QuantCFA
Quantitative Research

The mathematics of Roth Conversions, in full.

Most Roth-conversion advice collapses to one comparison: your tax rate today versus your tax rate later. That comparison hides the components that actually drive the answer. The papers here isolate each one, derive it formally, and explain it in plain English.

Start here

New to this? The Practitioner Guide walks through the conversion decision from first principles, in plain prose. For the math, see the Synthetic Roth Contribution paper.

The Synthetic Roth Contribution

When you pay Roth conversion tax from outside the retirement account, you've quietly made a Roth contribution equal to the tax — bypassing the IRS contribution limit. This paper proves it four ways.

Submitted to Journal of Financial Planning
Working paper · May 2026 · Posted on SSRN May 20, 2026

Quantifying Tax-Drag Shelter Benefits in Roth Conversions

Quantifies the two Tax-Drag Shelter alphas in a Roth conversion: RMD-reduction (from the Convert decision) and SRC (from the Outside-settlement decision).

Working paper · June 2026 · Posted on SSRN June 4, 2026

Roth Conversion Valuation & Mechanics

The paper that introduced the Synthetic Roth Contribution concept and decomposed conversion-tax payback into its components. The framework has been substantially extended in the two working drafts above.

Foundational paper · April 2025 · Published on SSRN June 2025
See the research applied

RothGPT

The frameworks developed here are implemented in a working calculator: RothGPT.com. Enter your own numbers and see the Synthetic Roth Contribution, Tax-Drag Shelter alpha, time-weighted distribution rate, and break-even tax rate computed for your actual situation.