Antonacci's Dual Momentum Taken Apart: Gate, Relative Leg, and Blends Across Four Lookbacks

Instruments, not indices. The published GEM is usually presented on index series reaching back to 1974. This study runs the tradable reading: SPY for US equity, VEU for all-world ex-US, AGG for the bond escape, BIL as the bill series. July 2008 is the first month at which every one of the four carries the full year of history the longest tested lookback reads, so the walk runs eighteen one-year windows anchored each July from 2008 through 2025, with the financial crisis inside the first window.

Every signal reads total returns. This is not a refinement, it is the difference between running the rule and running a different rule. A bill fund's entire return is its yield: priced on raw closes, BIL's trailing return reads near zero and the gate silently degrades into asking whether SPY went up at all. VEU yields roughly three percent to SPY's one and a half, so raw-close relative momentum would handicap the international leg by about the size of the margins being compared. The platform therefore builds each signal series from raw closes with cash distributions reinvested on their ex-dates, the same dividend record the profit and loss is credited from. The declared bill series is BIL's total return; Antonacci's original used the three-month Treasury yield, which is close but not identical, and the choice is stated here so the reader is not left to guess.

The rule, on the strategy's own clock. At each month-end close, compare SPY's trailing total return over the lookback against the same measure on BIL. At or below bills, the coming month is spent in AGG; ties retreat. Above bills, dual momentum holds the stronger of SPY and VEU by the same trailing measure, while the gate-only book holds SPY. Note that the published gate never looks at VEU: international equity is absent from the absolute test by Antonacci's own design, in every arm here. Signals fire on the month-end close and the book earns the new allocation from the next bar.

Costs. Ten basis points per one-way traded dollar, charged wherever the book moves, whether the momentum leg rotates between SPY and VEU or the gate moves the whole book to bonds and back.

The registered family. Each pairing is a two-arm registered study whose arms differ in exactly one sealed field. Dual momentum against absolute momentum only: the offensive book shrinks from the SPY and VEU pair to SPY alone. Dual momentum against relative momentum only: the gate node is welded open. Both pairings ran at trailing lookbacks of 3, 6, 9 and 12 months, eight walks in all, every one reported, none selected after the fact. The published arm is bit-identical across pairings at every lookback, so twelve configurations rest on eight runs and one shared record. The full search this paper draws on, counted in the search accounting of section 2.3, is eighteen evaluated books: those twelve, the three blended-signal books registered afterwards, and the three derived averages. The family matrix in the results section shows every one of them; nothing was run that is not in that table. What Antonacci searched before publishing the 12-month rule is not knowable from here, so this paper counts only its own search.

The combined runs, and their discount. After the eight walks were run and read, two more were registered: the same pairings with both legs reading the equal-weight average of the 3, 6, 9 and 12 month trailing returns, the unweighted cousin of the 13612W blend Keller published. Separately, a derived series averages the four sealed books themselves, a quarter of capital to each lookback, reset at each window boundary, computed from the frozen records without any new run. Both exist to answer the question the eight raise, whether the reader must pick a lookback at all. Both were results-motivated, are sealed or stated with that admission, and carry less evidential weight than the pre-specified eight.

Benchmarks. The platform reference in grey is SPY total return in every study on this site. The study benchmark is 60/40 SPY/AGG, rebalanced monthly from the same total-return series the signals read, shown in purple. GEM never claimed to beat equities; it claimed to cut drawdown, and it is judged here against the portfolio a reader would actually hold instead.

At the published 12-month lookback, over eighteen years: dual momentum returned 394 percent, 9.3 a year, Sharpe 0.63, worst drawdown 33.7 percent. Delete the international leg and the same gate on SPY alone returned 523 percent, 10.7 a year, Sharpe 0.73, the same worst drawdown. Weld the gate open and pure relative momentum returned 438 percent, 9.8 a year, Sharpe 0.56, drawdown 51 percent. SPY itself did 470 percent, 10.15 a year, Sharpe 0.59, drawdown 47.9. The 60/40 line reads 8.80 a year, Sharpe 0.77, worst loss 30.1, and against it the polite framing dissolves: strip the international leg, keep the gate, run it eighteen years at the published lookback, and you finish 1.9 points a year ahead of a monthly 60/40 with a slightly worse Sharpe and a slightly worse worst day. Across the family matrix exactly one book clears 60/40 on Sharpe: the gate alone at 3 months, 0.85, with the smallest drawdown of the eighteen, 22.1. It is a real cell in a declared search, reported like the rest, and one cell of eighteen is what it is. The derived gate-only average of the four lookbacks, Sharpe 0.78, also edges the benchmark, and this paper has already told the reader to discount it.

The international leg's ledger is short. In nine of eighteen windows it did nothing: VEU never out-ranked SPY and the two arms are identical to the decimal. In the other nine it acted, and it won once, 2025, by 3.8 points. Its losses: 11.4 points in the 2009 window, 6.2 in 2020, 4.9 in 2017, 2.9 in 2010, 2.6 in 2012. The book spent 41 of 212 months in VEU and paid for the privilege with 16 of its 25 switches. Removing the leg entirely, which is the one sealed field the first pairing varies, added 1.42 points a year. The same deletion added 1.44 points a year at 3 months, 1.74 at 6, 3.19 at 9. There is no tested speed at which the leg paid. The toll also survives the era split: set aside the two pre-2010 windows, one of which is the crisis, and removing the leg still added 2.1, 1.8, 3.4 and 0.9 points a window at 3, 6, 9 and 12 months over the sixteen windows since. The pre-2010 rows in the era table are two windows and should be read as two windows.

The gate's ledger is one payout and a stream of premiums. In the 2008 window the gate was worth 39.3 points against the welded book: it walked the strategy into AGG while equities halved. It never paid like that again. Its whipsaw years read 14.5 points given back in 2019, 14.2 in 2022, 13.1 in 2015, 11.0 in 2018, 8.7 in 2009, each one a retreat to bonds that equities did not honor. Head to head it won two windows of eighteen, and on net it cost about half a point a year at the published lookback. What it bought is the entire drawdown result: 51 percent worst loss welded open, 33.7 with the gate live, and a Sharpe of 0.63 against 0.56.

The gate filters crash speed, not crash size. The 2008 collapse unfolded over more than a year, slow enough for a month-end rule to read it: the gated books bottomed at 20.9 percent in that whole era, the gate-only book at 15.8, while the ungated book and SPY both halved. March 2020 was the opposite case, a full bear market inside twenty-three sessions, faster than any monthly clock: every book in the study, gated or not, bottomed within half a point of 34 percent on the same day, and that day, not 2009, is the gated books' worst loss in the record. A monthly gate protects against crashes that outlast its clock and eats the ones that do not; both halves of that sentence are in Figure 4.

The lookback dial is a U. Across 3, 6, 9 and 12 months, both gated books do their best work at the ends and sag in the middle. Dual momentum reads 8.9, 6.7, 5.7, 9.3 a year across the four speeds; the gate-only book 10.3, 8.5, 8.9, 10.7. The 9-month dual momentum book is the worst configuration in the family, at barely half of SPY's rate. Drawdown, unlike return, is flat: every gated configuration at every speed bottoms between 20 and 35.5 percent, every ungated one between 46.8 and 51. Only two configurations of fifteen beat SPY's rate of return, the gate-only book at 3 and at 12 months, and both did it with roughly half of SPY's drawdown.

The dial is also a live argument. In 2019 Corey Hoffstein published a fragility case study on GEM, arguing a single lookback is brittle and proposing a composite across several; Antonacci answered that twelve months is the convention the literature supports, citing Jegadeesh and Titman's 3, 6, 9 and 12 month grid. The four lookbacks walked here are that grid, out of sample. This paper does not settle Hoffstein's proposal: his composite ran roughly six to twelve months, and the blend registered here is the equal-weight average of all four. What the family does show is the shape of the neighborhood, a U rather than a cliff, with the published value at one of the two good ends.

Refusing to choose a lookback works only one way. The blended-signal walks, registered after the eight, average the four trailing returns into one decision, and that decision behaves like a mid-speed lookback: dual momentum on the blend returns 6.6 a year, deep in the valley. Averaging the four books instead, a quarter of capital to each, derived from the frozen records, returns 7.8 a year for dual momentum and 9.7 for the gate-only book at Sharpe 0.78, the second best in the whole family, with drawdown near 29. Blending signals buys the average opinion; blending books buys the disagreement between them, and only the second one diversifies.

The switch table below counts where the eighteen years were actually spent. Dual momentum changed instrument 25 times, and 16 of those were the international leg shuffling between SPY and VEU. The gate-only book changed 9 times in eighteen years, one move every two years, and beat everything in the family.

Antonacci's own 2012 paper already contains most of this verdict. He reported that both momentum ideas raise returns but that absolute momentum does far more to cut volatility and drawdown; the combination was his recommendation. This record sharpens that finding into something blunter: over 2008 through 2026, on tradable funds, with the yield handicap removed and costs charged, the relative leg did not merely trail the gate, it subtracted at every speed tested. The half of dual momentum that carries the famous chart is the gate. The half that gives the strategy its name spent eighteen years as a toll.

Judged on the thing it promised, the strategy delivered. GEM's claim was never that it beats equities; it was that it cuts the catastrophic loss. It did: no gated configuration in this family, at any lookback, lost more than 35.5 percent while SPY and every ungated book lost 47 to 51. The premium for that insurance at the published lookback was about half a point a year, which is cheap if drawdown is what a reader fears and expensive if it is not. What the insurance did not buy, in this window and at the published lookback, is superiority over sitting still: a monthly 60/40 of the same two instruments landed in the gated books' drawdown class with a better Sharpe and not one signal read. The 3-month gate is the family's one exception, and the discount for finding it in an eighteen-book search is stated where the search is. What the record adds to the sales brochure is the mechanism: the protection is conditional on crash speed. A grinding 2008 is exactly what a month-end rule reads well, and the gated books sailed through it at a fifth to a sixth off the peak. A twenty-three-session 2020 is invisible to the same rule until the month turns, and every book ate it whole. The gate's worst loss in the record is the crash it is famous for missing, shifted twelve years late.

The lookback result answers the quiet objection that 12 months was chosen because it worked. It was not the best possible choice in this record; it was one of the two good ones, and the shape around it is a U rather than a cliff, with the middle speeds worse and the ends similar. A reader who refuses to choose can hold all four books at a quarter each and land near the top of the family on risk-adjusted terms. The same reader averaging the four signals into one decision lands in the valley instead. The distinction matters beyond this strategy: a blend of signals is one opinion at one implied speed, while a blend of books is four opinions that disagree, and the disagreement is where the diversification lives. Keller's 13612W measure, the front-weighted cousin of the blend tested here, sits on the same spectrum and was priced in this platform's Bold Asset Allocation study.

What would change the verdict on the international leg is an era in which international equity leads for years at a time. This record does not contain one, and the leg's price here is the price of shuffling into the weaker market during the strongest US run in the sample's history. The gate's verdict rests on mechanics rather than era and travels better. Every number above is read from registered, frozen walk records on this platform, and the two combined runs are labeled with the order in which they were added.

The window is the great US era. 2008 through 2026 contains the longest stretch of US over international outperformance in modern records, and the international leg's toll is measured inside it. Antonacci's index-based history reaches eras where the leg led for years; a tradable-fund study cannot reach them, because VEU and BIL did not exist. The verdict on the leg is a verdict about this era, stated as such. The verdict on the gate rests on drawdown mechanics and is less era-bound, with its own conditionality shown in 2020.

The clock is monthly, and 2020 shows what that costs: a crash that completes inside the month is taken in full, gate or no gate. A faster clock would catch faster crashes and pay more whipsaw; that trade is not measured here.

The bill series is BIL's total return, not the three-month Treasury yield Antonacci used. The two are close; they are not the same number, and the gate's marginal months could differ under the other choice. Costs are a flat ten basis points per one-way traded dollar, which understates trading in stressed months and overstates it in calm ones; there are no taxes, and a taxable reader switching whole books between funds would keep less than every number above. Returns are stated raw, not as excess over cash, and no cash hurdle is applied to any comparison. Through the zero-rate decade that distinction is nearly empty; from 2023 on, with bills near five percent, it is not, and the family-against-60/40 reading is the one it touches most. Instrument switches are counted on the strategy's monthly clock inside each sealed window, so a flip occurring exactly at a window boundary is not counted; the tally understates by at most a handful.

The blended-signal walks were registered after the eight single-lookback walks were read, and the book-average line is derived from the frozen records rather than walked. Both are results-motivated extensions, both say so in their sealed texts or their captions, and a skeptical reader should weight the pre-specified eight above either.

Fifteen registered configurations and three derived averages is a family, and families flatter their best member. The claims this paper stands on are deliberately the two that hold across every member at once: the leg subtracted everywhere, and the gated and ungated drawdown ranges do not touch. The study benchmark is a US 60/40, which is what a reader of this literature would hold, but it contains no international exposure and therefore cannot isolate what the relative leg added or cost; that job belongs to the welded-open arm, which is why both are reported.

1. Antonacci, G. (2012, rev. 2017). Risk Premia Harvesting Through Dual Momentum. Journal of Management and Entrepreneurship 2(1), 27-55. SSRN 2042750.
2. Antonacci, G. (2014). Dual Momentum Investing: An Innovative Strategy for Higher Returns with Lower Risk. McGraw-Hill.
3. Keller, W. J. (2022). Relative and Absolute Momentum in Times of Rising/Low Yields: Bold Asset Allocation (BAA). SSRN 4166845.
4. Hoffstein, C. (2019). Fragility Case Study: Dual Momentum GEM. Newfound Research, Flirting with Models.
5. Antonacci, G. (2019). Whither Fragility? Dual Momentum GEM. dualmomentum.net.