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VTIP, cash and purchasing power — Merton 2.1

Research and implementation review: October 6, 2026. Reference market inputs through October 5. This corrects the VTIP return methodology in Merton 2.0; it does not rewrite that version’s historical research results.

Decision

Retain VTIP as rolling short-term inflation-linked bond exposure throughout the ten-year forecast. Remove the three-year current-carry / seven-year cash-return blend. Keep the nominal Central and Robust objectives as the production defaults. Publish a separate purchasing-power experiment and a one-year inflation/real-yield stress calculator. No minimum VTIP allocation is imposed.

The original blend was an unsupported simplification. Its three-year cutoff did not follow from duration, maturity, a fitted model, or a holding-period payoff. It replaced most of the return estimate with a cash anchor while retaining TIPS return covariance.

The reason for including TIPS matters: inflation-linked cash flows and real-yield exposure differ from cash’s nominal liquidity. Constan’s report separates cash from a purchasing-power portfolio containing inflation-protected bonds. That supports distinguishing their roles; it does not establish an optimal VTIP weight. Damped Spring, Always own beta!, pages 2–6.

Corrected return anchor

The central scenario uses:

VTIP nominal CAGR = exp(ln(1 + net real SEC carry) + inflation compensation) − 1
Merton drift = ln(1 + CAGR) + annual log-return variance / 2

At the reference inputs, net real carry is 2.29% and ten-year continuously compounded inflation compensation is 2.3334%. The corrected CAGR is 4.70%, versus 4.37% under the old blend. The existing 3% volatility floor gives a Merton drift of approximately 4.64%.

This is a constant-real-yield reinvestment scenario, not an empirically proven forecast. Replacements remain short TIPS throughout the horizon; future net real carry is anchored to its current value. The central case assumes no expected price gain/loss from changes in real yields and no extra roll premium. Vanguard’s SEC yield excludes inflation adjustments and is already net of fees, so we do not deduct the expense ratio a second time. Its 30-day convention is not an exact forecast of a rolling ETF’s total return. Vanguard VTIP.

Inflation compensation is a market-based proxy, not pure expected CPI: it includes risk and liquidity effects. We retain the ten-year compensation measure to match the strategic horizon, without pretending that a ten-year TIPS yield is VTIP’s real yield. Future real reinvestment yields, inflation, fees, turnover, and repricing remain uncertain. The ±1.5 percentage-point CAGR scenario support is retained as a judgment, not a confidence interval. Federal Reserve methodology.

A yield-curve path model would require expectations separated from term/liquidity premiums and ETF turnover assumptions. Available evidence does not establish that this extra complexity would forecast rolling VTIP returns better. We therefore use the simpler conditional anchor and expose sensitivity rather than claim a validated ten-year prediction.

Allocation consequences

With other reference inputs fixed, both γ=3 Central and Robust still assign VTIP 0%. Correcting an asset’s representation does not guarantee it enters a constrained optimum. The P90 VTIP allocation across 8,192 independent expected-CAGR draws rises from approximately 22% to 42%; P10 and median remain zero. These are distributions across assumptions, not probable future allocation paths.

The unchanged constraints allow no shorts or leverage, and require no minimum holding of VTIP. Higher risk aversion changes the result substantially; see the accompanying allocation sensitivity data.

One-year inflation and real-yield scenarios

The interactive calculator uses a separate one-year approximation:

VTIP nominal return ≈ (1 + net real carry) × (1 + CPI inflation) − 1
                      − duration × change in real yield
Real return = (1 + nominal return) / (1 + CPI inflation) − 1
Cash nominal return = average net cash yield earned during the year

The rate move is an end-of-year shock, so it changes the terminal price rather than the preceding year’s carry. This avoids silently counting higher future reinvestment yields as income already earned. It omits convexity, the CPI indexation lag, roll, changing duration, and intrayear timing. It is a stress illustration, not a total-return forecasting engine.

Vanguard’s retrieved characteristics report 2.4 years duration as of August 31, 2026. The duration field is editable, including 2.3 years. Duration measures price sensitivity; it is neither a maturity date nor a cutoff for inflation-linked exposure.

Using 2.29% net real carry, 2.4-year duration and 3.49% average cash yield:

One-year scenario	VTIP nominal	VTIP real	Cash nominal	Cash real
CPI 6%; real yields unchanged	8.4%	2.3%	3.5%	−2.4%
CPI 6%; real yields rise 1 pp	6.0%	0.0%	3.5%	−2.4%
CPI 1%; real yields fall 1 pp	5.7%	4.7%	3.5%	2.5%

Users can vary cash yield independently to test whether it keeps up with inflation. These cases illustrate why TIPS and bills are distinct; they do not assign probabilities to macro regimes. Underlying TIPS principal adjusts with CPI, but the maturity floor of an individual bond does not guarantee an ETF purchase price or a positive short-term real return. TreasuryDirect.

Purchasing-power Merton experiment

Let nominal portfolio wealth be W and the consumer-price index be P. For constant-coefficient diffusions and CRRA utility of W/P, the allocation-dependent objective is:

wᵀ(μ − r) − γ wᵀΣw / 2 + (γ − 1) wᵀc
cᵢ = covariance of asset i’s nominal return with inflation

Ito’s correction matters: the term is γ−1, not γ. Nominal cash has zero instantaneous market variance here but uncertain purchasing power. Applying a common deterministic inflation deduction to all forecasts does not change weights. At γ=1, maximizing expected log wealth gives the same allocation in nominal and real units. This experiment is still a static diffusion approximation, not a full consumption/liability or stochastic-real-rate model. Campbell and Viceira, Who Should Buy Long-Term Bonds?.

We estimated monthly asset/CPI covariances in two windows, using both seasonally adjusted and unadjusted CPI. Asset returns include distributions. GLD proxies GLDM and BTC-USD proxies FBTC. Correlations are rescaled to the production forward volatilities while retaining the production asset covariance; joint covariance feasibility is checked. All four cases passed without rescaling the inflation covariance vector further.

CPI series / window	Complete monthly observations	VTIP/CPI correlation	VTIP at γ=3, nominal → real	VTIP at γ=6, nominal → real
Seasonally adjusted, Jan 2015–Aug 2026	138	−0.054	0% → 0%	28.8% → 30.0%
Seasonally adjusted, Jan 2020–Aug 2026	78	−0.089	0% → 0%	28.8% → 29.0%
Unadjusted, Jan 2015–Aug 2026	138	−0.002	0% → 0%	28.8% → 29.2%
Unadjusted, Jan 2020–Aug 2026	78	−0.056	0% → 0%	28.8% → 28.8%

October 2025 CPI is missing in the retrieved series; October and November monthly inflation changes are therefore omitted rather than interpolated. This accounts for the two missing observations in each window.

These weak contemporaneous correlations do not disprove TIPS’ contractual inflation linkage. Real-yield price changes, CPI seasonality and publication/indexation lags obscure it in short samples. Monthly realized inflation is not the unexpected-inflation innovation required by the diffusion model. Annualization also ignores serial dependence.

This is descriptive sensitivity with revised data, not an out-of-sample backtest. The cutoff excludes September CPI, which was not available at the review date. We do not use these sample estimates as live hedging coefficients: they lack enough evidence of stability or forecasting usefulness. The experiment therefore remains research rather than a third selectable allocation target. Central and Robust remain nominal-wealth portfolios; Robust addresses expected-return uncertainty, not inflation protection specifically.

Reproduction and validation

• node scripts/test-merton-v2.mjs covers independent carry examples, negative real yields, no double fee deduction, and independence of VTIP’s forecast from the cash anchor. The carry regression fails on the old three/seven-year implementation.
• node scripts/analyze-merton-inflation-portfolios.mjs reproduces the Central/Robust risk-aversion sensitivity from the frozen 2.1 fixture.
• python scripts/analyze-merton-inflation.py reproduces the descriptive CPI analysis using the pinned environment in scripts/merton-v2-requirements.txt and the existing ignored public-price cache from scripts/collect-merton-v2-research.py.
• python scripts/test-merton-inflation.py compares the adjusted nominal optimization against an independent seven-asset real-return optimization, including risky purchasing power of nominal cash.
• Research results and CPI source hashes. Public price provenance is in the original research manifest. Raw provider prices are not redistributed.
• Frozen 2.0 and 2.1 fixtures preserve reproducible comparisons. The feed stays schema 2; methodology advances to merton-2.1.0. Agora continues applying private caps, reserves and CAGR overrides without changing stored preferences.