№ 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.
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.
| The product | Stated use | The measured record | Plain 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.23 | equity exposure with an upside cap |
| 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(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 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(as of 2026-05-31) | lower-volatility equity with an option-income overlay |
| 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(as of 2026-06-30) | Tesla exposure with recurring call sales |
| TQQQ 2022 vs QQQ 2022 | 3× the Nasdaq, daily | calendar 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, daily | since 2/11/2010: −46.0%/yr; $10,000 → $0.40.38(as of 2026-07-07) | inverse daily exposure intended for short holding periods |
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.
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