Simulation and the Quantum Retirement Score

What the score is made of

The headline score is a weighted blend of four pillars, each scored from zero to one hundred. The pillar weights are firm constants; the full score anatomy — each pillar's contribution, any hazard cap that applied, and the reason for the zone shown — is emitted with every result and displayed in the product.

• Funding: the share of simulation trials in which essential spending is funded net of tax in every year and the portfolio is never depleted, less a bounded penalty when the downside of the outcome distribution is wide relative to its median.
• Allocation fit: how many years of essential spending the safer buckets can cover, combined with an age-based equity band, adjusted for whether the portfolio's expected return clears the return the plan actually requires.
• Guaranteed floor: how much of essential spending is covered by Social Security, pensions, other guaranteed income, and modeled annuity income, plus an annuity-equivalent credit for the safest assets.
• Stress resilience: the average of four deterministic re-runs of the plan under a sequence-of-returns crash, a sustained inflation shock, a long-term-care cost, and extra longevity, each scored by how many years of essential spending remain covered.

The blended score can then be lowered — never raised — by a registry of hazards (for example concentration or an elevated withdrawal rate) that cap the headline.

The zone shown beside the score (from at-risk to surplus-flexible) is banded off the capped score and then gated: a failing resilience grade forces the at-risk zone at any score, and the top zone additionally requires over-funding and a passing self-funding runway.

How returns are generated

Each trial resamples whole calendar years from a bundled historical series of annual US returns — the S&P 500 total return, the 10-year Treasury bond total return, and the 3-month Treasury bill — covering 1928 through 2025 (98 years, sourced from the NYU Stern Damodaran dataset and version-stamped in the engine). Years are sampled in blocks of random length, so runs of good and bad years persist as they did historically.

Because equity, bond, and cash returns are always taken from the same historical year, cross-asset co-movement, fat tails, and autocorrelation are inherited directly from the record.

The five risk buckets a client's portfolio is organized into are derived from those three series through a two-factor model: each bucket carries a firm-constant equity loading and bond loading over cash, plus an independent residual. The residual volatility and a drift term are solved so that each bucket's modeled mean return and volatility equal the assumption resolved for that bucket. Residuals are independent across buckets and years.

The random number generator is seeded with a fixed firm constant. Identical inputs produce byte-identical results, so a client's score does not move between views, and the difference between two runs — the proposed strategy versus the current portfolio, or a what-if lever versus the base plan — reflects the change in inputs, not sampling noise.

Portfolio weights versus the return model

Two different things are easy to conflate. The return model above describes how each bucket's return is generated. The portfolio weights — how much of the client's investable assets sit in each bucket — come from the advisor: a custom allocation entered for the client, the allocation on the Bucket tab, or an allocation derived from the products attached to each bucket. When none of those exist, the engine applies the firm's default allocation, and that source is labeled beside the score in the product.

Products the advisor attaches to a bucket carry their own expected return, volatility, and expense ratio, and those override the firm's bucket assumptions in proportion to the product's allocation. Every resolved assumption is shown next to the score with its source labeled.

Advisor-controlled assumptions

Values are shown in the product beside the score; this page documents who controls each one.

Inside each simulated year

Every trial walks the plan one year at a time, in this order, with real tax law applied at each step.

1. 01 Set the year's spending Essential and discretionary spending follow an age-based spending curve. Under the default withdrawal policy, discretionary spending is raised or cut in steps when the portfolio withdrawal rate drifts outside a band around its starting level; essential spending never flexes.
2. 02 Take the required minimum distribution first The RMD is computed on the prior year-end tax-deferred balance using the client's birth-year start age and the IRS Uniform Lifetime Table.
3. 03 Apply any elected Roth conversion An elected conversion moves assets in kind from tax-deferred to Roth, pro-rata across buckets, and is taxed as ordinary income in that year.
4. 04 Solve the tax-aware withdrawal The gross draw is solved so that the net amount after federal, state, Social Security, and Medicare IRMAA taxes meets the year's need — using the same closed-form tax engine as the Tax Analysis tab — sequencing taxable, then tax-deferred, then Roth accounts, and drawing safest-first within each.
5. 05 Reinvest any excess After-tax RMD dollars beyond the year's need are reinvested in the taxable account at fresh cost basis.
6. 06 Grow, then charge fees Each bucket in each account grows at that year's sampled return, then the bucket's fee drag is deducted.

Before retirement, salary covers spending and the advisor's annual contribution is deposited into the portfolio at year end. The plan horizon runs to a joint-life survival age at the advisor's chosen longevity percentile, using a blended unisex Social Security Administration period life table.

What the simulation reports

A trial succeeds only if essential spending is funded net of tax in every year, the portfolio is never depleted, and — under the guardrail policy — it never survived only by cutting discretionary spending more deeply than a firm threshold. Each failing trial is classified by its first failure mode, and the breakdown is reported.

Outcome bands are reported at the P10, P25, P50, P75, and P90 of ending real-dollar principal. A trajectory of P10, P50, and P90 balances at fixed waypoint years is emitted with every result; the P10 path also feeds the downside-depletion hazard check. The P10 and P50 terminal bands feed the funding pillar's dispersion penalty and that same hazard.

As a deterministic cross-check, the engine also replays the realized return sequences beginning in 1973, 2000, and 2008 through the same plan and reports the worst ending principal alongside the score.

The engine runs twice per view — once for the proposed Quantum strategy and once for the client's current portfolio — and eight what-if levers each re-run the full engine with one input changed.

Sequence-of-returns risk

Because whole historical years are resampled in blocks, bad early sequences occur inside the simulation at their historical frequency and fail trials that the same returns in a different order would not. Sequence risk is then tested explicitly in three deterministic places: a product-aware crash shock in the stress battery, hazard rules that cap the score when early-retirement withdrawal rates are elevated, and a self-funding-runway check that values the safe and protected assets at their modeled crash value against planned spending.

Assumptions

Questions advisors ask about the simulation

How many simulation trials does Quantum run?

2,000 per run, with a fixed random seed, so the same client data always produces the same score. The count is a firm constant and is reported with every result in the product.

Is the Quantum Retirement Score a probability of success?

No. It is a composite of four pillars — funding, allocation fit, guaranteed floor, and stress resilience — that can then be capped by hazard rules. The funding pillar is the simulation's success rate; the product shows every pillar and every hazard rule that applied.

Does the simulation use a fat-tailed return distribution?

It resamples real history. Whole calendar years of US equity, bond, and cash returns from 1928 through 2025 are drawn in blocks, so the fat tails, autocorrelation, and cross-asset behavior of the historical record are preserved.

Does the same client always get the same score?

Yes, within a calendar year. The engine is pure — no clock, no live data, no unseeded randomness — so identical inputs give byte-identical output. When the calendar year advances, the schedule and RMD ages shift by one year and the score can legitimately move.

Which assumptions can an advisor change?

Bucket allocation, expected return and volatility through attached products or a growth override, inflation, fees through product expense ratios, the longevity percentile, spending floor and goals, contributions, long-term-care coverage, and any elected Roth conversion. Every resolved value is shown beside the score with its source.

Does live market data affect the score?

No. The historical return series is bundled with the engine and version-stamped, the bucket loadings are static constants, and no external feed is read at runtime.

Every assumption is shown beside the score

See it on a real client

Run the Quantum Retirement Score on your own client data and open the score anatomy and assumptions behind it. Licensed to financial professionals.