Notes
Notes.
Shorter pieces than the research library. Retirement accounts, index investing, and portfolio mechanics, each one anchored on an original chart rather than a summary of what other sites already say.
What these are
The research library holds long-form quantitative work. These notes are the shorter companion: single questions about how retirement accounts and index funds actually behave, answered with a number and a chart instead of a paragraph of generalities.
They are grouped below by the question they answer rather than by date, because most of them only make sense next to the two or three notes on either side of them.
Every note is educational. Nothing here is personalised investment advice, and nothing here is a recommendation to buy or sell any security. Figures are computed from public data and the assumptions behind each chart are stated on the chart itself.
How the accounts actually work
The rules that govern each retirement wrapper, and who controls what inside it.
What Does Vested Mean in a 401(k)? Vesting Schedules Explained
10 min readVested means the share of your employer's 401(k) match you actually keep if you leave. Your own contributions are always 100% yours from day one.
401(a) vs 401(k): Who Controls the Contribution, and Why It Matters
13 min readA 401(a) runs on contributions your employer sets and often makes mandatory. A 401(k) runs on the deferral you elect yourself. Same tax code, opposite control.
Roth 403(b) vs Roth IRA: Same Tax Treatment, Different Ceilings
11 min readBoth are Roth: after-tax in, tax-free out. The difference is the container. One takes 24,500 a year with no income test, the other 7,500 with one. They stack.
457(b) vs 401(k): The Plan With No Early Withdrawal Penalty
12 min readA governmental 457(b) distribution after you leave the job skips the 10% early withdrawal penalty at any age. Here is how that works, and where it fails.
SEP IRA vs Solo 401(k): Where the Self-Employed Ceiling Actually Sits
10 min readA SEP IRA allows 20% of net self-employment earnings. A solo 401(k) adds a flat deferral layer on top, so it permits far more until income runs high.
How Many Roth IRAs Can You Have? Unlimited Accounts, One Limit
11 min readYou can have multiple Roth IRAs and there is no cap on accounts. But all of them share one annual contribution limit. Here is the math on what splitting costs.
HSA Investment: The Only Triple-Tax-Free Account in the Code
12 min readAn HSA is the only US account where contributions deduct, growth is untaxed, and qualified withdrawals come out untaxed. Here is how HSA investment works.
Moving money between accounts
Rollovers, conversions and transfers, and the rules that decide what each one costs.
What Happens to Your 401(k) When You Leave a Job: Four Options, One Costly Default
14 min readNothing moves automatically when you leave. Four doors open: stay in the old plan, roll to the new one, roll to an IRA, or cash out. Only one of them is expensive.
Backdoor Roth IRA Limits: The Pro-Rata Rule Most People Miss
11 min readThe backdoor Roth limit for 2026 is still the ordinary IRA limit. What changes the math is the pro-rata rule, which taxes the conversion against every IRA.
529 to Roth IRA: The Rules, the Caps, and How Long It Really Takes
9 min readSECURE 2.0 lets you roll leftover 529 funds into a Roth IRA. Here are the five gates a 529 to Roth IRA rollover must pass, and why it takes years.
What Happens to Your 401(k) When You Die: The 10-Year Clock on Inherited Accounts
13 min readYour 401(k) passes by beneficiary form, not by will. Most non-spouse heirs must empty the account within 10 years. Here is how the clock actually works.
Taking money out early
Loans, hardship distributions and the exceptions to the 10% additional tax.
How Much Can You Borrow From Your 401(k)? The Limit and the Repayment Trap
11 min readYour 401(k) loan ceiling is half your vested balance, capped at 50,000 dollars. Here is how the formula works and why leaving your job is the expensive part.
Hardship Withdrawal From a 401(k): What Qualifies, and What It Permanently Costs
10 min readA 401(k) hardship withdrawal is taxed as income, usually triggers the 10% early distribution tax, and can never be repaid. Here is what one really costs by 65.
Can I Use My 401(k) to Buy a House? The Loan, the Withdrawal, and What Each Costs
10 min readCan you use a 401(k) to buy a house? Yes, via a loan or a hardship withdrawal. Here is the tax, the penalty, and the compounding each one costs you.
What the products cost
Fee structures, and the charges that never appear as a line on a statement.
Hidden Mutual Fund Fees to Avoid (And Why Your Statement Never Shows Them)
11 min readExpense ratios, 12b-1 fees, loads and turnover costs: the hidden mutual fund fees to avoid, why they never hit your statement, and what 1% costs over 40 years.
Are Annuities a Good Investment? Why They're Insurance, Not an Investment
11 min readAre annuities a good investment? An annuity is insurance against outliving your money. The math on SPIAs, variable annuity fees, and annuity vs 401(k).
Why IUL Is a Bad Investment for Retirement: The Cap Math
11 min readWhy IUL is a bad investment for retirement comes down to three numbers: a capped index return, no dividends, and a cost of insurance that rises every year.
Building the portfolio
What goes inside the wrapper, and who carries which risk.
How to Invest in the S&P 500: What You Actually Buy, and What It Costs
11 min readYou can't buy the S&P 500 itself. How to invest in the S&P 500 through an index fund or ETF, what the expense ratio costs over 30 years, and what you own.
Pension vs 401(k): The Real Difference Is Who Carries the Risk
12 min readPension vs 401(k): the real difference is who carries the risk. A pension puts investment and longevity risk on your employer. A 401(k) puts both on you.
Roth IRA for Kids: The Earned Income Rule, and What a 17-Year Head Start Is Worth
10 min readA Roth IRA for kids hinges on one thing: earned income. What counts, who controls the account, how financial aid treats it, and the arithmetic of starting at 8.
More notes
Does a Roth IRA Earn Interest? Why the Account Has No Rate of Its Own
9 min readA Roth IRA does not pay interest and has no rate. It is a tax wrapper, and the return comes entirely from what you hold inside it. Here is how that works.
What Can You Hold in a Roth IRA? The Short List of What You Cannot
10 min readThe tax code bans only two things from a Roth IRA: life insurance and collectibles. Everything else you cannot buy is your custodian's rule, not the law's.
Last updated: August 2, 2026