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          "XLK_alpha": 4.62,
          "XLF": 58.28,
          "XLF_alpha": 18.96,
          "XLV": 19.66,
          "XLV_alpha": -19.66,
          "XLY": 45.21,
          "XLY_alpha": 5.89,
          "XLC": 45.57,
          "XLC_alpha": 6.25,
          "XLI": 52.98,
          "XLI_alpha": 13.66,
          "XLP": 20.74,
          "XLP_alpha": -18.58,
          "XLE": 34.35,
          "XLE_alpha": -4.97,
          "XLB": 52.69,
          "XLB_alpha": 13.37,
          "XLU": 15.5,
          "XLU_alpha": -23.82,
          "XLRE": 28.02,
          "XLRE_alpha": -11.3
        }
      }
    ],
    "etfs": [
      "XLK",
      "XLF",
      "XLV",
      "XLY",
      "XLC",
      "XLI",
      "XLP",
      "XLE",
      "XLB",
      "XLU",
      "XLRE",
      "SPY"
    ],
    "method": "Per-sector cumulative total return during NBER recession peaks/troughs and the 12-month period immediately after each recession ('early recovery'). alpha = sector return − SPY return for that window. ETFs without coverage (e.g. XLC inception 2018, XLRE 2015) show n/a."
  },
  "data_sources": {
    "sector_weights": "S&P / State Street SPDR fact sheets, 2026-Q1",
    "industry_breakdown": "State Street SPDR ETF fact sheets, 2026-Q1",
    "trailing_pe": "yfinance live (sector SPDR ETF .info.trailingPE)",
    "forward_pe_sector": "Yardeni / FactSet 2026-Q1 public releases",
    "forward_pe_industry": "yfinance live, market-cap-weighted aggregation across the industry's top constituents (≥80% AUM coverage). Industries not yet in INDUSTRY_TICKERS fall back to inheriting the parent sector's fwd P/E.",
    "ust10y_yield": "yfinance ^TNX (CBOE 10Y Treasury Yield Index), live close",
    "earnings_yield": "EY = 1 / forward P/E (盈利收益率, 类似债券 yield)",
    "erp": "ERP = EY - 10Y Treasury yield (Equity Risk Premium 简化版, 越高股票相对债券越有吸引力)",
    "implied_peg": "PEG = forward P/E / implied growth %, 其中 implied_growth% = (trail/fwd - 1) * 100",
    "composite_score": "Composite Value Score (简化 2-factor): score = 0.6 × z(1/PEG) + 0.4 × z(ERP), z-score 在 11 个板块内部标准化. 越高 = 综合性价比越好. 完整 3-factor 版还需历史 PE z-score (需付费源 / 手工 Yardeni 数据).",
    "historical_prices": "yfinance full-history monthly closes (auto-adjusted), 用于价格走势图. 覆盖范围: 9 核心 sector ETF (XLK/XLF/XLV/XLY/XLP/XLI/XLB/XLE/XLU) 1998-12 起, XLRE 2015-10 起, XLC 2018-06 起 (GICS 改版). 注: 这不是历史 PE 时间序列, 仅是价格走势; 因 yfinance 对 ETF 无历史 EPS, 真历史 PE 需要付费源 (FactSet/Bloomberg) 或 SimFin/AV 重建.",
    "sector_weight_history": "Per-sector approx SPX weight, monthly, 1998-12+. 重建公式: w_i(t) = w_i(today) × (ETF_i(t)/ETF_i(today)) ÷ (SPY(t)/SPY(today)), 再 normalize 使各时点 11 板块加和 = 100%. 假设 sector 内 share-count 比例稳定. 近似精度: 5y ±0.5pp, 27y 长期 ±2pp 量级 (有 GICS 改版导致结构性偏差, 主要是 2018 XLC 重组). 真实历史 SPX 板块权重需要 S&P/FactSet 付费源.",
    "sector_rotation": "板块在 NBER 衰退/复苏 regime 下的累计回报 + 相对 SPY 的 alpha. Recession 期 = NBER 顶到 NBER 底; Early Recovery = NBER 底 + 12 个月. 覆盖 2001 dot-com / 2008 GFC / 2020 COVID 三次衰退. XLC (inception 2018), XLRE (inception 2015) 仅覆盖 2020 COVID. ETF 来自 yfinance auto-adjusted 月线."
  },
  "sectors": [
    {
      "sector": "Information Technology",
      "etf": "XLK",
      "weight_pct": 30.5,
      "trailing_pe": 37.821636,
      "forward_pe": 27.5,
      "earnings_yield_pct": 3.64,
      "erp_pct": -0.78,
      "implied_peg": 0.733,
      "industry_total_check": 100.0,
      "industries": [
        {
          "name": "Software",
          "weight_in_sector_pct": 32.0,
          "weight_in_spx_pct": 9.76,
          "etf_hints": [
            "IGV"
          ],
          "forward_pe": 22.12,
          "forward_pe_meta": {
            "value": 22.12,
            "method": "portfolio P/E (= Σ mcap / Σ forward earnings, harmonic mcap-weighted)",
            "constituents_used": 19,
            "constituents_skipped": [],
            "total_mcap_billion_usd": 5437.0,
            "total_forward_earnings_billion_usd": 245.8
          },
          "earnings_yield_pct": 4.52,
          "erp_pct": 0.1
        },
        {
          "name": "Semiconductors",
          "weight_in_sector_pct": 25.0,
          "weight_in_spx_pct": 7.625,
          "etf_hints": [
            "SOXX",
            "SMH"
          ],
          "forward_pe": 19.12,
          "forward_pe_meta": {
            "value": 19.12,
            "method": "portfolio P/E (= Σ mcap / Σ forward earnings, harmonic mcap-weighted)",
            "constituents_used": 19,
            "constituents_skipped": [],
            "total_mcap_billion_usd": 11243.1,
            "total_forward_earnings_billion_usd": 588.0
          },
          "earnings_yield_pct": 5.23,
          "erp_pct": 0.81
        },
        {
          "name": "Technology Hardware, Storage & Peripherals",
          "weight_in_sector_pct": 18.0,
          "weight_in_spx_pct": 5.49,
          "etf_hints": []
        },
        {
          "name": "Semiconductor Materials & Equipment",
          "weight_in_sector_pct": 7.0,
          "weight_in_spx_pct": 2.135,
          "etf_hints": [
            "SOXX (partial)"
          ]
        },
        {
          "name": "IT Services",
          "weight_in_sector_pct": 8.0,
          "weight_in_spx_pct": 2.44,
          "etf_hints": []
        },
        {
          "name": "Communications Equipment",
          "weight_in_sector_pct": 5.0,
          "weight_in_spx_pct": 1.525,
          "etf_hints": []
        },
        {
          "name": "Electronic Equipment, Instruments & Components",
          "weight_in_sector_pct": 5.0,
          "weight_in_spx_pct": 1.525,
          "etf_hints": []
        }
      ],
      "composite_score": -1.019,
      "composite_score_breakdown": {
        "z_inv_peg": -0.626,
        "z_erp": -1.609,
        "alpha": 0.6,
        "beta": 0.4
      }
    },
    {
      "sector": "Financials",
      "etf": "XLF",
      "weight_pct": 14.2,
      "trailing_pe": 17.51094,
      "forward_pe": 15.5,
      "earnings_yield_pct": 6.45,
      "erp_pct": 2.03,
      "implied_peg": 1.195,
      "industry_total_check": 100.0,
      "industries": [
        {
          "name": "Financial Services (incl. BRK.B, V, MA, AXP)",
          "weight_in_sector_pct": 46.0,
          "weight_in_spx_pct": 6.532,
          "etf_hints": [],
          "forward_pe": 18.63,
          "forward_pe_meta": {
            "value": 18.63,
            "method": "portfolio P/E (= Σ mcap / Σ forward earnings, harmonic mcap-weighted)",
            "constituents_used": 8,
            "constituents_skipped": [
              "FI",
              "DFS"
            ],
            "total_mcap_billion_usd": 2552.5,
            "total_forward_earnings_billion_usd": 137.0
          },
          "earnings_yield_pct": 5.37,
          "erp_pct": 0.95
        },
        {
          "name": "Banks (Diversified & Regional)",
          "weight_in_sector_pct": 26.0,
          "weight_in_spx_pct": 3.692,
          "etf_hints": [
            "KBE",
            "KRE"
          ],
          "forward_pe": 11.23,
          "forward_pe_meta": {
            "value": 11.23,
            "method": "portfolio P/E (= Σ mcap / Σ forward earnings, harmonic mcap-weighted)",
            "constituents_used": 13,
            "constituents_skipped": [
              "CMA"
            ],
            "total_mcap_billion_usd": 2102.4,
            "total_forward_earnings_billion_usd": 187.3
          },
          "earnings_yield_pct": 8.9,
          "erp_pct": 4.48
        },
        {
          "name": "Insurance",
          "weight_in_sector_pct": 17.0,
          "weight_in_spx_pct": 2.414,
          "etf_hints": [],
          "forward_pe": 10.67,
          "forward_pe_meta": {
            "value": 10.67,
            "method": "portfolio P/E (= Σ mcap / Σ forward earnings, harmonic mcap-weighted)",
            "constituents_used": 13,
            "constituents_skipped": [
              "MMC"
            ],
            "total_mcap_billion_usd": 746.9,
            "total_forward_earnings_billion_usd": 70.0
          },
          "earnings_yield_pct": 9.37,
          "erp_pct": 4.95
        },
        {
          "name": "Capital Markets",
          "weight_in_sector_pct": 8.0,
          "weight_in_spx_pct": 1.136,
          "etf_hints": []
        },
        {
          "name": "Consumer Finance",
          "weight_in_sector_pct": 3.0,
          "weight_in_spx_pct": 0.426,
          "etf_hints": []
        }
      ],
      "composite_score": -0.16,
      "composite_score_breakdown": {
        "z_inv_peg": -0.961,
        "z_erp": 1.042,
        "alpha": 0.6,
        "beta": 0.4
      }
    },
    {
      "sector": "Health Care",
      "etf": "XLV",
      "weight_pct": 10.5,
      "trailing_pe": 25.16284,
      "forward_pe": 17.5,
      "earnings_yield_pct": 5.71,
      "erp_pct": 1.29,
      "implied_peg": 0.4,
      "industry_total_check": 100.0,
      "industries": [
        {
          "name": "Pharmaceuticals",
          "weight_in_sector_pct": 32.0,
          "weight_in_spx_pct": 3.36,
          "etf_hints": [
            "IHE"
          ],
          "forward_pe": 14.63,
          "forward_pe_meta": {
            "value": 14.63,
            "method": "portfolio P/E (= Σ mcap / Σ forward earnings, harmonic mcap-weighted)",
            "constituents_used": 8,
            "constituents_skipped": [],
            "total_mcap_billion_usd": 2274.8,
            "total_forward_earnings_billion_usd": 155.5
          },
          "earnings_yield_pct": 6.84,
          "erp_pct": 2.42
        },
        {
          "name": "Health Care Equipment & Supplies",
          "weight_in_sector_pct": 26.0,
          "weight_in_spx_pct": 2.73,
          "etf_hints": [],
          "forward_pe": 17.47,
          "forward_pe_meta": {
            "value": 17.47,
            "method": "portfolio P/E (= Σ mcap / Σ forward earnings, harmonic mcap-weighted)",
            "constituents_used": 18,
            "constituents_skipped": [],
            "total_mcap_billion_usd": 938.4,
            "total_forward_earnings_billion_usd": 53.7
          },
          "earnings_yield_pct": 5.72,
          "erp_pct": 1.3
        },
        {
          "name": "Biotechnology",
          "weight_in_sector_pct": 14.0,
          "weight_in_spx_pct": 1.47,
          "etf_hints": [
            "IBB",
            "XBI"
          ],
          "forward_pe": 14.46,
          "forward_pe_meta": {
            "value": 14.46,
            "method": "portfolio P/E (= Σ mcap / Σ forward earnings, harmonic mcap-weighted)",
            "constituents_used": 8,
            "constituents_skipped": [
              "MRNA"
            ],
            "total_mcap_billion_usd": 620.9,
            "total_forward_earnings_billion_usd": 42.9
          },
          "earnings_yield_pct": 6.92,
          "erp_pct": 2.5
        },
        {
          "name": "Life Sciences Tools & Services",
          "weight_in_sector_pct": 12.0,
          "weight_in_spx_pct": 1.26,
          "etf_hints": []
        },
        {
          "name": "Health Care Providers & Services",
          "weight_in_sector_pct": 11.0,
          "weight_in_spx_pct": 1.155,
          "etf_hints": []
        },
        {
          "name": "Health Care Technology",
          "weight_in_sector_pct": 5.0,
          "weight_in_spx_pct": 0.525,
          "etf_hints": []
        }
      ],
      "composite_score": 0.196,
      "composite_score_breakdown": {
        "z_inv_peg": 0.097,
        "z_erp": 0.344,
        "alpha": 0.6,
        "beta": 0.4
      }
    },
    {
      "sector": "Consumer Discretionary",
      "etf": "XLY",
      "weight_pct": 10.4,
      "trailing_pe": 31.508455,
      "forward_pe": 24.0,
      "earnings_yield_pct": 4.17,
      "erp_pct": -0.25,
      "implied_peg": 0.767,
      "industry_total_check": 100.0,
      "industries": [
        {
          "name": "Broadline Retail (AMZN-driven)",
          "weight_in_sector_pct": 26.0,
          "weight_in_spx_pct": 2.704,
          "etf_hints": []
        },
        {
          "name": "Automobiles (TSLA-driven)",
          "weight_in_sector_pct": 17.0,
          "weight_in_spx_pct": 1.768,
          "etf_hints": []
        },
        {
          "name": "Hotels, Restaurants & Leisure",
          "weight_in_sector_pct": 21.0,
          "weight_in_spx_pct": 2.184,
          "etf_hints": []
        },
        {
          "name": "Specialty Retail",
          "weight_in_sector_pct": 13.0,
          "weight_in_spx_pct": 1.352,
          "etf_hints": []
        },
        {
          "name": "Textiles, Apparel & Luxury Goods",
          "weight_in_sector_pct": 7.0,
          "weight_in_spx_pct": 0.728,
          "etf_hints": []
        },
        {
          "name": "Household Durables",
          "weight_in_sector_pct": 7.0,
          "weight_in_spx_pct": 0.728,
          "etf_hints": []
        },
        {
          "name": "Leisure Products",
          "weight_in_sector_pct": 4.0,
          "weight_in_spx_pct": 0.416,
          "etf_hints": []
        },
        {
          "name": "Distributors",
          "weight_in_sector_pct": 5.0,
          "weight_in_spx_pct": 0.52,
          "etf_hints": []
        }
      ],
      "composite_score": -0.842,
      "composite_score_breakdown": {
        "z_inv_peg": -0.664,
        "z_erp": -1.109,
        "alpha": 0.6,
        "beta": 0.4
      }
    },
    {
      "sector": "Communication Services",
      "etf": "XLC",
      "weight_pct": 9.6,
      "trailing_pe": 18.665174,
      "forward_pe": 19.5,
      "earnings_yield_pct": 5.13,
      "erp_pct": 0.71,
      "implied_peg": null,
      "industry_total_check": 100.0,
      "industries": [
        {
          "name": "Interactive Media & Services (GOOGL, META)",
          "weight_in_sector_pct": 49.0,
          "weight_in_spx_pct": 4.704,
          "etf_hints": [],
          "forward_pe": 24.11,
          "forward_pe_meta": {
            "value": 24.11,
            "method": "portfolio P/E (= Σ mcap / Σ forward earnings, harmonic mcap-weighted)",
            "constituents_used": 5,
            "constituents_skipped": [],
            "total_mcap_billion_usd": 10154.7,
            "total_forward_earnings_billion_usd": 421.2
          },
          "earnings_yield_pct": 4.15,
          "erp_pct": -0.27
        },
        {
          "name": "Entertainment (NFLX, DIS, WBD)",
          "weight_in_sector_pct": 19.0,
          "weight_in_spx_pct": 1.824,
          "etf_hints": []
        },
        {
          "name": "Wireless Telecom (TMUS, VZ, T)",
          "weight_in_sector_pct": 24.0,
          "weight_in_spx_pct": 2.304,
          "etf_hints": []
        },
        {
          "name": "Diversified Telecommunication Services",
          "weight_in_sector_pct": 5.0,
          "weight_in_spx_pct": 0.48,
          "etf_hints": []
        },
        {
          "name": "Media (advertising/cable)",
          "weight_in_sector_pct": 3.0,
          "weight_in_spx_pct": 0.288,
          "etf_hints": []
        }
      ],
      "composite_score": null,
      "composite_score_breakdown": {
        "z_inv_peg": null,
        "z_erp": -0.203,
        "alpha": 0.6,
        "beta": 0.4,
        "note": "PEG undefined (implied growth ≤ 0); composite score unavailable"
      }
    },
    {
      "sector": "Industrials",
      "etf": "XLI",
      "weight_pct": 8.6,
      "trailing_pe": 30.62879,
      "forward_pe": 22.0,
      "earnings_yield_pct": 4.55,
      "erp_pct": 0.13,
      "implied_peg": 0.561,
      "industry_total_check": 100.0,
      "industries": [
        {
          "name": "Aerospace & Defense",
          "weight_in_sector_pct": 18.0,
          "weight_in_spx_pct": 1.548,
          "etf_hints": [
            "ITA",
            "XAR"
          ],
          "forward_pe": 25.31,
          "forward_pe_meta": {
            "value": 25.31,
            "method": "portfolio P/E (= Σ mcap / Σ forward earnings, harmonic mcap-weighted)",
            "constituents_used": 12,
            "constituents_skipped": [],
            "total_mcap_billion_usd": 1219.4,
            "total_forward_earnings_billion_usd": 48.2
          },
          "earnings_yield_pct": 3.95,
          "erp_pct": -0.47
        },
        {
          "name": "Machinery",
          "weight_in_sector_pct": 14.0,
          "weight_in_spx_pct": 1.204,
          "etf_hints": []
        },
        {
          "name": "Ground Transportation (Rail / Trucking)",
          "weight_in_sector_pct": 9.0,
          "weight_in_spx_pct": 0.774,
          "etf_hints": []
        },
        {
          "name": "Air Freight & Logistics",
          "weight_in_sector_pct": 7.0,
          "weight_in_spx_pct": 0.602,
          "etf_hints": []
        },
        {
          "name": "Building Products",
          "weight_in_sector_pct": 7.0,
          "weight_in_spx_pct": 0.602,
          "etf_hints": []
        },
        {
          "name": "Electrical Equipment",
          "weight_in_sector_pct": 8.0,
          "weight_in_spx_pct": 0.688,
          "etf_hints": []
        },
        {
          "name": "Industrial Conglomerates (GE, HON)",
          "weight_in_sector_pct": 9.0,
          "weight_in_spx_pct": 0.774,
          "etf_hints": []
        },
        {
          "name": "Professional Services",
          "weight_in_sector_pct": 9.0,
          "weight_in_spx_pct": 0.774,
          "etf_hints": []
        },
        {
          "name": "Commercial Services & Supplies",
          "weight_in_sector_pct": 6.0,
          "weight_in_spx_pct": 0.516,
          "etf_hints": []
        },
        {
          "name": "Trading Companies & Distributors",
          "weight_in_sector_pct": 5.0,
          "weight_in_spx_pct": 0.43,
          "etf_hints": []
        },
        {
          "name": "Construction & Engineering",
          "weight_in_sector_pct": 4.0,
          "weight_in_spx_pct": 0.344,
          "etf_hints": []
        },
        {
          "name": "Passenger Airlines",
          "weight_in_sector_pct": 4.0,
          "weight_in_spx_pct": 0.344,
          "etf_hints": []
        }
      ],
      "composite_score": -0.516,
      "composite_score_breakdown": {
        "z_inv_peg": -0.36,
        "z_erp": -0.75,
        "alpha": 0.6,
        "beta": 0.4
      }
    },
    {
      "sector": "Consumer Staples",
      "etf": "XLP",
      "weight_pct": 5.6,
      "trailing_pe": 26.10763,
      "forward_pe": 21.0,
      "earnings_yield_pct": 4.76,
      "erp_pct": 0.34,
      "implied_peg": 0.863,
      "industry_total_check": 100.0,
      "industries": [
        {
          "name": "Beverages (KO, PEP)",
          "weight_in_sector_pct": 22.0,
          "weight_in_spx_pct": 1.232,
          "etf_hints": []
        },
        {
          "name": "Household Products (PG)",
          "weight_in_sector_pct": 18.0,
          "weight_in_spx_pct": 1.008,
          "etf_hints": []
        },
        {
          "name": "Tobacco (PM, MO)",
          "weight_in_sector_pct": 12.0,
          "weight_in_spx_pct": 0.672,
          "etf_hints": []
        },
        {
          "name": "Food Products",
          "weight_in_sector_pct": 12.0,
          "weight_in_spx_pct": 0.672,
          "etf_hints": []
        },
        {
          "name": "Consumer Staples Merchandise Retail (COST, WMT)",
          "weight_in_sector_pct": 24.0,
          "weight_in_spx_pct": 1.344,
          "etf_hints": []
        },
        {
          "name": "Food & Staples Retailing",
          "weight_in_sector_pct": 8.0,
          "weight_in_spx_pct": 0.448,
          "etf_hints": []
        },
        {
          "name": "Personal Care Products",
          "weight_in_sector_pct": 4.0,
          "weight_in_spx_pct": 0.224,
          "etf_hints": []
        }
      ],
      "composite_score": -0.675,
      "composite_score_breakdown": {
        "z_inv_peg": -0.757,
        "z_erp": -0.552,
        "alpha": 0.6,
        "beta": 0.4
      }
    },
    {
      "sector": "Energy",
      "etf": "XLE",
      "weight_pct": 3.4,
      "trailing_pe": 22.753471,
      "forward_pe": 13.5,
      "earnings_yield_pct": 7.41,
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