{
  "kind": "merton-elm-four-fund-experiment",
  "schemaVersion": 1,
  "publishable": false,
  "marketAsOf": "2026-10-06",
  "inputIdentity": {
    "publicationId": "7cf1fa94-4d3b-4fcd-8544-d09940aae946",
    "methodologyVersion": "merton-3.0.0",
    "publishedModelSha256": "49d37ac06c1f7e7464046fde47956dac876f7cb901fd4e449b085015c701b1b2",
    "elmInputsSha256": "8f35454ff200b549e63b93e9f038e65d0c0823c742a915c062c14c80b22b45a6",
    "analysisSourceSha256": "03987bd16063f3e7a309d6e38608b81565beb580e24d3da497eaba75981de116"
  },
  "settings": {
    "gamma": 3,
    "minimumCashWeight": 0,
    "maxWeights": {
      "ELM": 1,
      "FBTC": 1,
      "GLDM": 1,
      "PDBC": 1
    },
    "simulationDraws": 8192,
    "simulationSeed": 20261006,
    "robustStrength": 1
  },
  "sources": {
    "publishedModel": "https://themacrodashboard.com/data/merton-model.json",
    "elm": "https://www.elmfunds.com/elm-market-navigator-etf"
  },
  "interpretation": "Conditional fixed-mix approximation to ELM, not an empirical model of its dynamic strategy. Current targets are not actual holdings or a forecast of its future average allocation. Baseline is a sensitivity, not a second proposed portfolio.",
  "limitations": [
    "ELM is represented by fixed current target weights, not its actual changing holdings. No momentum alpha is assumed.",
    "ELM risk is a look-through transformation of the published covariance, not measured ELM volatility. Existing floors and shrinkage are inherited; no extra ELM floor or manager risk is added.",
    "Regional, REIT, nominal-bond and TIPS mappings are approximations described in elm-inputs.json.",
    "Forecast uncertainty propagates existing joint draws but does not model uncertainty about future ELM allocations or the proxy mappings.",
    "No historical performance or dynamic ELM backtest is calculated. Portfolio expected CAGR is conditional on central assumptions, including for Robust.",
    "Cash within ELM and residual cash are reported separately. Both inherit zero modeled cash volatility.",
    "BTC, gold and commodity forecasts and covariance are unchanged. ELM is eligible, not required; no minimum core allocation is imposed."
  ],
  "publishedComparison": {
    "central": {
      "weights": {
        "SPY": 0,
        "IEF": 0.15938178642340828,
        "VTIP": 0,
        "GLDM": 0.20160040970048987,
        "PDBC": 0.17784979854979455,
        "FBTC": 0.28098710973666247,
        "VXUS": 0,
        "SCHP": 0,
        "LTPZ": 0.1801808955896445,
        "SPAXX": 4.440892098500626e-16
      },
      "nominalPortfolioDrift": 0.15236146373999943,
      "expectedCagr": 0.14400473279139597,
      "annualVolatility": 0.1888196691848326,
      "objective": 0.0613781646829769,
      "kktResidual": 5.204170427930421e-17,
      "feasibilityResidual": 0,
      "forecastUtilitySD": null,
      "uncertaintyPenalty": null,
      "diagnostics": {
        "solverVersion": "merton-next-working-set-1",
        "robustMethod": null,
        "iterations": 12,
        "budgetMultiplier": 0.007898863476372472,
        "unconstrainedWeights": {
          "SPY": -0.5325724500185035,
          "IEF": 0.41295169178027075,
          "VTIP": 2.1398477291112714,
          "GLDM": 0.10835070969825066,
          "PDBC": 0.27986480808141406,
          "FBTC": 0.29607230293783526,
          "VXUS": 0.4399017681352861,
          "SCHP": -0.1334588285598108,
          "LTPZ": 0.07432441439996808
        },
        "varianceContributions": {
          "SPY": 0,
          "IEF": 0.01040034495667392,
          "VTIP": 0,
          "GLDM": 0.07784114701963533,
          "PDBC": 0.04423212967616786,
          "FBTC": 0.8325657427423032,
          "VXUS": 0,
          "SCHP": 0,
          "LTPZ": 0.034960635605219725
        },
        "certificate": null
      },
      "bindingConstraints": [
        "SPY:lower",
        "VTIP:lower",
        "VXUS:lower",
        "SCHP:lower",
        "cash:minimum"
      ]
    },
    "robust": {
      "weights": {
        "SPY": 0,
        "IEF": 0.20879706798962266,
        "VTIP": 0,
        "GLDM": 0.0929547879182363,
        "PDBC": 0.20261476856427663,
        "FBTC": 0.18534472268732935,
        "VXUS": 0.10034607142209569,
        "SCHP": 0.040834429829684604,
        "LTPZ": 0.16910815158875458,
        "SPAXX": 1.1102230246251565e-16
      },
      "nominalPortfolioDrift": 0.1218856849326029,
      "expectedCagr": 0.1189695634300409,
      "annualVolatility": 0.13767683731956243,
      "objective": 0.0338294171521835,
      "kktResidual": 1.237514231713921e-10,
      "feasibilityResidual": 0,
      "forecastUtilitySD": 0.020389546372504678,
      "uncertaintyPenalty": 0.020389546372504678,
      "diagnostics": {
        "solverVersion": "merton-next-working-set-1",
        "robustMethod": "ellipsoidal-excess-mean-conic-dual",
        "iterations": 1692,
        "budgetMultiplier": 0.0053970498507076,
        "unconstrainedWeights": {
          "SPY": -0.5525891915271514,
          "IEF": 0.450278622675419,
          "VTIP": 2.153827191417171,
          "GLDM": 0.0344361527393869,
          "PDBC": 0.2998195724516591,
          "FBTC": 0.2915855573344251,
          "VXUS": 0.47760891129443,
          "SCHP": -0.10757626251886412,
          "LTPZ": 0.0628067420610143
        },
        "varianceContributions": {
          "SPY": 0,
          "IEF": 0.027522054916161522,
          "VTIP": 0,
          "GLDM": 0.048397550448266574,
          "PDBC": 0.08924214596962197,
          "FBTC": 0.7084242678611239,
          "VXUS": 0.05732578659136213,
          "SCHP": 0.005573553196833065,
          "LTPZ": 0.06351464101663083
        },
        "certificate": {
          "kind": "smooth",
          "dual": [
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            -0.049278829647002476,
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            0.23622873154510193,
            -0.21434735740852012,
            0,
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          ],
          "dualNorm": 1,
          "normResidual": 0.020389546372504678,
          "dualityGap": 0
        }
      },
      "bindingConstraints": [
        "SPY:lower",
        "VTIP:lower",
        "cash:minimum"
      ],
      "meanUtility": 0.05421896352468818,
      "worstCaseDrift": 0.09976578230407748
    }
  },
  "experiments": [
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        "VXUS": 0.2668,
        "SCHP": 0.0931,
        "IEF": 0.0466,
        "SPAXX": 0.3259
      },
      "assumptions": {
        "riskyAssetOrder": [
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          "FBTC",
          "GLDM",
          "PDBC"
        ],
        "nominalDrifts": {
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          "PDBC": 0.07200399785041808,
          "SPAXX": 0.037503997850418094
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        "expectedCagrs": {
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          "FBTC": 0.19999999999999998,
          "GLDM": 0.07,
          "PDBC": 0.057390412630660734,
          "SPAXX": 0.038216147706388454
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        "annualVolatilities": {
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          "FBTC": 0.6,
          "GLDM": 0.19515451465345984,
          "PDBC": 0.18
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        "covariance": [
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        "forecastExcessMeanOffsets": [
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        "forecastExcessMeanCovariance": [
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            0.000026063991881192107,
            0.00002381853189997905
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        "elmCentralEntryCagr": 0.05197928681769172
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        "expectedCagr": 0.14243259089206217,
        "annualVolatility": 0.19560761006440183,
        "nominalPortfolioDrift": 0.15229100919573935,
        "objective": 0.057393505672660605,
        "kktResidual": 5.551115123125783e-17,
        "forecastUtilitySD": null,
        "lookThrough": {
          "usEquities": 0,
          "internationalEquities": 0,
          "nominalBonds": 0,
          "tips": 0,
          "bitcoin": 0.28579861555878144,
          "gold": 0.2890985836534551,
          "commodities": 0.22410826051700897,
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          "totalCash": 0.20099454027075458
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      "robust": {
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        "lookThrough": {
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      "verification": {
        "centralMaxWeightDifference": 5.551115123125783e-17,
        "robustMaxWeightDifference": 1.2813503869057996e-9,
        "alternativeCovariancePreservedExactly": true,
        "alternativeAndCashDrawsPreservedExactly": true
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    },
    {
      "label": "baseline-sensitivity",
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        "VXUS": 0.295,
        "SCHP": 0.1,
        "IEF": 0.05,
        "SPAXX": 0.1
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      "assumptions": {
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          "GLDM",
          "PDBC"
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          "nominalBonds": 0,
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        "robustMaxWeightDifference": 4.1180713006294667e-10,
        "alternativeCovariancePreservedExactly": true,
        "alternativeAndCashDrawsPreservedExactly": true
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    }
  ]
}