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Solved Problems in Personal Finance

№3 in the series

The Yield Illusion

a working paper on distributions, total return, and friction · No.3 in the series · drewbreyer.com

A cow for her milk
A hen for her eggs,
And a stock, by heck,
For her dividends.

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 compare three strategies often presented as income. In the dividend model, an investor who sells 3% of her shares each year has the same pre-tax terminal wealth as an investor paid a 3% dividend. Under the displayed tax assumptions, the seller pays 34% less cumulative tax for the same withdrawals. A covered call exchanges returns above a strike for a monthly premium; at the modeled retail terms, its median terminal wealth is 21% lower over 30 years. At the stated daily-reset costs, modeled median growth is 6.7% at 2× and 4.8% at 3×, versus 7.0% for the index. Each comparison is a total-return result under stated assumptions, not a claim that the strategy has no legitimate use.

Extra lifetime tax from preferring dividends
$134,773
on a 25×-spending portfolio, same consumption
≈ 2.2 years of your spending
Median terminal forfeited to the covered-call fund
21%
vs the index over 30 years
3× fund median growth vs the index
4.8% vs 7.0%
daily-reset drag plus fees plus borrow
The only free number
7.0%
the index total return, g

A note on posture

Dividends, option premiums, and leverage are real financial mechanisms. A preference for dividends can change diversification and tax timing; a call premium is compensation for giving up returns above the strike; leverage changes both exposure and path dependence. The paper separates those mechanisms from the way products are labeled, then identifies cases where each strategy may fit.

№ I — MEASURED + MODELED

Dividends and equivalent withdrawals

A cash dividend transfers value from the company to the shareholder, and the share price adjusts on the ex-dividend date. The model compares that payment with an equivalent investor-directed sale, then isolates the tax-timing difference under the displayed assumptions.

Market world — governs every modeled figure
Preset

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.

Fig. 1

Same company, same growth, same spending money. The only thing the dividend changes is the tax bill.

The costume. Left: the payer and the seller trace the same wealth line, twice. Right: cumulative tax per $1 diverges — payer 0.261 vs seller 0.171. MODELED
…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.
— Miller & Modigliani, “Dividend Policy, Growth, and the Valuation of Shares,” Journal of Business (1961)1
Annual drag δ·τ_d
0.45%
per year — a fee you can’t waive (compare №1)
Bequest-case gap
12.7%
reinvesting, never selling (step-up at death)
≈ 24 years of your spending
Sell-everything gap
7.0%
after capital-gains tax on liquidation
≈ 12 years of your spending
Fig. 2

Under the displayed taxable-account assumptions, recurring dividend tax reduces reinvested wealth each year.

The tax meter. Pre- and post-liquidation terminal wealth per $1, for the reinvesting non-payer (blue) and dividend payer (red). MODELED
It puzzles them that we relish the dividends we receive from most of the stocks that Berkshire owns, but pay out nothing ourselves.
— Warren Buffett, 2012 Berkshire Hathaway letter, p. 1914

№ II — MEASURED

Distribution reliability

Reliability can mean stable aggregate market dividends, stable company-level payments, or stable household cash flow. The historical record below separates those claims and shows where company-level cuts have occurred.

Fig. 3
−21%

S&P 500 dividend payouts fell ~21% in 2009 — the worst since 1938 (−38.6%); ~74 companies cut or suspended.15

42 + 25

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

−12.2%

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

≈ −1 div

On the ex-dividend morning the price opens lower by roughly (historically slightly less than) the dividend. A dividend is not interest.4,5

0.7%

Investors treat dividends as disconnected from price; exact reinvestment happens in ~0.7% of holdings — the free-dividends fallacy, measured.8

+2.6%

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.

The reliability record. Dividend cuts and suspensions at the moments reliability was the point; the ex-day price drop; the free-dividends fallacy — with one honesty card. MEASURED
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.
— Hartzmark & Solomon, “The Dividend Disconnect,” Journal of Finance (2019), abstract8

№ III — MEASURED + MODELED

Selling the right tail

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. Its economic source is the question.

Write-the-call console
Moneyness k
Fund fee

premium ≈ 2.08%/mo · P(capped) = 54.9% · horizon 30y

Fig. 5

You keep the bad months, cap the good ones, and are paid a fixed fee for the difference.

One month, drawn honestly. The covered call caps at k = 1.00 and adds a premium of ≈2.1%/mo; the shaded wedge is the upside you sold. MODELED
Fig. 4

The premium is real compensation for selling returns above the strike, reduced by product costs.

Thirty years of writing calls. Terminal-wealth distributions over 30 years: the index (blue) against the covered strategy DIY (outline) and as an ETF at its fee (red). The case rests on the premium slider; the fee does not. MODELED
P(fund beats the index over the horizon)
0%
stated honestly — mostly it doesn’t
Median forfeited
0%
—
p95 forfeited (the good outcomes)
0%
—
The boom

Derivative-income ETFs: ~$1B AUM (2018) → ~$100B (Nov 2024) → ≈$145B by mid-July 2025, absorbing ≈$31.5B of net flows in H1 2025 alone and more than $100B over the trailing three years. Asset growth does not change the underlying option exposure.27,29,41

Price targets, downside protection, and income generation are diversions.
— Israelov & Nielsen, “Covered Calls Uncovered,” Financial Analysts Journal (2015), p. 4419
These strategies are mechanically expected to underperform their underlying equity, and increasingly so at higher targeted levels of distributions.
— Benjamin Felix, “Covered Calls: A Devil’s Bargain” (2025)40

№ IV — MEASURED + MODELED

Daily leverage and path dependence

Modest leverage has a serious academic case under specific objectives and implementation assumptions. Daily-reset products add fees, borrowing costs, and path dependence. The model below separates the leverage idea from the retail wrapper used to obtain it.

Leverage console
Fund leverage L
Underlying

median growth at L = 3.0×: 4.8%/yr · 1× index at 3bp: 7.0%/yr

Fig. 6

Leverage can increase expected growth over part of the modeled range. Fees, borrowing costs, volatility, and daily resetting narrow that range.

The leverage frontier. Modeled median growth per year against leverage L. The growth-maximizing point in the frictionless approximation is 3.1×; with the stated fees and borrowing cost it is approximately 1.8×. This point is not an allocation recommendation. MODELED

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.

underlying
1.0000
2× fund
0.9818

Same path, different result: daily resetting leaves a 1.82% loss over the two-day round trip.

…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.
— the regulator, in bold, in 2009 — FINRA Regulatory Notice 09-3132

№ V — MEASURED

Where the strategies fit

Each mechanism can serve a defined liability, risk, or implementation need. The useful question is whether that need justifies the exposure, tax treatment, and recurring cost.

The productStated useThe measured recordPlain description
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.23equity exposure with an upside cap
QYLD vs QQQ (since 2013)a ~12% distribution rate8.9%/yr total return vs QQQ 19.4%/yr; $10,000 → ~$28,500 vs ~$92,700; price-only −27.8%.24(as of 2026-06-30)Nasdaq exposure with monthly call sales and a 0.60% fee
JEPI vs S&P 500 (since 2020)equity-like return, bond-like volatility10.91%/yr at NAV vs the S&P’s 18.53%/yr total return; $10,000 → $18,670 (the sponsor’s own sheet).25(as of 2026-05-31)lower-volatility equity with an option-income overlay
TSLY vs TSLA (since 2022)a ~51% headline distribution rateprice −86% split-adjusted (two reverse splits, 10× cumulative); total return with distributions ~+14%/yr NAV — roughly half of TSLA’s ~24%/yr.26(as of 2026-06-30)Tesla exposure with recurring call sales
TQQQ 2022 vs QQQ 20223× the Nasdaq, dailycalendar 2022: TQQQ −79.1% vs QQQ −32.6%; the recovery needed is +378% vs +48%.38(as of 2022-12-31)3× daily exposure with path dependence
SQQQ (since inception)−3× the Nasdaq, dailysince 2/11/2010: −46.0%/yr; $10,000 → $0.40.38(as of 2026-07-07)inverse daily exposure intended for short holding periods
Product records and category context. In the long term, these ETFs are unlikely to outperform the market as a buy-and-hold strategy. 27 MEASURED

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.

These promises are priced against a moving target: even the index’s own decade forecast doubled inside two years — one major bank moved its 10-year S&P estimate from 3% to 7%. → A Wide & Deep Pond, §VI: High water

Where covered calls live

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 some equity upside into current payments, or an institution writing at scale. It does not create a return source that was absent from the underlying portfolio. 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.

Where leverage lives

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 ability to maintain it through adverse paths. Many retail products instead offer 2–3× daily-reset exposure to volatile market segments at roughly 1% annual fees plus financing. Their prospectuses describe the intended daily objective and holding risk.

Where dividends live

Receiving a dividend is not itself a problem. Selecting primarily for yield can narrow the opportunity set, introduce factor tilts, and accelerate taxable income. A planned sale is an alternative source of household cash flow whose tax and transaction effects should be compared directly.

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.
— Benjamin Felix, PWL Capital (2023)40
Notes on method— formulas, RNG, closed-form cross-checks

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. Withdrawals and taxes are applied at year end, so the model does not represent intra-year tax timing.

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%. Growth-maximizing L in this continuous approximation: frictionless 3.14, with the stated frictions 1.78. This is an objective-specific model result, not a recommended allocation. 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%. The model does not select a filing status, account type, state tax, NIIT status, or holding-period qualification. Basis step-up at death per IRC §1014 is relevant only to the no-liquidation comparison. This is a simplified federal-tax illustration, not tax 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

References

  1. 1.Miller, M. H. & Modigliani, F. (1961). “Dividend Policy, Growth, and the Valuation of Shares.” Journal of Business 34(4), 411–433. www.jstor.org/stable/2351143
  2. 2.Black, F. (1976). “The Dividend Puzzle.” Journal of Portfolio Management 2(2), 5–8.
  3. 3.Williams, J. B. (1938). The Theory of Investment Value. Harvard University Press.
  4. 4.Elton, E. J. & Gruber, M. J. (1970). “Marginal Stockholder Tax Rates and the Clientele Effect.” Review of Economics and Statistics 52(1), 68–74.
  5. 5.Elton, Gruber & Blake (2005). “Marginal Stockholder Tax Effects and Ex-Dividend Day Behavior — Thirty-Two Years Later.” Review of Economics and Statistics 87(3), 579–586.
  6. 6.Fama, E. F. & French, K. R. (2001). “Disappearing Dividends.” Journal of Financial Economics 60(1), 3–43.
  7. 7.Michaely, R. & Moin, A. (2022). “Disappearing and reappearing dividends.” Journal of Financial Economics 143(1), 207–226.
  8. 8.Hartzmark, S. M. & Solomon, D. H. (2019). “The Dividend Disconnect.” Journal of Finance 74(5), 2153–2199. papers.ssrn.com/sol3/papers.cfm?abstract_id=2876373
  9. 9.Harris, Hartzmark & Solomon (2015). “Juicing the Dividend Yield: Mutual Funds and the Demand for Dividends.” Journal of Financial Economics 116(3), 433–451.
  10. 10.Chen, Y. & Israelov, R. (2024). “Income illusions: Challenging the high yield stock narrative.” Journal of Asset Management 25(2), 190–202.
  11. 11.Schlanger, T. & Kesidis, S. (2017). “An analysis of dividend-oriented equity strategies.” Vanguard Research.
  12. 12.Padmawar, S. & Jacobs, V. (2023). “Asset location for equity.” Vanguard Research. corporate.vanguard.com/content/dam/corp/research/pdf/asset_location_for_equity.pdf
  13. 13.IRS Topic No. 404 (Dividends), Topic No. 409 (Capital Gains and Losses); IRC §1014 (basis of inherited property). www.irs.gov/taxtopics/tc409
  14. 14.Buffett, W. E. (2013). Berkshire Hathaway 2012 Shareholder Letter, “Dividends,” pp. 19–21. www.berkshirehathaway.com/letters/2012ltr.pdf
  15. 15.S&P / Silverblatt, via Bloomberg (Dec 2009): 2009 S&P 500 dividend decline, worst since 1938; CNNMoney (Nov 2009).
  16. 16.S&P Dow Jones Indices (July 2020). $42.5B decrease in Q2 2020 US indicated dividends — worst quarter since Q1 2009.
  17. 17.CNBC (Oct 28, 2020). 42 S&P 500 suspensions + 25 cuts in 2020 (Silverblatt).
  18. 18.Janus Henderson Global Dividend Index (Feb 2021): global 2020 dividends −12.2%; one company in eight cancelled; UK −41.6% (Q3); US total +2.6% to a record.
  19. 19.Israelov, R. & Nielsen, L. N. (2015). “Covered Calls Uncovered.” Financial Analysts Journal 71(6), 44–57. images.aqr.com/-/media/AQR/Documents/Insights/Journal-Article/Covered-Calls-Uncovered.pdf
  20. 20.Israelov, R. & Nielsen, L. N. (2014). “Covered Call Strategies: One Fact and Eight Myths.” Financial Analysts Journal 70(6).
  21. 21.Carr, P. & Wu, L. (2009). “Variance Risk Premiums.” Review of Financial Studies 22(3), 1311–1341.
  22. 22.Bakshi, G. & Kapadia, N. (2003). “Delta-Hedged Gains and the Negative Market Volatility Risk Premium.” Review of Financial Studies 16(2).
  23. 23.Wilshire Associates (2019). “Options-Based Benchmark Indexes: Performance, Risk” (6/1986–12/2018). cdn.cboe.com/resources/spx/wilshire-options-based-benchmark-indexes-2019.pdf
  24. 24.Global X, QYLD fund page (as of 6/30/2026); totalrealreturns.com QYLD/QQQ (as of 7/7/2026). www.globalxetfs.com/funds/qyld
  25. 25.J.P. Morgan Asset Management (2026). JEPI Fact Sheet, May 31, 2026. am.jpmorgan.com/us/en/asset-management/adv/products/jpmorgan-equity-premium-income-etf-etf-shares-46641q332
  26. 26.YieldMax, TSLY fund page (6/30/2026); reverse-split announcements (Feb 2024, Dec 2025); totalrealreturns.com TSLY/TSLA. www.yieldmaxetfs.com/our-etfs/tsly/
  27. 27.Morningstar (2025). Morningstar’s Guide to ETF Trends in 2025, derivative-income section.
  28. 28.Rekenthaler, J. (2024). “Covered-Call Funds: A Mystery Wrapped in an Enigma.” Morningstar, Jan 25, 2024.
  29. 29.Natixis IM (2025), citing ISS SimFund: US derivative-income ETF AUM ~$1B (2018) → ~$100B (Nov 2024).
  30. 30.Cheng, M. & Madhavan, A. (2009). “The Dynamics of Leveraged and Inverse Exchange-Traded Funds.” Journal of Investment Management 7(4).
  31. 31.Avellaneda, M. & Zhang, S. (2010). “Path-Dependence of Leveraged ETF Returns.” SIAM Journal on Financial Mathematics 1, 586–603.
  32. 32.FINRA (2009). Regulatory Notice 09-31: Non-Traditional ETFs. www.finra.org/rules-guidance/notices/09-31
  33. 33.SEC. “Updated Investor Bulletin: Leveraged and Inverse ETFs.” www.investor.gov
  34. 34.Crenshaw, C. A. (2022). “Statement on Single-Stock ETFs.” SEC, July 11, 2022. www.sec.gov/newsroom/speeches-statements/crenshaw-single-stock-etfs-20220711
  35. 35.ProShares UltraPro QQQ (TQQQ) summary prospectuses, SEC Form 497K (Oct 2017; Sept 2024), via EDGAR.
  36. 36.Guedj, I., Li, G. & McCann, C. (2010). “Leveraged ETFs, Holding Periods and Investment Shortfalls.” Journal of Index Investing (Winter 2010).
  37. 37.Ptak, J. (2025). “Why Leveraged ETFs Are for the Birds.” Morningstar, Feb 19, 2025.
  38. 38.Market-data computations from dividend/split-adjusted price series (Yahoo Finance), corroborated by totalrealreturns.com and financecharts.com. Methodology in Notes on method. totalrealreturns.com/
  39. 39.Ayres, I. & Nalebuff, B. (2010). Lifecycle Investing. Basic Books.
  40. 40.Felix, B. — PWL Capital / Rational Reminder: the videos in §further watching, and the 2023 post quoted as QY8.
  41. 41.Morningstar (2025). “Covered-Call ETFs Are Booming. But Not All Yield Is Good.” Derivative-income category ≈$145B by mid-July 2025; ≈$31.5B of net flows in H1 2025.

Further watching

  • Ben Felix (PWL Capital): “The Irrelevance of Dividends” (Sept 14, 2019)
  • “The Relevance of Dividend Irrelevance” (June 9, 2022; Rational Reminder ep. 201)
  • “Covered Calls: A Devil’s Bargain” (Sept 14, 2025; Rational Reminder ep. 375)
  • “How Leverage Can Boost Returns (And What Can Go Wrong)” (Dec 21, 2019)

This paper’s synthesis follows the academic literature these videos popularized.

In the series

Series index
← Previous · No.2A Wide & Deep PondWhy diversification changes the range of outcomes even when expected return looks similar.Next · No.4 →The Myth LedgerTen familiar rules tested against theory, evidence, examples, and household boundaries.

Solved Problems in Personal Finance

№1 The Arithmetic of Fees·№2 A Wide & Deep Pond·№3 The Yield Illusion·№4 The Myth Ledger·№5 Retirement Money Secrets: An Evidence Review·№6 The Employer Stock Transition Guide·№7 The House Percentage: A Note for Michael Batnick·№8 What Money Is For·№9 The Bearer Asset: Bitcoin, Crypto, and the Price of Control

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