{
  "version": "literature_forward_returns_2026_v3_wealth_linked_gold",
  "as_of": "2026-11-01",
  "currency": "USD",
  "horizon": "Published gold forecast center retained for ten years; years 10-15 transition to the shared nominal wealth-growth curve, followed exactly thereafter. Other fixed long-run returns remain author scenarios.",
  "annual_nominal_log_growth": {
    "equity": 0.06470932669856183,
    "gold": 0.052116940621773966,
    "bond": 0.04592847577079079,
    "cash": 0.036331929247390274
  },
  "interpretation": "Long-horizon annualized compound-return/median forecasts are translated into expected log growth. Arithmetic expectations are calculated from the joint stochastic model, not identified with CAGR. Equal log-weight literature centers are descriptive, not independent Bayesian evidence or confidence intervals.",
  "expected_cash_rate_initial": 0.03714245888762903,
  "estimation": {
    "equity": "Equal log-weight center of JPM 2027 global equity 7.5% and Vanguard 2026Q3 global approximation: US weight 62% at 5.8%, ex-US 38% at 6.0%; source US weight is UBS Yearbook start-2026. No diversification bonus for the regional approximation.",
    "gold": "First ten years: WGC GLTER 5.2% and JPM 2027 5.5% in equal log weights. At years 10-15 transition to the SAME world-household-net-wealth nominal log-growth curve as BTC and all size comparisons. Arithmetic expected price growth is higher by half diffusion variance. Compare constant institutional growth, historical real 1.3% plus long-run CPI, and inflation-only scenarios.",
    "bond": "Equal log-weight center of JPM 2027 US intermediate Treasury 4.6% and Vanguard 2026Q3 US intermediate Treasury median 4.8%; IEF (7-10y) is a somewhat longer-duration historical risk proxy than these broad intermediate categories.",
    "cash": "Vanguard 2026Q3 cash median 3.7%, quoted 50th-percentile band 3.2-4.2%. Initial rate uses the French September 2026 one-month bill return of 0.31%; mean reversion speed and uncertainty are estimated from SHV monthly total returns.",
    "low_rate_adjustment": "Historical excess returns subtract each month's actual one-month bill return. Forward estimates are forecasts at current valuations and interest rates. Never add historical total returns to the current cash yield, and never add the historical premium on top of a forecast already including it.",
    "tail_events": "Price-volatility calibration includes observed selloffs with their original observation weights. Other assets receive no additional catastrophe jump. Independent BTC permanent failure remains separate because it is not an ordinary historical drawdown."
  },
  "sources": [
    {
      "id": "jpm2027",
      "title": "2027 Long-Term Capital Market Assumptions press release",
      "published": "2026-10-19",
      "url": "https://am.jpmorgan.com/us/en/asset-management/institutional/about-us/media/press-releases/jp-morgan-releases-2027-long-term-capital-market-assumptions/",
      "values": {
        "equity": 0.075,
        "gold": 0.055,
        "bond": 0.046
      },
      "method": "Equity earnings/dividends/valuations/FX; fixed-income cash rates and term premium; gold demand/inflation/currency scenario."
    },
    {
      "id": "vanguard2026q3",
      "title": "VCMM forecasts as of 2026-09-30",
      "published": "2026-10-21",
      "url": "https://corporate.vanguard.com/content/corporatesite/us/en/corp/vemo/vemo-return-forecasts.html",
      "embedded_data_url": "https://corporate.vanguard.com/etc.clientlibs/corporatesite/clientlibs/clientlib-site/resources/dwcharts/i0PwL-4.htm",
      "values": {
        "us_equity_median": 0.058,
        "ex_us_equity_median": 0.06,
        "bond_median": 0.048,
        "cash_median": 0.037
      },
      "method": "Statistical dynamic risk-factor model since 1960, current valuations and sovereign yields, 10,000 paths; published bands are around the median geometric return, not arithmetic mean-return intervals."
    },
    {
      "id": "wgc2024glter",
      "title": "Gold long-term expected return",
      "published": "2024-10-17",
      "url": "https://www.gold.org/goldhub/research/golds-long-term-expected-returns/building-block-approach",
      "nominal_return": 0.052,
      "method": "Long-run gold levels linked to nominal world GDP and equity/bond capitalization. Published forecast is not a 2026 fair-value update."
    },
    {
      "id": "ubs2026",
      "title": "Global Investment Returns Yearbook 2026",
      "published": "2026-03-03",
      "url": "https://www.ubs.com/global/en/media/display-page-ndp/en-20260303-global-investment-returns-yearbook-2026.html",
      "context": "US share of world equity 62%. Real gold compound return 1900-2025 1.3%; post-Bretton-Woods 1972-2025 4.7% in USD. Illustrates horizon sensitivity, not a 126-year stationary price process."
    },
    {
      "id": "bis2023correlation",
      "url": "https://www.bis.org/publications/correlation-equity-and-bond-returns",
      "context": "Growth/demand shocks can make stock and bond returns negatively correlated; inflation/supply shocks can make them positively correlated."
    },
    {
      "id": "fed2026correlation",
      "url": "https://www.federalreserve.gov/econres/notes/feds-notes/government-bonds-safe-haven-property-and-inflationary-pressures-20261016.html",
      "context": "Return-vs-yield correlations have the OPPOSITE sign from stock-vs-bond-return correlations. The note finds loss of bond hedging after 2021, with possible restoration if inflation/supply pressures subside."
    },
    {
      "id": "imf2026correlation",
      "url": "https://www.imf.org/en/blogs/articles/2026/02/18/stock-bond-diversification-offers-less-protection-from-market-selloffs",
      "context": "Stock-bond diversification has weakened since 2020."
    },
    {
      "id": "harvey2026gold",
      "title": "Gold 2026, Duke University course presentation",
      "published": "2026-01-10",
      "url": "https://people.duke.edu/~charvey/Teaching/656_2026/Public_Presentations_656/656_Gold_2026.pdf",
      "context": "High real starting valuations have historically been associated with weaker subsequent real returns. Structural demand shifts can change the relationship. Useful diversification is distinct from high expected growth."
    },
    {
      "id": "amundi2026cma",
      "title": "Capital Market Assumptions 2026",
      "published": "2026-04",
      "url": "https://research-center.amundi.com/files/nuxeo/dl/5c4c71be-baf1-4e0d-827a-ae400506af64?inline=",
      "gold_return": 0.06,
      "context": "Forward 10-year nominal local-currency gold forecast. Confirms that 5-6% exists in contemporary institution scenarios, not a consensus or a 2060 forecast."
    },
    {
      "id": "aqr2026cma",
      "title": "2026 Capital Market Assumptions for Major Asset Classes",
      "published": "2026-01-14",
      "url": "https://www.aqr.com/-/media/AQR/Documents/Alternative-Thinking/AQR-Alternative-Thinking---2026-Capital-Market-Assumptions.pdf?sc_lang=en",
      "context": "The 4.3% real forecast is for a diversified commodity-futures basket, not gold. AQR explicitly provides no medium-term expected returns for individual commodities. Excluded from numeric gold averaging."
    }
  ],
  "future_correlation": "Adopt the complete 120-month innovation correlation matrix as a central mixed-regime forward scenario. Contemporary IMF/Fed/BIS/JPM evidence supports allowing positive stock-bond correlation. Recompute with five-year (persistent supply/inflation) and full-common-history (greater restoration of hedging) matrices. No sign is hard-coded and no pair is replaced in isolation.",
  "sensitivities": [
    {
      "case": "returns_low",
      "annual_nominal_log_growth": {
        "equity": 0.05709799181749753,
        "gold": 0.050693114315518116,
        "bond": 0.044973365642731154,
        "cash": 0.03149866705937099
      }
    },
    {
      "case": "returns_high",
      "annual_nominal_log_growth": {
        "equity": 0.07232066157962612,
        "gold": 0.053540766928029816,
        "bond": 0.04688358589885042,
        "cash": 0.04114194333117518
      }
    },
    {
      "case": "correlation_recent",
      "correlation_window": "five_year"
    },
    {
      "case": "correlation_long",
      "correlation_window": "long"
    }
  ],
  "gold_long_horizon": {
    "forecast_years": 10.0,
    "transition_end_years": 15.0,
    "long_run_rule": "gold_unit_price_compound_growth_equals_world_household_net_wealth_growth",
    "wealth_source": "macro_path.py / portfolio_inputs.json macro_annual",
    "interpretation": "The NOMINAL expected LOG growth of one unit of gold equals dlog(W)/dt after year 15. It is a compound/median-growth convention, not equality of arithmetic mean growth or of total gold capitalization. Historical diffusion remains; E[G]/median(G)=exp(sigma_G^2*t/2). Mining changes total gold quantity, never the return of an existing unit.",
    "transition": "Keep WGC/JPM near-term compound forecasts for ten years, then linearly blend expected log growth with the shared wealth-growth curve over years 10-15. This user-selected long-run assumption is not an institution forecast or a fitted minimum gold weight."
  }
}