Quantitative study · 1985–2026 · 10,291 trading days

Gating leverage by volatility, not by trend

A rule for switching between TQQQ and T-bills, tested on 41 years of reconstructed and real data. It roughly doubles the compound return of buy & hold while cutting the maximum drawdown from total ruin to something survivable — and the reason it works is not the one most timing systems rely on. A second variant, tuned for taxable accounts, halves the round trips.

Synthetic TQQQ before Feb 2010, actual fund prices after. 5bp costs, one-day execution lag, idle cash earning the real 13-week T-bill rate.

Today's signal

The signal above names the defensive leg — what the money sits in when the gates block. The rest of this document tests T-bills in that slot; the section below tests longer Treasuries, which is what the signal now reads.

What the money sits in while the gates are shut

The three gates decide TQQQ or not-TQQQ. What not means is a separate question, and for a rule that spends 40% of its life out of the market it is worth about as much as the gates themselves. Cash is the safe default. Longer Treasuries pay a term premium for holding duration, and they have historically risen when equities fall — which is precisely when this rule is holding them.

Everything below is the identical gate, identical dates, identical costs. Only the out-of-market asset changes. Treasury returns are reconstructed as a constant-maturity par bond from the 10-year yield, less a 0.15% fund fee; the reconstruction was validated against the traded ETFs, correlating 0.95 with IEF and 0.90 with TLT over their overlaps.

1985-10-02 to 2026-08-14, 10,296 sessions, 40.9 years. Invested 59.6% of the time, 2.33 round trips a year — unchanged, because the gates are unchanged.

Swapping T-bills for 20-year Treasuries is worth +4.36 points of CAGR for 1.4 points of extra drawdown, and it holds in both halves of the sample: 42.52% in-sample against the T-bill version's 36.52%, and 39.08% out-of-sample against 36.68%. Growth of $1 goes from $342k to $1.23m.

The last row is the one to sit with. 2022 took the Nasdaq down 32.6% and 20-year Treasuries down 29.0% at the same time — the hedge and the risk asset falling together. Duration only protects while the stock/bond correlation is negative, and that correlation was positive through the 1970s–90s inflation era and turned positive again in 2022.

Gold was tested in the same slot and rejected. Over 2000–2026 it looked better than Treasuries, but that window begins at the bottom of gold's twenty-year bear market. Extended back to 1986 using the longest daily bullion series available — the Central Fund of Canada, a listed physical gold and silver trust — gold adds only +1.3 points of CAGR while pushing max drawdown from −46.8% to −56.3%. Through 1986–2000 it cost 5.2 points a year. It fails on the full record.

The rule

Three gates, computed on the Nasdaq-100 index at the close. All three must pass, and the combined verdict must hold two consecutive sessions before the position changes. Otherwise the money sits in the defensive leg — 20-year Treasuries (TLT), for the reasons set out above.

Growth of $1, 1985–2026

Drawdown

Every major crash

The two events that would have ended a leveraged account — 2000–02 and 2022 — are the two the rule sat out almost entirely. Slower grinding declines like 1990 and 2015 are where it bleeds.

What the complexity buys

The volatility gate alone does most of the work. The other two gates mainly convert drawdown into return — MAR nearly doubles from 0.40 to 0.78.

Validation

Roughly 6,000 indicator and combination variants were searched, which makes any single backtest number untrustworthy on its own. These four tests are the ones that selection bias cannot manufacture.

Walk-forward — does the process work?

Every January, all 1,944 parameter combinations are scored on the expanding history to date; the best is chosen and traded blind for the next twelve months. No forward information enters the choice.

The 9-point CAGR gap between the two top rows is the hindsight premium. Treat 31% as the estimate and 40% as fantasy. Notably, the annual search converged on one parameter set in 2009 and never changed it again through 2026 — seventeen independent re-selections landing on the same answer.

Cross-asset transfer — is it a mechanism or a Nasdaq artefact?

The identical rule with identical parameters, frozen at their Nasdaq-fitted values, applied to a synthetic 3× S&P 500 (UPRO-like). Nothing was re-tuned.

It transfers — MAR more than doubles on a market it was never fitted to. But note the improvement is far less dramatic than on the Nasdaq, and −68% is still a brutal drawdown. The edge is real but not equally strong everywhere.

Random-timing bootstrap — is the timing itself informative?

5,000 random signals were generated from a two-state Markov chain matched to the strategy's exact time-in-market and switching frequency. They trade as often and are invested as often; only when they switch is random.

Zero of 5,000 matched it on any metric. Random switching at the same frequency produces a median −99.6% drawdown, so the trading intensity is not what saves the strategy — the timing is.

Parameter stability

Moving each parameter one at a time across its full tested range moves CAGR only between 26.1% and 38.7%, and MAR between 0.42 and 0.78. Across all 1,944 combinations, 100% beat buy & hold's MAR of 0.15; the median combination returns 25.1% with a −64% drawdown. There is no knife-edge here — the result is a broad plateau, not a spike.

Split-sample symmetry

36.5% versus 36.7% across two independent halves of history whose buy & hold returns differ by a factor of five. The last row uses actual TQQQ prices with no reconstruction — same drawdown reduction, and there the strategy only matches buy & hold's return rather than beating it.

Where this fails

• The drawdown is still −47%. That is better than −99.98%, but it is not safe. Half the account, twice in 41 years, with a 528-day recovery in the worst case.
• Pre-2010 data is reconstructed, not real. The synthetic series tracks the real fund at 0.9989 daily correlation with 2.9%/yr tracking error, but it assumes financing was always available at T-bill + 0.45%. In a genuine funding crisis that assumption breaks, and 1985–2009 is 60% of the sample.
• It beats buy & hold in only 17 of 42 calendar years. All the outperformance is concentrated in the handful of years it avoids a crash; in a normal bull year it simply lags. It lost money in eight years, including 2011 (−27%) and 2015 (−21%) while buy & hold gained. You pay the insurance premium in every year nothing goes wrong, and that is most years.
• Tax costs the base rule 10.7 points of CAGR. At 2.3 round trips a year, nearly every gain is short-term. Buy & hold surrenders only 0.7 points, because it never realises anything. The taxable variant below recovers much of that gap, but a sheltered account remains the better home for this.
• A gap-down defeats it. Every gate reads a closing price. An overnight collapse is taken at full 3× exposure — the rule reduces the number of crashes you sit through, it does not make any single one survivable.
• Macro indicators went untested. The unemployment-trend and credit-spread rules could not be fetched (FRED was unreachable from this machine). The yield-curve proxy that was tested ranked near the bottom, but that gap is real.
• One market, one asset class, one regime of monetary policy. 41 years sounds long; it contains perhaps five genuinely independent bear markets.

The defensive variant

If a −47% drawdown is more than you want, the same three gates can size the position by a volatility target instead of switching all-or-nothing: allocation = min(1, 25% ÷ 3σ₆₀). This gives up roughly half the return for a materially calmer ride.

The vol-targeted version beats unleveraged QQQ on return while taking a third of its drawdown — arguably the more sensible product for most holders.

The taxable-account variant

Everything above assumes a sheltered account. In a taxable one the ranking changes, because buy & hold has a structural advantage the gross numbers hide: it never realises a gain, so it compounds untaxed for 41 years and settles once at the end. Priced properly at top federal rates, buy & hold gives up 0.7 points of CAGR to tax — the switching rule gives up 10.7.

What works is leaving the gates alone and changing only which exits you take:

50 round trips over 41 years instead of 95. Median holding period more than doubles, and 36% of exits land at the long-term rate instead of 2%. Split-sample: 30.5% after tax in 1985–2007, 35.0% in 2008–2026.

How much of this is actually tax?

Less than you would hope, and this is the part to be sceptical about. The deferral rule raises returns even when there is no tax at all — because holding through short-term dips pays in a trending index. Running the same comparison across brackets separates the two effects:

Read on its own this table suggests deferral is only partly a tax effect, since it still adds 3.9 points at zero tax. That reading is wrong — it ignores risk. See below.

Risk-matched: the comparison that actually decides it

At equal risk the advantage is +2.2 points, not +7.4. About two-thirds of the raw gap was leverage, not skill and not tax.

Which rule for which bracket

Once risk is controlled, the deferral rule is a tax strategy and nothing else — at zero tax the base rule beats it by six points. Use deferral at the 32% bracket or above; below that, or in a sheltered account, use the base rule. The crossover sits between the 24% and 32% brackets. Checked in the other direction too: levering the base rule up to the deferral variant's drawdown (111% exposure) reaches only 26.12% against 31.80%, so the result is not an artefact of which rule was scaled.

The risk-matched figures come from a cash/sleeve-separated tax engine that tracks cost basis when tax is paid out of the position, so its absolute levels sit about one point below the simpler engine used in the table above (24.38% against 25.91%). The rankings and gaps are unaffected.

What the extra risk costs

Deferral means occasionally staying invested when the gates want out. Pre-tax it is a worse rule — MAR falls from 0.78 to 0.71 and drawdown deepens from −46.8% to −57.0%. Here is exactly where that bites:

The pattern is the reassuring part: deferral never costs anything in the catastrophic declines, because the drawdown gate fires and overrides it. It costs in the middling ones — where the gates want out but the index never falls the full 20%. That is the right way round for a rule whose job is avoiding ruin.

Walk-forward, after tax

A smaller edge than the fixed-parameter 32.5%, and the yearly choice was not stable — it moved between deferring everything and deferring nothing. Treat +2 points and a third fewer round trips as the honest claim, not +6.6.

Also rejected

• Minimum holding periods (126 / 252 / 366 days) — roughly neutral after tax, and they blunt the crash response.
• Deferring only mature positions (wait until day 200 or 250 before deferring) — my own first guess, and it tested worse than not deferring at all.
• A tighter crash override (15% or 12% instead of 20%) — worse on both turnover and drawdown, because it whipsaws inside choppy declines. Tightening to 15% deepened max drawdown to −71.7%.

Running it

python fetch_data.py       # refresh prices from Yahoo
python signal_today.py     # sheltered-account position, gate by gate
python signal_taxable.py   # taxable-account position (add --entry-date YYYY-MM-DD)
python validate.py         # walk-forward, plateau, crisis, cost sensitivity
python robustness.py       # cross-asset transfer + random-timing bootstrap
python taxable_validate.py # after-tax search, brackets, deferral tests
python net_compare.py      # risk-matched base vs deferral, bracket crossover

Check once daily after the close and act the next session — that one-day lag is exactly how the backtest is scored, so acting sooner would be trading ahead of the tested rule rather than behind it. Expect to do nothing for months at a stretch: 2.3 round trips a year sheltered, 1.2 taxable. The taxable script needs to know your real lot, so pass --entry-date if your position differs from the simulated one.

If you contribute every month instead

Dollar-cost averaging is not the same strategy with more money. Three things change: return has to be measured as the IRR of the actual cash flows (most of the money arrives late and compounds for far fewer years); drawdowns move late, because that is when the balance is large; and every monthly buy becomes its own tax lot with its own 365-day clock. That last point makes the deferral rule better — on an exit it can now sell the seasoned and losing lots while holding back only the short-term winners, so the position goes partial rather than all-or-nothing. Average-cost basis is not used; it is not permitted for ETFs.

Start in any year, contribute for N years

Over ten years the medians are nearly tied (25.2% against 26.3%) — the strategy earns its keep at the bottom of the distribution, not the middle. Over twenty years no starting month lost money with the strategy and its worst case was +16.3% annualised, while a third of buy & hold starts lost money outright, worst case −22.4%.

The awkward cases

Starting in 1987 or 1995 the strategy wins overwhelmingly — buy & hold begun in 1987 turned $240,000 of contributions into $192,011, a negative IRR over two decades. But plans begun in 2000 and 2006 went the other way: contributing straight into a crash means buying the cheapest shares of the cycle, and the strategy is deliberately not in the market then. This is a real cost of timing under DCA that does not exist for a lump sum, and it is why the ten-year medians tie.

Appendix — full data at NYC rates

32% federal + 3.8% NIIT + 6.85% New York State + 3.876% New York City = 46.53% short-term / 29.53% long-term. New York and NYC both tax capital gains as ordinary income, so the entire 17-point long/short spread is federal. Every figure below is measured on the after-tax equity curve — the balance actually in the account, with tax paid out of it each year.

Summary, $100,000 over 40.8 years

Rolling returns, annualised

The ten-year row is the one to sit with: the deferral variant has no negative ten-year window in 41 years and a worst case of +2.1%. Buy & hold is negative in 33.2% of ten-year windows, worst case −48.7% annualised.

Every drawdown below −15%, deferral variant

Time underwater

Calendar-year returns, after tax

Exposure by decade

67.6% invested overall, 50 completed round trips in 41 years. The rule was least invested through the 2000s (45.0%) and most through the 2010s (84.8%) — it is not a fixed allocation, it tracks whether leverage was survivable.

Data: Yahoo Finance (^NDX, QQQ, TQQQ, ^GSPC, ^VIX, ^VXN, ^IRX, ^TNX), 10,291 daily observations from 1 October 1985 to 7 August 2026. Synthetic TQQQ = 3×QQQ total return − (2×(13-week T-bill + 0.45%) + 0.95% expense)/252, validated against the real fund at ρ = 0.9989. All results net of 5bp round-trip costs with a one-day execution lag. This is a backtest, not a forecast, and not investment advice.