Drew Breyer

Research and writing · nine-part series

Solved Problems in Personal Finance

Interactive papers about recurring financial decisions: what the arithmetic establishes, what the evidence measures, and where household circumstances still control the answer.

The title refers to durable decision structures, not certainty about markets or people. Each paper separates identities, observed evidence, model output, and limitations so the reader can inspect the reasoning rather than inherit a recommendation.

The series

Nine questions, in sequence

Last evidence review: August 2026

  1. The Arithmetic of Fees ↗

    Identity + modeled

    What do recurring costs do to long-horizon wealth?

    How recurring costs, inflation, and allocation assumptions affect long-horizon wealth.

    Method and boundary
    Method
    Monthly cash-flow recursion and seeded return paths
    What changes
    Change contributions, horizon, allocation, inflation, returns, and fee levels.
    Boundary
    No taxes, withdrawal phase, stochastic inflation, or individualized portfolio constraints.
  2. A Wide & Deep Pond ↗

    Measured + modeled

    Why does diversification change the range of outcomes?

    Why diversification changes the range of outcomes even when expected return looks similar.

    Method and boundary
    Method
    Closed-form calibration, historical records, and seeded return paths
    What changes
    Compare market and single-stock outcomes, portfolio width, and speculative sleeves.
    Boundary
    Historical samples and calibrated return distributions are descriptive, not forecasts.
  3. The Yield Illusion ↗

    Identity + measured + modeled

    When is investment income a label for total return?

    How dividends, option premiums, and leveraged products relate to total return after friction.

    Method and boundary
    Method
    After-tax identities, option payoffs, product records, and daily return paths
    What changes
    Change tax rates, option assumptions, leverage, volatility, fees, and holding period.
    Boundary
    Tax and product examples are simplified and depend on account, jurisdiction, and period.
  4. The Myth Ledger ↗

    Literature review + illustrative

    Where do familiar personal-finance rules stop working?

    Ten familiar rules tested against theory, evidence, examples, and household boundaries.

    Method and boundary
    Method
    Evidence ledger with foundation, measurement, model, and boundary labels
    What changes
    Test how assumptions change examples involving saving, housing, debt, and investing.
    Boundary
    A rule can be incomplete without being wrong for every household or circumstance.
  5. What does an income-first closed-end-fund strategy establish?

    A CEF retirement strategy tested against distribution accounting, wrapper risk, and simple benchmarks.

    Method and boundary
    Method
    Claim audit, distribution accounting, deterministic stress cases, and seeded sensitivity paths
    What changes
    Inspect distribution sources, matched exposures, stress cases, sleeve size, and reserves.
    Boundary
    Public evidence cannot reproduce a proprietary portfolio record; modeled cases are not forecasts.
  6. The Employer Stock Transition Guide ↗

    Decision framework + modeled

    How should a household price the decision to diversify employer stock?

    How to diversify employer stock while pricing taxes, fees, implementation, and retained risk.

    Method and boundary
    Method
    Household exposure, tax-lot, transition, charitable, and recurring-fee calculations
    What changes
    Enter exposure, basis, losses, tax assumptions, sale schedule, and proposal fees.
    Boundary
    Employer rules and individual tax, legal, charitable, and estate facts require professional review.
  7. What does the vig take, and how sharp do you have to be to clear it?

    Posted betting prices, parlay juice, and prediction-market fees — with the sample size required before a winning season is evidence.

    Method and boundary
    Method
    American-odds identities, parlay compounding, posted taker-fee schedules, and a power calculation for claimed edge
    What changes
    Change the ticket, the number of legs, true skill, venue fees, and a prepaid entertainment budget.
    Boundary
    Independence and extra-margin stand-ins are not a book’s correlation model; household studies are population-level; this is not a betting system.
  8. What Money Is For ↗

    Primary texts + source criticism

    Once the arithmetic is sound, what is the money for?

    Fourteen public-domain texts set in tension over provision, labor, power, accumulation, finitude, and use.

    Method and boundary
    Method
    Paired close reading, primary-edition and rights verification, historical context, and original commentary
    What changes
    Read seven paired movements, inspect visible source dossiers and facsimiles, and write a private stopping rule.
    Boundary
    A curated moral, literary, and political argument, not a universal creed or individualized advice.
  9. The Bearer Asset: Bitcoin, Crypto, and the Price of Control ↗

    Decision framework + protocol facts + scenarios

    What can a non-sovereign asset be worth when it pays no cash flow?

    A field guide to Bitcoin value, sleeve sizing, custody, wrappers, stablecoins, programmable networks, privacy, and failure modes.

    Method and boundary
    Method
    Monetary-theory review, source-led protocol comparison, ownership threat model, and deterministic scenario labs
    What changes
    Stress a sleeve, test monetary-premium assumptions, compare custody routes, and trace stablecoin risk.
    Boundary
    No cash-flow valuation, expected-return forecast, universal allocation, product recommendation, or guarantee of protocol or custody safety.

Reading paths

Start with the decision at hand

Portfolio foundations

Fees, Pond, and Yield move from recurring friction to diversification and total-return accounting.

Household rules

Myths tests familiar advice against evidence and the conditions that make a rule useful or incomplete.

Applied decisions

Retirement and Equity apply the same discipline to CEF income claims and concentrated employer stock.

Consumption versus investment

Vig prices sports books and prediction markets as posted holes, not as ways to build wealth.

Purpose and enough

Enough asks what financial competence is meant to protect, release, and return to ordinary life.

Alternative assets and control

Crypto separates Bitcoin’s non-sovereign thesis from valuation, sizing, custody, stablecoins, networks, and privacy.

Shared method

A consistent burden of proof

Label the evidence

Identities, historical measurements, literature findings, and model outputs answer different questions. The papers label them accordingly.

Show the assumptions

Inputs, units, dates, return conventions, and known exclusions sit beside the model or in an attached method note.

Keep comparisons matched

Fees, exposures, taxes, and time periods are aligned before a strategy is compared with a simpler alternative.

Bound the conclusion

A model is not a forecast, a distribution is not necessarily income, and a general result is not an individualized decision.

Shared language

Short glossary

Arithmetic return
The simple average of periodic returns. It describes an average period, not the compounded growth of one dollar.
Geometric return
The constant annual rate that links a starting value to an ending value. It reflects compounding and volatility drag.
Real and nominal dollars
Nominal dollars are the amounts shown at the time. Real dollars remove assumed inflation so purchasing power is comparable across years.
Total return
Price change plus distributions, before or after costs and taxes as stated. A cash payment is only one component.
Terminal wealth
Portfolio value at the end of the modeled horizon. It depends on cash-flow timing, returns, costs, taxes, and the unit used.
Volatility drag
The gap between arithmetic and compounded return created by fluctuating returns. Larger swings generally widen the gap.
Sequence risk
The risk that poor returns arrive when withdrawals make recovery difficult, even if the long-run average return is unchanged.
Idiosyncratic risk
Company-specific risk that broad diversification can largely remove without requiring a lower market exposure.
Monte Carlo simulation
A set of model-generated paths used to examine a range of outcomes under stated assumptions. It is not a probability forecast unless the model is calibrated for that purpose.
Distribution and income
A distribution is cash paid to an owner. Its source may be income, realized gain, borrowed money, principal, or a mixture.
Net asset value
The per-share value of a fund’s assets minus liabilities. A closed-end fund can trade above or below that value.
Tax-loss harvesting
Realizing a loss to offset taxable gains or income while maintaining an intended exposure. Wash-sale rules and later realization can reduce the benefit.
Separately managed account
A portfolio of securities owned directly by a client and managed under a mandate. Personalization and tax-lot control come with fees and implementation constraints.
Vig
The share of turnover a two-way posted price extracts if the book is balanced: 1 − 1/overround. On −110/−110 it is 4.545 cents per dollar. It is not the same quantity as hold.
Hold
Gross gaming revenue divided by handle over a period. It moves with mix, limits, and one-sided action. A year’s hold is a measured mix, not the juice on one moneyline.
Overround
The sum of implied probabilities on a complete market. A fair two-way book sums to 1. Everything above 1 is the house.
Implied probability
The win rate baked into American or decimal odds, including juice. It is the break-even hurdle for that side, not a forecast of the event.
Break-even win rate
The true win probability at which expected value is zero after the posted price or fee. Below it, more activity loses more money.
Favorite–longshot bias
The regular finding that long shots are overbet relative to their win frequency. Calibration of a price and profitability of buying the long shot are different sentences.
Kelly criterion
The bankroll fraction that maximizes long-run geometric growth for a known edge. It is zero when expected value is not positive, and it is usually smaller than a recreational stake.
Statistical power
The chance a test detects an effect of a stated size. A two-point betting edge needs thousands of independent trials before a winning season is evidence rather than weather.
Taker fee
A charge paid by the side that crosses the spread on a prediction market. Common schedules are of the form C · r · p · (1 − p) and peak near a 50-cent contract. Makers are often uncharged.
Intrinsic value
A framework-dependent estimate of value from future cash flows, use, or other fundamentals. Bitcoin has no contractual owner cash flow, so a monetary-premium scenario is not a discounted-cash-flow valuation.
Bearer control
The practical ability to authorize a transfer with valid signing authority. It can reduce reliance on a custodian while adding key, recovery, physical-security, and estate responsibilities.
Spot crypto ETP
An exchange-traded security whose vehicle holds a crypto asset through service providers. The shareholder owns the security and generally cannot use or individually redeem the vehicle’s on-chain asset.
Payment stablecoin
A token intended to be redeemed for a fixed monetary value. Its stability depends on the issuer, reserves, redemption rights, contract controls, banking access, law, and the network carrying it.

Scope

Educational work, not a personal prescription

These publications are independent educational research. They are not individualized investment, tax, legal, or accounting advice. Models depend on their stated assumptions and are not forecasts. Decisions involving taxes, legal restrictions, or concentrated positions warrant qualified review.

Drew Breyer’s portfolio  ·  Reading and references

Optional support

The work is public and independent. Bitcoin support is optional and does not change access, coverage, or conclusions.

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