Merton Portfolio

Unchecking an asset jointly reoptimizes both top portfolios and their metrics. Cash remains residual. All assets are eligible by default; eligibility does not promise a positive allocation.

Observation dates belong to the source. Retrieval and publication dates do not make older evidence new. Cached and curated values expire under the same source policy.

Central Merton maximizes wᵀ(μ − r) − γ wᵀΣw / 2 at the central forecasts. Robust Merton maximizes average utility across scenarios minus one standard deviation of that utility. With fixed return covariance, the penalty is √(wᵀCw), where C is covariance of forecast errors in excess means, not annual return covariance Σ. This joint ellipsoid avoids charging every asset its full individual downside simultaneously. It does not average scenario-optimal weights. The one-standard-deviation penalty is a modeling choice, not a confidence level; γ separately describes investor risk preference.

The penalty measures dispersion on both sides of the mean; it is not a CVaR guarantee. The prior box method and unpenalized expected utility are compared in the research report. Correlated forecast mistakes, return jumps, changing volatility, taxes and the choice of uncertainty ranges remain material risks. A higher assumed asset volatility also increases the drift needed to maintain a fixed CAGR; the conversion is not evidence that risk earns a higher return.

The model maximizes expected excess drift minus γ / 2 times portfolio variance, subject to long-only weights, asset caps and a minimum cash allocation.

• Initial research scenario: 5% compounded nominal per-share earnings growth represents roughly 2% long-run inflation plus 3% real per-share growth; these are underwriting judgments, not measured forecasts. Terminal weighted-harmonic FY1 P/E 18 (5.56% forward earnings yield) allows normalization from the issuer observation without fitting a desired return or allocation. Ten-year normalization is strategic, not the optimizer holding period. Futures premium 2% is a selected continuous geometric excess-growth scenario, equivalent to 3.62% gross arithmetic excess drift at 18% volatility. Long-run diversified futures evidence supports a positive but unstable premium; 2% is judgmental, not estimated for PDBC.
• Educational conditional model, not individualized investment advice or executable orders. Taxes, spreads, trading costs, liabilities and consumption needs are excluded.
• Elm values are small attributed facts from its public quarterly CMA, not a reconstructed P-CAEY model. Effective annual arithmetic, gross/net fees and ETF mappings are adopted conditional interpretations, not publisher-confirmed; no redistribution/reuse license has been obtained.
• Ten years is our disclosed strategic modeling horizon, not a promise of the provider forecast horizon or a locked holding return.
• SCHP/LTPZ real zero-curve proxies retain their original dated maturity anchors and are NOT current real ETF YTMs. Real reinvestment yields are assumed unchanged; no real-yield repricing premium is added.
• Risk floors, coherent regression extension, forecast supports and latent dependence are selected and uncalibrated. Forecast-error covariance is distinct from realized-return covariance.
• Robust maximizes mean cash-relative utility minus a selected multiple of scenario utility standard deviation. Cash remains residual; no spending reserve is inferred.
• Annual drift is not CAGR; diffusion expected log growth is drift minus half variance. Zero modeled cash volatility omits purchasing-power and reinvestment risk. Source refresh timestamps never refresh observation dates.

A 0% VTIP allocation means this nominal-wealth objective does not select it under these assumptions. Real spending, purchasing-power preservation and liability matching can justify TIPS in a different objective.

Read the v2.2 research and robust-method comparison →

Risk estimate

Estimated 2026-10-09, histories through 2026-10-08. Ten-year proxy and available actual ETF covariances receive equal weight. Correlations shrink 20% toward independence; marginal volatility floors preserve low-volatility assets.

• Complete common dates before log returns; weekend BTC moves aggregate to next shared session
• UTC spot BTC closes differ from ETF market closes
• Blend historical covariance 50/50; shrink correlation 20%; apply declared marginal floors
• Multivariate common-date OLS transport into freshly estimated baseline covariance + PSD correlation-shrunk residual covariance + diagonal volatility-floor increments. Baseline block preserved exactly; floors and transport are selected uncalibrated assumptions.

Fundamentals expire after 90 calendar days; yields and market observations after five weekdays (eight for the weekly Federal Reserve model estimates). Risk estimates expire after 45 days and assumptions require review within 100 days. Weekday aging is conservative around market holidays.

Numerical residual: 3.38e-17. Methodology merton-3.0.0; assumptions 2026-10-07.v3; solver merton-next-working-set-1.

Reconstruction merton-weekly-reconstruction-v1; methodology merton-3.0.0. These estimates do not establish what was published or knowable at the time.

Reconstruction assumptions

• Retrospective application of the finally deployed nine-asset methodology and current underwriting; not allocations published or recommended in those earlier weeks.
• Week labels are Mondays; inputs use the last common ETF close on or before Friday. Only completed historical weeks are reconstructed; actual published records take precedence.
• IEF gross yield uses historical Treasury 7/10-year yields interpolated at the selected fixed 8.45-year mapping, not historical portfolio-average issuer YTM. Treasury observations are lagged one weekday.
• VTIP net real carry uses the trailing 30-calendar-day mean of Fed real par yields interpolated between 2 and 3 years at a selected 2.5-year mapping, less dated expenses. It is not historical issuer net real SEC yield; no yield-spread calibration to today is applied.
• Elm quarterly values are selected only after a 30-calendar-day assumed release lag; Fed fitted curves and Kim-Wright strategic cash use a 7-calendar-day assumed lag. Neither lag is verified historical availability.
• VTIP proxy expenses use 0.04% before 2025-02-03 and 0.03% from its explicit supplement date. Other net fee/maturity mappings remain the deployed fixed assumptions where complete historical effective ledgers are absent.
• Gold 7% and bitcoin 20% net geometric CAGR, futures 2% premium, risk floors, supports, dependence, gamma 3, caps and seeded 8192-draw Robust model are the deployed retrospective specification.
• Risk uses only prices through each cutoff; deployed actual/proxy covariance plus added-sleeve regression transport is retained unchanged. No future covariance fills the 13 ineligible late-2024 weeks.

Reconstruction caveats

• Current revised adjusted prices, quarterly forecast levels and fitted Fed curves are not original historical vintages. This is best-effort reconstruction, not a strict point-in-time backtest or actual performance record.
• Treasury/real-yield proxies are not issuer fund yields; fixed maturities and expense mappings, unknown historical release dates and uncalibrated forecasts can materially change weights.
• Weights are model allocations, not realized returns. Taxes, execution costs, spreads, liquidity needs and liability matching are excluded.