Solved Problems

№3 in the series

The Yield Illusion

a working paper on income that isn’t · №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 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.

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

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.

IMEASURED + MODELED

The relabeling machine

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.

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

Reinvest the dividend and you still trail — the tax leaks out every year, whether or not you ever sell.

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

IIMEASURED

The reliability myth

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.

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

IIIMEASURED + 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. What it is made of 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 income was real. It was made of your own upside, minus a fee.

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%
Price targets, downside protection, and income generation are diversions.
Israelov & Nielsen, “Covered Calls Uncovered,” Financial Analysts Journal (2015), p. 4419

IVMEASURED + MODELED

Borrowing the left tail

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.

Leverage console
Fund leverage L
Underlying

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

Fig. 6

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 leverage frontier. Median growth per year against leverage L. The frictionless optimum sits near 3.1×; with fees and borrow it falls to ≈1.8×. The products (red) live past it. 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, 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.
the regulator, in bold, in 2009 — FINRA Regulatory Notice 09-3132

VMEASURED

Where they fit

Instruments are not sins. Below, the legitimate home of each — and what distinguishes a decision from a subscription.

The productThe promiseThe measured recordThe 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.23equity minus its best months
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%.24the Nasdaq, capped, for 0.60%
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).25lower-vol equity, relabeled
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.26a Tesla position that sells its reason to exist
TQQQ 2022 vs QQQ 20223× the Nasdaqcalendar 2022: TQQQ −79.1% vs QQQ −32.6%; the recovery needed is +378% vs +48%.38three times the fall
SQQQ (since inception)−3× the Nasdaq, dailysince 2/11/2010: −46.0%/yr; $10,000 → $0.40.38a melting ice cube, by design
The shelf, priced. 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.

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 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.

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 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.

Where dividends live

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.
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.

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

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).
  25. 25.J.P. Morgan Asset Management (2026). JEPI Fact Sheet, May 31, 2026.
  26. 26.YieldMax, TSLY fund page (6/30/2026); reverse-split announcements (Feb 2024, Dec 2025); totalrealreturns.com TSLY/TSLA.
  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.
  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.

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.

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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