№3 in the series
a working paper on income that isn’t · №3 in the series · drewbreyer.com
an old farmer’s rhyme, quoted in John Burr Williams, The Theory of Investment Value (1938)3
The harder we look at the dividend picture, the more it seems like a puzzle, with pieces that just don’t fit together.
Fisher Black, “The Dividend Puzzle,” Journal of Portfolio Management (1976), p. 52
Abstract
We consider three ways of buying income that is not there. A dividend is a withdrawal in costume: pre-tax, the investor who sells 3% of her shares each year finishes with exactly the same wealth as the investor paid a 3% dividend — to the dollar — and pays 34% less lifetime tax for the same consumption. A covered call converts the market’s right tail into monthly payments and calls the conversion income: at the terms retail funds actually offer, it forfeits 21% of median terminal wealth over 30 years. A daily-reset leveraged fund at realistic costs turns twice the risk into less than the market’s return: 6.7% median growth at 2×, 4.8% at 3×, against 7.0% for the boring index. Total return is the only return; everything else on this menu is that number, relabeled, minus friction.
A note on posture
Nothing below argues that dividends are bad news, that option premiums are fake, or that leverage is immoral. Dividends are fine to receive; they are expensive to prefer. Option premiums are real; they are payment for a tail you no longer own. Leverage has a literature; the products sold on it have a fee schedule. The argument is an accounting identity plus a fee schedule, and identities do not negotiate. Where a strategy has a legitimate home, §V says so plainly.
№ I — MEASURED + MODELED
Every dollar a company pays you is a dollar the company is no longer worth. The market re-prices this with tedious reliability on the ex-dividend morning. What remains, after the costume comes off, is a withdrawal you did not choose, taxed on a schedule you did not choose.
Nominal units only. Every instrument here compares a strategy against the index under identical draws, so the deflator cancels — there is no real/nominal toggle.
Same company, same growth, same spending money. The only thing the dividend changes is the tax bill.
…given a firm’s investment policy, the dividend payout policy it chooses to follow will affect neither the current price of its shares nor the total return to its shareholders.
Reinvest the dividend and you still trail — the tax leaks out every year, whether or not you ever sell.
It puzzles them that we relish the dividends we receive from most of the stocks that Berkshire owns, but pay out nothing ourselves.
№ II — MEASURED
The dividend investor’s stated reason is reliability: the check arrives whatever prices do. The record disagrees at exactly the moments reliability was the point.
S&P 500 dividend payouts fell ~21% in 2009 — the worst since 1938 (−38.6%); ~74 companies cut or suspended.15
2020: 42 S&P 500 companies (nearly 1 in 10) suspended dividends and 25 cut; Q2 2020 saw 639 US issues cut or suspend — the worst quarter since Q1 2009.16,17
Global dividends fell 12.2% in 2020; one company in eight cancelled its payout entirely; UK payouts fell 41.6% underlying in Q3 2020.18
On the ex-dividend morning the price opens lower by roughly (historically slightly less than) the dividend. A dividend is not interest.4,5
Investors treat dividends as disconnected from price; exact reinvestment happens in ~0.7% of holdings — the free-dividends fallacy, measured.8
The honesty card: US aggregate dividends still rose 2.6% to a record in 2020. Reliability failed company-by-company and abroad — not in the US total.18
When reliability mattered most, the checks were cut — and the price had already told you.
Many individual investors, mutual funds and institutions trade as if dividends and capital gains are disconnected attributes, not fully appreciating that dividends result in price decreases.
№ III — MEASURED + MODELED
A covered call is a trade, not a yield: you sell the market’s best months to strangers, in advance, at a discount that only looks generous next to a money-market rate. The monthly payment is real. What it is made of is the question.
premium ≈ 2.08%/mo · P(capped) = 54.9% · horizon 30y
You keep the bad months, cap the good ones, and are paid a fixed fee for the difference.
The income was real. It was made of your own upside, minus a fee.
Price targets, downside protection, and income generation are diversions.
№ IV — MEASURED + MODELED
Leverage is the one instrument here with an honest academic case — and the retail implementation manages to lose it. The arithmetic of daily resetting is not evil; it is merely indifferent to your holding period, your fees, and your nerve.
median growth at L = 3.0×: 4.8%/yr · 1× index at 3bp: 7.0%/yr
A little leverage is a defensible idea. The products sell a lot of it, on the most volatile things, at a daily reset, for a fee.
The two-day reset
The underlying rises 10%, then falls 1/11 — a round trip to where it began. The 2× fund does not come back.
Same path, opposite fates: the reset tax is 1.82% in two days.
…inverse and leveraged ETFs that are reset daily typically are unsuitable for retail investors who plan to hold them for longer than one trading session, particularly in volatile markets.
№ V — MEASURED
Instruments are not sins. Below, the legitimate home of each — and what distinguishes a decision from a subscription.
| The product | The promise | The measured record | The honest name |
|---|---|---|---|
| BXM vs S&P 500 (since 1986) | equity return with less risk, plus “income” | 8.50%/yr at 10.6% vol vs the S&P’s 9.80%/yr at 14.9% (6/1986–12/2018). Competitive Sharpe — at the price of the market’s best months.23 | equity minus its best months |
| QYLD vs QQQ (since 2013) | a ~12% distribution rate | 8.9%/yr total return vs QQQ 19.4%/yr; $10,000 → ~$28,500 vs ~$92,700; price-only −27.8%.24 | the Nasdaq, capped, for 0.60% |
| JEPI vs S&P 500 (since 2020) | equity-like return, bond-like volatility | 10.91%/yr at NAV vs the S&P’s 18.53%/yr total return; $10,000 → $18,670 (the sponsor’s own sheet).25 | lower-vol equity, relabeled |
| TSLY vs TSLA (since 2022) | a ~51% headline distribution rate | price −86% split-adjusted (two reverse splits, 10× cumulative); total return with distributions ~+14%/yr NAV — roughly half of TSLA’s ~24%/yr.26 | a Tesla position that sells its reason to exist |
| TQQQ 2022 vs QQQ 2022 | 3× the Nasdaq | calendar 2022: TQQQ −79.1% vs QQQ −32.6%; the recovery needed is +378% vs +48%.38 | three times the fall |
| SQQQ (since inception) | −3× the Nasdaq, daily | since 2/11/2010: −46.0%/yr; $10,000 → $0.40.38 | a melting ice cube, by design |
Myth check, both directions: covered calls are not risk-free yield — they are net-long equity with the upside sold, and the downside stays yours19. A dividend is not interest — the stock opens lower on the ex-date by roughly (historically slightly less than) the dividend4,5. And the covered-call record is not all grim: the BuyWrite index earned a competitive Sharpe ratio over three decades, at the price of the market’s best months23. None of the claims in this paper’s favor need exaggerating; the identities are enough.
A covered call is legitimate exactly where its cash flows match a real liability: a known spending need on a known date, a mandate that must convert equity risk into current payments, an institution writing at scale for basis points. What it is never: income discovered inside a stock that everyone else somehow missed. If you want 10% a year from an index that grows at 7%, the extra 3% must be manufactured from principal, premium, or tail — there is no fourth ingredient.
There is a serious academic case for modest leverage early in a saving life (lifecycle investing — see References), implemented with cheap broad instruments and the temperament of an actuary. The retail shelf instead offers 2–3× daily-reset exposure to the most volatile slices of the market, at ~1% fees plus borrow, wrapped in a prospectus that tells you, in bold, not to hold it. Believe the prospectus.
Receive them gladly; reinvest them promptly; never select for them. A portfolio built on yield is a portfolio with fewer companies, familiar factor tilts available cheaper elsewhere, and a standing appointment with the tax office. If you need income, sell shares on your schedule, not the board’s.
The sleeve rules from №2 apply unchanged to option “income” strategies. → A Wide & Deep Pond
Dividends are not investment returns. They are not free money.
Units. Nominal only. Every instrument here compares a strategy against the index under identical draws, so the inflation deflator cancels exactly; there is no real/nominal toggle. Returns are lognormal in log space; geometric inputs convert with ln(1+g).
Y1 — the relabeling machine. Deterministic, annual, per $1. The payer’s share price grows (1+g) then pays a δ dividend; the seller sells the same fraction δ of shares (basis $1/share, never repurchased). Pre-tax terminal wealth is identical to machine precision. Tax: payer τ_d·dividend; seller τ_g·proceeds·(1 − 1/Q). DRIP leg: W ← W·(1+g)·(1 − δ·τ_d); the annual drag is δ·τ_d.
Y2 — covered calls. Monthly. m_mo = ln(1+g_m)/12, s_mo = σ_m/√12. Premium from Black–Scholes with σ_iv = σ_m + vrp, r = g_cash, T = 1/12. Per month the covered factor is (min(G,k) + c)·(1−fee)^(1/12) under the same draw as the index. Live cross-check: E[G] = 1.00673, E[min(G,k)] = 0.98468, P(capped) = 54.9%, premium = 2.08%/mo. MC: 4,000 base → 8,000 effective (antithetic), CRN with the index.
Y3 — leverage. Continuous frontier growth(L) = L·m + (L − L²)σ²/2 − fee(L) − max(0, L−1)·(g_cash + 0.5%), fee(L) = 3bp at 1× else 0.95%. Optimal L: frictionless 3.14, with frictions 1.78. Live cross-check: 1× 6.97%, 2× 6.74%, 3× 4.78% per year. The daily-reset truth simulation uses 252 steps/yr, w ← max(0, w·(1 + L·(e^{r_d} − 1) − cost_d)), seed 42, antithetic. Growth-rate: 0.0467 log/yr at 3×.
Gap-risk caveat. Overnight gaps beyond −1/L are not modeled; real leveraged funds can and do terminate. The two-day reset exhibit is exact: +10% then −1/11 returns the underlying to 1.0000 while the 2× fund lands at 0.9818.
Tax constants. Qualified-dividend and long-term capital-gains rates share brackets (0/15/20%, 2025 IRS thresholds); both sliders default to 15%. Basis step-up at death per IRC §1014. This is arithmetic, not advice.13
Market-data methodology. Product-table figures are computed from dividend/split-adjusted price series and corroborated against totalrealreturns.com and financecharts.com, pinned to their as-of dates.38
Further watching
This paper’s synthesis follows the academic literature these videos popularized.
Continue the series →
№1 The Arithmetic of Fees
What fees, inflation, and the equity risk premium do to terminal wealth.
Solved Problems in Personal Finance
№1 The Arithmetic of Fees·№2 A Wide & Deep Pond·№3 The Yield Illusion
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