGO"
        ],
        "sector": "Information Technology",
        "marketWeightPct": 2.578868
      },
      {
        "name": "Meta Platforms",
        "symbols": [
          "META"
        ],
        "sector": "Communication Services",
        "marketWeightPct": 2.443082
      },
      {
        "name": "Micron Technology",
        "symbols": [
          "MU"
        ],
        "sector": "Information Technology",
        "marketWeightPct": 1.762297
      },
      {
        "name": "Tesla, Inc.",
        "symbols": [
          "TSLA"
        ],
        "sector": "Consumer Discretionary",
        "marketWeightPct": 1.580896
      },
      {
        "name": "Advanced Micro Devices",
        "symbols": [
          "AMD"
        ],
        "sector": "Information Technology",
        "marketWeightPct": 1.501863
      },
      {
        "name": "JPMorgan Chase",
        "symbols": [
          "JPM"
        ],
        "sector": "Financials",
        "marketWeightPct": 1.398688
      },
      {
        "name": "Berkshire Hathaway",
        "symbols": [
          "BRK.B"
        ],
        "sector": "Financials",
        "marketWeightPct": 1.397444
      },
      {
        "name": "Lilly (Eli)",
        "symbols": [
          "LLY"
        ],
        "sector": "Health Care",
        "marketWeightPct": 1.393167
      },
      {
        "name": "ExxonMobil",
        "symbols": [
          "XOM"
        ],
        "sector": "Energy",
        "marketWeightPct": 0.972901
      },
      {
        "name": "Johnson & Johnson",
        "symbols": [
          "JNJ"
        ],
        "sector": "Health Care",
        "marketWeightPct": 0.970627
      },
      {
        "name": "Visa Inc.",
        "symbols": [
          "V"
        ],
        "sector": "Financials",
        "marketWeightPct": 0.942292
      },
      {
        "name": "Intel",
        "symbols": [
          "INTC"
        ],
        "sector": "Information Technology",
        "marketWeightPct": 0.904448
      },
      {
        "name": "Walmart",
        "symbols": [
          "WMT"
        ],
        "sector": "Consumer Staples",
        "marketWeightPct": 0.71566
      },
      {
        "name": "AbbVie",
        "symbols": [
          "ABBV"
        ],
        "sector": "Health Care",
        "marketWeightPct": 0.698553
      },
      {
        "name": "Mastercard",
        "symbols": [
          "MA"
        ],
        "sector": "Financials",
        "marketWeightPct": 0.686059
      }
    ]
  },
  "comparisons": [
    {
      "metric": "revenue",
      "label": "Revenue",
      "fundamentalCoverageCompanyCount": 468,
      "fundamentalCoveragePercent": 93.6,
      "positiveCompanyCount": 468,
      "fundamentalTop10PositivePoolSharePct": 26.32,
      "sameTop10CompaniesMarketWeightPct": 24.9667,
      "top10MarketMinusFundamentalPctPoints": -1.3533,
      "fundamentalTop20PositivePoolSharePct": 39.37,
      "sameTop20CompaniesMarketWeightPct": 40.0241,
      "top20MarketMinusFundamentalPctPoints": 0.6541,
      "positivePoolHhi": 113.58,
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        {
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          "marketMinusFundamentalSharePctPoints": -0.4183
        },
        {
          "rank": 2,
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          ],
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        },
        {
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          ],
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          "marketMinusFundamentalSharePctPoints": -2.1235
        },
        {
          "rank": 4,
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          ],
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        },
        {
          "rank": 5,
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          ],
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          "marketMinusFundamentalSharePctPoints": -2.2155
        },
        {
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          ],
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        },
        {
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          ],
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          "marketMinusFundamentalSharePctPoints": -2.1925
        },
        {
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          ],
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        },
        {
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        {
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          ],
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          "marketMinusFundamentalSharePctPoints": -1.7997
        }
      ],
      "top20Companies": [
        {
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        },
        {
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        },
        {
          "rank": 3,
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          ],
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        {
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        {
          "rank": 5,
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        {
          "rank": 6,
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        {
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        },
        {
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        },
        {
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        {
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        },
        {
          "rank": 11,
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          ],
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        },
        {
          "rank": 12,
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          ],
          "sector": "Health Care",
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        },
        {
          "rank": 13,
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          ],
          "sector": "Health Care",
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        },
        {
          "rank": 14,
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        },
        {
          "rank": 15,
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          ],
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        },
        {
          "rank": 16,
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          ],
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        {
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        {
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        {
          "rank": 19,
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        {
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      ],
      "sectors": [
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        {
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          "sector": "Consumer Staples",
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        {
          "sector": "Consumer Discretionary",
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          "fundamentalPositivePoolSharePct": 12.34,
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        {
          "sector": "Energy",
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        {
          "sector": "Industrials",
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          "marketMinusFundamentalSharePctPoints": -2.0762
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        {
          "sector": "Communication Services",
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        {
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        {
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        {
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      ]
    },
    {
      "metric": "operatingIncome",
      "label": "Operating income",
      "fundamentalCoverageCompanyCount": 384,
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        {
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        {
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        {
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        {
          "rank": 5,
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        {
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        },
        {
          "rank": 7,
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          ],
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        {
          "rank": 8,
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            "VZ"
          ],
          "sector": "Communication Services",
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        },
        {
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          ],
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        },
        {
          "rank": 10,
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          ],
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      ],
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        {
          "rank": 2,
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          ],
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        {
          "sector": "Utilities",
          "marketWeightPct": 1.9081,
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          "marketMinusFundamentalSharePctPoints": 1.6581
        },
        {
          "sector": "Consumer Discretionary",
          "marketWeightPct": 8.7717,
          "fundamentalPositivePoolSharePct": 7.37,
          "marketMinusFundamentalSharePctPoints": 1.4017
        },
        {
          "sector": "Real Estate",
          "marketWeightPct": 1.7404,
          "fundamentalPositivePoolSharePct": 0.44,
          "marketMinusFundamentalSharePctPoints": 1.3004
        },
        {
          "sector": "Industrials",
          "marketWeightPct": 8.0738,
          "fundamentalPositivePoolSharePct": 8.46,
          "marketMinusFundamentalSharePctPoints": -0.3862
        },
        {
          "sector": "Materials",
          "marketWeightPct": 1.7017,
          "fundamentalPositivePoolSharePct": 1.39,
          "marketMinusFundamentalSharePctPoints": 0.3117
        },
        {
          "sector": "Energy",
          "marketWeightPct": 3.3846,
          "fundamentalPositivePoolSharePct": 3.57,
          "marketMinusFundamentalSharePctPoints": -0.1854
        }
      ]
    },
    {
      "metric": "capex",
      "label": "Capital expenditures",
      "fundamentalCoverageCompanyCount": 331,
      "fundamentalCoveragePercent": 66.2,
      "positiveCompanyCount": 331,
      "fundamentalTop10PositivePoolSharePct": 50.68,
      "sameTop10CompaniesMarketWeightPct": 19.889,
      "top10MarketMinusFundamentalPctPoints": -30.791,
      "fundamentalTop20PositivePoolSharePct": 62.42,
      "sameTop20CompaniesMarketWeightPct": 29.7587,
      "top20MarketMinusFundamentalPctPoints": -32.6613,
      "positivePoolHhi": 431.4,
      "top10Companies": [
        {
          "rank": 1,
          "name": "Microsoft",
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          ],
          "sector": "Information Technology",
          "fundamentalValueUsd": 115948000000,
          "fundamentalPositivePoolSharePct": 12.97,
          "marketWeightPct": 5.56722,
          "marketMinusFundamentalSharePctPoints": -7.4028
        },
        {
          "rank": 2,
          "name": "Alphabet Inc.",
          "symbols": [
            "GOOG",
            "GOOGL"
          ],
          "sector": "Communication Services",
          "fundamentalValueUsd": 91447000000,
          "fundamentalPositivePoolSharePct": 10.23,
          "marketWeightPct": 5.606115,
          "marketMinusFundamentalSharePctPoints": -4.6239
        },
        {
          "rank": 3,
          "name": "Meta Platforms",
          "symbols": [
            "META"
          ],
          "sector": "Communication Services",
          "fundamentalValueUsd": 69691000000,
          "fundamentalPositivePoolSharePct": 7.79,
          "marketWeightPct": 2.443082,
          "marketMinusFundamentalSharePctPoints": -5.3469
        },
        {
          "rank": 4,
          "name": "Oracle Corporation",
          "symbols": [
            "ORCL"
          ],
          "sector": "Information Technology",
          "fundamentalValueUsd": 55663000000,
          "fundamentalPositivePoolSharePct": 6.22,
          "marketWeightPct": 0.383761,
          "marketMinusFundamentalSharePctPoints": -5.8362
        },
        {
          "rank": 5,
          "name": "ExxonMobil",
          "symbols": [
            "XOM"
          ],
          "sector": "Energy",
          "fundamentalValueUsd": 28358000000,
          "fundamentalPositivePoolSharePct": 3.17,
          "marketWeightPct": 0.972901,
          "marketMinusFundamentalSharePctPoints": -2.1971
        },
        {
          "rank": 6,
          "name": "Walmart",
          "symbols": [
            "WMT"
          ],
          "sector": "Consumer Staples",
          "fundamentalValueUsd": 26642000000,
          "fundamentalPositivePoolSharePct": 2.98,
          "marketWeightPct": 0.71566,
          "marketMinusFundamentalSharePctPoints": -2.2643
        },
        {
          "rank": 7,
          "name": "Berkshire Hathaway",
          "symbols": [
            "BRK.B"
          ],
          "sector": "Financials",
          "fundamentalValueUsd": 20927000000,
          "fundamentalPositivePoolSharePct": 2.34,
          "marketWeightPct": 1.397444,
          "marketMinusFundamentalSharePctPoints": -0.9426
        },
        {
          "rank": 8,
          "name": "Micron Technology",
          "symbols": [
            "MU"
          ],
          "sector": "Information Technology",
          "fundamentalValueUsd": 15857000000,
          "fundamentalPositivePoolSharePct": 1.77,
          "marketWeightPct": 1.762297,
          "marketMinusFundamentalSharePctPoints": -0.0077
        },
        {
          "rank": 9,
          "name": "Intel",
          "symbols": [
            "INTC"
          ],
          "sector": "Information Technology",
          "fundamentalValueUsd": 14646000000,
          "fundamentalPositivePoolSharePct": 1.64,
          "marketWeightPct": 0.904448,
          "marketMinusFundamentalSharePctPoints": -0.7356
        },
        {
          "rank": 10,
          "name": "Duke Energy",
          "symbols": [
            "DUK"
          ],
          "sector": "Utilities",
          "fundamentalValueUsd": 14024000000,
          "fundamentalPositivePoolSharePct": 1.57,
          "marketWeightPct": 0.136048,
          "marketMinusFundamentalSharePctPoints": -1.434
        }
      ],
      "top20Companies": [
        {
          "rank": 1,
          "name": "Microsoft",
          "symbols": [
            "MSFT"
          ],
          "sector": "Information Technology",
          "fundamentalValueUsd": 115948000000,
          "fundamentalPositivePoolSharePct": 12.97,
          "marketWeightPct": 5.56722,
          "marketMinusFundamentalSharePctPoints": -7.4028
        },
        {
          "rank": 2,
          "name": "Alphabet Inc.",
          "symbols": [
            "GOOG",
            "GOOGL"
          ],
          "sector": "Communication Services",
          "fundamentalValueUsd": 91447000000,
          "fundamentalPositivePoolSharePct": 10.23,
          "marketWeightPct": 5.606115,
          "marketMinusFundamentalSharePctPoints": -4.6239
        },
        {
          "rank": 3,
          "name": "Meta Platforms",
          "symbols": [
            "META"
          ],
          "sector": "Communication Services",
          "fundamentalValueUsd": 69691000000,
          "fundamentalPositivePoolSharePct": 7.79,
          "marketWeightPct": 2.443082,
          "marketMinusFundamentalSharePctPoints": -5.3469
        },
        {
          "rank": 4,
          "name": "Oracle Corporation",
          "symbols": [
            "ORCL"
          ],
          "sector": "Information Technology",
          "fundamentalValueUsd": 55663000000,
          "fundamentalPositivePoolSharePct": 6.22,
          "marketWeightPct": 0.383761,
          "marketMinusFundamentalSharePctPoints": -5.8362
        },
        {
          "rank": 5,
          "name": "ExxonMobil",
          "symbols": [
            "XOM"
          ],
          "sector": "Energy",
          "fundamentalValueUsd": 28358000000,
          "fundamentalPositivePoolSharePct": 3.17,
          "marketWeightPct": 0.972901,
          "marketMinusFundamentalSharePctPoints": -2.1971
        },
        {
          "rank": 6,
          "name": "Walmart",
          "symbols": [
            "WMT"
          ],
          "sector": "Consumer Staples",
          "fundamentalValueUsd": 26642000000,
          "fundamentalPositivePoolSharePct": 2.98,
          "marketWeightPct": 0.71566,
          "marketMinusFundamentalSharePctPoints": -2.2643
        },
        {
          "rank": 7,
          "name": "Berkshire Hathaway",
          "symbols": [
            "BRK.B"
          ],
          "sector": "Financials",
          "fundamentalValueUsd": 20927000000,
          "fundamentalPositivePoolSharePct": 2.34,
          "marketWeightPct": 1.397444,
          "marketMinusFundamentalSharePctPoints": -0.9426
        },
        {
          "rank": 8,
          "name": "Micron Technology",
          "symbols": [
            "MU"
          ],
          "sector": "Information Technology",
          "fundamentalValueUsd": 15857000000,
          "fundamentalPositivePoolSharePct": 1.77,
          "marketWeightPct": 1.762297,
          "marketMinusFundamentalSharePctPoints": -0.0077
        },
        {
          "rank": 9,
          "name": "Intel",
          "symbols": [
            "INTC"
          ],
          "sector": "Information Technology",
          "fundamentalValueUsd": 14646000000,
          "fundamentalPositivePoolSharePct": 1.64,
          "marketWeightPct": 0.904448,
          "marketMinusFundamentalSharePctPoints": -0.7356
        },
        {
          "rank": 10,
          "name": "Duke Energy",
          "symbols": [
            "DUK"
          ],
          "sector": "Utilities",
          "fundamentalValueUsd": 14024000000,
          "fundamentalPositivePoolSharePct": 1.57,
          "marketWeightPct": 0.136048,
          "marketMinusFundamentalSharePctPoints": -1.434
        },
        {
          "rank": 11,
          "name": "Southern Company",
          "symbols": [
            "SO"
          ],
          "sector": "Utilities",
          "fundamentalValueUsd": 12737000000,
          "fundamentalPositivePoolSharePct": 1.42,
          "marketWeightPct": 0.146941,
          "marketMinusFundamentalSharePctPoints": -1.2731
        },
        {
          "rank": 12,
          "name": "Apple Inc.",
          "symbols": [
            "AAPL"
          ],
          "sector": "Information Technology",
          "fundamentalValueUsd": 12715000000,
          "fundamentalPositivePoolSharePct": 1.42,
          "marketWeightPct": 7.394309,
          "marketMinusFundamentalSharePctPoints": 5.9743
        },
        {
          "rank": 13,
          "name": "PG&E Corporation",
          "symbols": [
            "PCG"
          ],
          "sector": "Utilities",
          "fundamentalValueUsd": 11787000000,
          "fundamentalPositivePoolSharePct": 1.32,
          "marketWeightPct": 0.042596,
          "marketMinusFundamentalSharePctPoints": -1.2774
        },
        {
          "rank": 14,
          "name": "Comcast",
          "symbols": [
            "CMCSA"
          ],
          "sector": "Communication Services",
          "fundamentalValueUsd": 11750000000,
          "fundamentalPositivePoolSharePct": 1.31,
          "marketWeightPct": 0.121298,
          "marketMinusFundamentalSharePctPoints": -1.1887
        },
        {
          "rank": 15,
          "name": "Charter Communications",
          "symbols": [
            "CHTR"
          ],
          "sector": "Communication Services",
          "fundamentalValueUsd": 11659000000,
          "fundamentalPositivePoolSharePct": 1.3,
          "marketWeightPct": 0.020612,
          "marketMinusFundamentalSharePctPoints": -1.2794
        },
        {
          "rank": 16,
          "name": "T-Mobile US",
          "symbols": [
            "TMUS"
          ],
          "sector": "Communication Services",
          "fundamentalValueUsd": 9955000000,
          "fundamentalPositivePoolSharePct": 1.11,
          "marketWeightPct": 0.119239,
          "marketMinusFundamentalSharePctPoints": -0.9908
        },
        {
          "rank": 17,
          "name": "General Motors",
          "symbols": [
            "GM"
          ],
          "sector": "Consumer Discretionary",
          "fundamentalValueUsd": 9303000000,
          "fundamentalPositivePoolSharePct": 1.04,
          "marketWeightPct": 0.110101,
          "marketMinusFundamentalSharePctPoints": -0.9299
        },
        {
          "rank": 18,
          "name": "Exelon",
          "symbols": [
            "EXC"
          ],
          "sector": "Utilities",
          "fundamentalValueUsd": 8529000000,
          "fundamentalPositivePoolSharePct": 0.95,
          "marketWeightPct": 0.064769,
          "marketMinusFundamentalSharePctPoints": -0.8852
        },
        {
          "rank": 19,
          "name": "Tesla, Inc.",
          "symbols": [
            "TSLA"
          ],
          "sector": "Consumer Discretionary",
          "fundamentalValueUsd": 8527000000,
          "fundamentalPositivePoolSharePct": 0.95,
          "marketWeightPct": 1.580896,
          "marketMinusFundamentalSharePctPoints": 0.6309
        },
        {
          "rank": 20,
          "name": "Walt Disney Company (The)",
          "symbols": [
            "DIS"
          ],
          "sector": "Communication Services",
          "fundamentalValueUsd": 8024000000,
          "fundamentalPositivePoolSharePct": 0.9,
          "marketWeightPct": 0.268999,
          "marketMinusFundamentalSharePctPoints": -0.631
        }
      ],
      "sectors": [
        {
          "sector": "Communication Services",
          "marketWeightPct": 10.1006,
          "fundamentalPositivePoolSharePct": 23.26,
          "marketMinusFundamentalSharePctPoints": -13.1594
        },
        {
          "sector": "Information Technology",
          "marketWeightPct": 39.0369,
          "fundamentalPositivePoolSharePct": 27.19,
          "marketMinusFundamentalSharePctPoints": 11.8469
        },
        {
          "sector": "Utilities",
          "marketWeightPct": 1.9081,
          "fundamentalPositivePoolSharePct": 11.54,
          "marketMinusFundamentalSharePctPoints": -9.6319
        },
        {
          "sector": "Financials",
          "marketWeightPct": 11.7649,
          "fundamentalPositivePoolSharePct": 5.14,
          "marketMinusFundamentalSharePctPoints": 6.6249
        },
        {
          "sector": "Health Care",
          "marketWeightPct": 9.1602,
          "fundamentalPositivePoolSharePct": 5.5,
          "marketMinusFundamentalSharePctPoints": 3.6602
        },
        {
          "sector": "Industrials",
          "marketWeightPct": 8.0738,
          "fundamentalPositivePoolSharePct": 4.56,
          "marketMinusFundamentalSharePctPoints": 3.5138
        },
        {
          "sector": "Energy",
          "marketWeightPct": 3.3846,
          "fundamentalPositivePoolSharePct": 6.64,
          "marketMinusFundamentalSharePctPoints": -3.2554
        },
        {
          "sector": "Consumer Discretionary",
          "marketWeightPct": 8.7717,
          "fundamentalPositivePoolSharePct": 6.17,
          "marketMinusFundamentalSharePctPoints": 2.6017
        },
        {
          "sector": "Consumer Staples",
          "marketWeightPct": 4.3572,
          "fundamentalPositivePoolSharePct": 6.19,
          "marketMinusFundamentalSharePctPoints": -1.8328
        },
        {
          "sector": "Materials",
          "marketWeightPct": 1.7017,
          "fundamentalPositivePoolSharePct": 3.3,
          "marketMinusFundamentalSharePctPoints": -1.5983
        },
        {
          "sector": "Real Estate",
          "marketWeightPct": 1.7404,
          "fundamentalPositivePoolSharePct": 0.5,
          "marketMinusFundamentalSharePctPoints": 1.2404
        }
      ]
    }
  ],
  "selectedFindings": {
    "marketTop10IssuerWeightPct": 40.4509,
    "marketTop20IssuerWeightPct": 50.5307,
    "revenueTop10GapPctPoints": -1.3533,
    "netIncomeTop10GapPctPoints": -0.5306,
    "operatingCashFlowTop10GapPctPoints": 5.3436,
    "capexTop10GapPctPoints": -30.791,
    "capexTop20GapPctPoints": -32.6613,
    "capexCoveragePercent": 66.2,
    "freeCashFlowCoveragePercent": 65
  },
  "sources": {
    "ivvHoldingsUrl": "https://www.ishares.com/us/products/239726/ishares-core-s-p-500-etf/latest-holdings.csv",
    "fundamentalAtlasPath": "/research/sp500-fundamental-concentration-atlas"
  },
  "methodology": {
    "marketDenominator": "Market weights use the September 21, 2026 IVV equity market values for the exact frozen 503 S&P 500 security lines, renormalized to 100% and aggregated to 500 issuer CIKs.",
    "sameCohortRule": "For each fundamental, Grizzly Bulls takes the exact reviewed top 10 or top 20 positive contributors from the Fundamental Concentration Atlas and compares their share of that covered positive-value pool with the market weight carried by those same issuers.",
    "coverageBoundary": "Fundamental coverage remains metric-specific. Revenue and operating cash flow are broad, while free cash flow and capital expenditures cover materially smaller issuer sets.",
    "interpretationBoundary": "A positive gap means the same cohort carries more market weight than its share of the covered fundamental pool. A negative gap means it generates more of the covered fundamental than its market weight. Neither direction is a valuation, quality, efficiency, or recommendation judgment.",
    "residualBoundary": "The source fund contained one tiny residual Hologic equity position worth $28,433.88. Hologic was outside the frozen S&P 500 universe, so the position is excluded from the normalized denominator."
  }
}
