RET-BILL-001 — All Bills in Retirement

A retiree can currently get about 4% on short Treasury bills with no market risk at all. The question this study answers is whether that removes the reason to hold equities — and if not, what yield it would take.

The three arms

All three run on identical simulated market paths, with the same seed, and withdraw the same real dollars on the same day. That is what makes the comparison paired rather than a contest between two different random samples.

• Bills — the whole balance rolls short T-bills, accruing at the simulated short rate less the fund expense. No duration, no credit risk, no reinvestment decision.
• Equities — 100% index, bought on day one and held. Withdrawals are funded by selling shares at that day's price. This is the arm carrying sequence-of-returns risk: a withdrawal during a drawdown removes shares permanently, before the recovery.
• 60/40 — 60% index and 40% bills, rebalanced annually, withdrawing pro-rata.

A path is depleted the first day the balance reaches zero. Depleted paths stay depleted and are counted as failures; they are not allowed to recover.

The 60/40 arm is not decoration. All-bills versus all-equity is a strawman — nobody advising a retiree recommends either corner — and without a middle arm the study can say what not to do but nothing about what to do instead.

The rate process, which is the whole risk of the study

The bill yield is a mean-reverting annual process, and inflation is the same shape, with correlated innovations. Both are fitted to FRED data over 78 overlapping years, 1948–2025, using TB3MS (3-month bill, monthly average) and CPIAUCSL (CPI-U, December over December).

The rate is floored at zero, because nominal bills do not pay negative in the US. That floor truncates the left tail and therefore raises the realised average rate slightly above the fitted mean — a small effect that runs in favour of the bills arm, and is disclosed rather than hidden.

Why ρ is the number to attack

When inflation rises the Fed raises, and bills reprice within weeks. That is the mechanism by which cash partially self-hedges inflation, and it is exactly what long bonds cannot do. Set ρ to 0 and bills are destroyed by every inflation shock because the yield never responds; set it to 1 and bills become a near-perfect real instrument. Neither is true, and the fitted 0.449 sits where the historical record puts it — positive, but well under one, because the policy response lags the shock. The 1970s are in the sample precisely because that is the only regime in the record where bills were genuinely destroyed.

ρ is a control on the lab page. Move it and watch the answer move; if a conclusion only survives at one setting, it is not a conclusion.

Verification

Three checks, all run before any distribution was looked at:

• Closed form. With rate volatility and inflation set to zero, the bill arm must equal a deterministic annuity drawdown, Bn = B0(1+i)n − w(1+i)((1+i)n−1)/i. It matches to the cent.
• Against the previous study. At RET-CC-001's exact settings the equity arm reproduces its published buy-and-hold success rate: 92.9% against 93.0%. Because this engine uses an independent random stream, that is a distributional match rather than a path-for-path identity — a genuine weakening of the test, and it is recorded as such rather than glossed.
• Correlation round-trip. Raising ρ must tighten the spread of realised real yields across paths, because it ties the two processes together. It does.

What is not modelled

• TIPS. If the objection to bills is inflation, inflation-linked bonds are the direct answer rather than equities, and comparing nominal bills to stocks and concluding "you need stocks" would be a false dichotomy. TIPS need a real-yield process and a breakeven this engine does not have. This is the strongest objection to the study and it is stated here rather than left to be found.
• Taxes. The premise is an IRA. That is an advantage, not a simplification: in a taxable account equities gain a further structural edge from deferred capital gains and qualified dividends against bill interest taxed as ordinary income. The taxable version would move the answer further in the same direction.
• Dynamic withdrawal. Every arm spends blindly through a crash, which no real retiree does. This omission is not neutral — it specifically overstates the equity arm's sequence risk, which is the arm most exposed to it.
• Other income. No Social Security, no pension. The portfolio carries 100% of spending, which raises failure rates for every arm roughly equally.
• Longevity. A fixed 30-year horizon with no mortality overstates the cost of running out at year 31.
• SGOV is not a short rate. It carries about 0.09% of expense and 0–3 months of duration, so it lags the modelled rate slightly on the way up and leads it on the way down. The expense is subtracted explicitly; the duration lag is not modelled.
• Inflation is AR(1). A mean-reverting process understates a sustained 1970s-style regime. That caps how badly the bills arm can lose — the most important limitation here, because it runs in favour of the strategy most likely to be criticised. The equity arm has the mirror-image cap: the bootstrap cannot invent a crash worse than 2001–2026 contains. Neither arm is flattered alone.

Reproducing it

Every parameter above is a control on the lab page, and the page runs the whole thing in your browser in about a second. The node reference implementation, the calibration script and the raw FRED extracts live alongside the study; the browser engine and the node engine agree to within Monte Carlo error at every setting tested.