What a European country fund is made of, and whether the country part is worth rotating

Instruments. Ten USD-listed iShares MSCI single-country funds, the first tier by listing date: Germany, France, Italy, Spain, the Netherlands, Switzerland, the United Kingdom, Sweden, Belgium and Austria (EWG, EWQ, EWI, EWP, EWN, EWL, EWU, EWD, EWK, EWO). Ten iShares Global sector funds: technology, health care, financials, energy, telecommunications, materials, industrials, consumer staples, consumer discretionary and utilities (IXN, IXJ, IXG, IXC, IXP, MXI, EXI, KXI, RXI, JXI); the last five list in September 2006, which sets the start of every fit. Everything is in dollars, so a country's residual carries its currency. A bill fund, BIL, is the trend gate's sleeve. Fees, read from the fund data on 2026-09-07: the country funds charge 0.50 percent a year (0.49 to 0.51), the sector funds 0.37 (0.37 to 0.38), IEV 0.60; every return in this paper is net of them, because the funds' own prices are.

The mimic. At every month-end each country fund is regressed on the ten sector funds over the trailing 252 sessions of daily returns, weights constrained to be non-negative and to sum to one, no intercept, so the weights read as a long-only sector portfolio. Two outputs per fit: the in-sample R squared and the residual. The forward residual is last month's weights applied to this month's returns; every residual figure in the paper is that forward residual. The correlation gap is the mean pairwise correlation among the ten countries that the weights imply, W times the sector covariance times W transposed, against the realised one over the same window.

The arms. One machine, three rankings, monthly: the country arm ranks the ten country funds on their trailing return over the lookback; the residual arm ranks them on the trailing sum of their forward residuals; the sector arm ranks the ten sector funds on their trailing return. Each buys its top three at the next session, equal weight, and holds them until the next month-end. Lookbacks of 3, 6 and 12 months. Costs of 10 basis points a side on every trade; no financing, no borrow, no shorts.

The gates. None; a trend gate that holds the arm when IEV, the iShares Europe fund, closes above its 200-day average and a bill sleeve otherwise; a dispersion gate that holds the arm when the cross-sectional dispersion of the ten funds' trailing returns sits above its own trailing median and every fund equally otherwise, the label decided at month-ends. The three arms at six months were rerun with the dispersion threshold at its 70th percentile. Three arms by three lookbacks by three gates plus three more cells is 30 sealed studies. On the platform each gate is a two-lane router: lane A is the arm's own book, lane B the fallback, and the gate's two labels decide which lane holds the month; the registration record of a gated cell reads that way.

The walk. Eighteen one-year windows anchored on the first session of each year from 2008 to 2025, 540 windows in all. Every window was registered with its hypothesis before it ran, and the family of 30 is declared on every cell, so the deflation statistics answer to the whole search. Fourteen windows were excluded and printed as excluded, all at the 2008 anchor: the ten residual cells could not fit the mimic on sixteen months of sector history, and the four sector-arm cells under the dispersion gate could not form the gate's threshold. Every like-for-like comparison in this paper runs on the 17 windows all 30 cells share, 2009 to 2025; one table runs the cells that have 2008 on all 18, and says so.

The rulers. The engine benchmarks each window against SPY, the wrong yardstick for a European book; it is kept off every figure and printed once, in the rulers table. Two European rulers were computed from the same loader on the same sessions as each walk window, the first session of January to the last of December: IEV's total return, and an equal-weight book of the ten country funds rebalanced monthly, also total return. The second is the one a rotation has to beat: it is what the arm holds when it stops choosing, and it is the dashed grey line on every figure.

What a country is made of. Across 220 monthly fits the mimic explains 74 percent of a country's daily variance on average, from 68 for Austria to 81 for the United Kingdom; forward, with last month's weights, 71 percent. Financials carry Italy (0.56), Spain (0.59) and Austria (0.43); Switzerland is consumer staples and health care; Sweden is materials and industrials; the United Kingdom is materials and financials. Figure 3 prints the map.

The gap. The sector weights imply a mean pairwise correlation among the countries of 0.93 to 0.99 every year; the realised one ran 0.72 to 0.92. The gap averaged 0.14 and ran from 0.07 in 2011 to 0.21 in 2017: 0.10 in 2008, 0.07 in 2011 and 0.09 in 2022, when everything European fell together and the mimic was nearly right; 0.21 in 2017, 0.20 in 2019 and 0.19 in 2024, when the countries went their own ways. Part of the implied level is the constraint: weights forced non-negative and summing to one on ten global sectors make every country a variant of the same financials-and-materials blend, so the finding is the gap's movement through time, from 0.07 to 0.21, and the level of 0.14 carries the constraint's own overstatement. Figure 2 prints every year.

The arms, ungated, on the 17 shared windows. Sector arm: +11.8, +9.8 and +11.7 percent a year at 3, 6 and 12 months, mean window Sharpe 0.73 to 0.90, mean window drawdown 14 percent, compounded over the seventeen windows to 6.2x, 4.5x and 5.9x. Country arm: +9.1, +10.9 and +10.4, Sharpe 0.57 to 0.67, drawdown 19 percent, 3.2x, 4.3x and 4.0x. Residual arm: +9.9, +11.3 and +9.7, Sharpe 0.63 to 0.67, drawdown 19 percent, 3.7x, 4.5x and 3.6x. The equal-weight ten-country ruler returned +9.7 a year on the same windows and compounded to 3.8x; IEV +8.5 and 3.4x. Two pairs of measures run through this paper and neither pair reconciles. Mean window drawdown is the mean, across windows, of the deepest fall inside each one-year window, while the family table prints each walk's worst drawdown over its whole stitched track, which is deeper. Mean annual return is the average of the one-year window returns, while the CAGR column in that table is the compounded rate, which is why the host cell reads +9.1 a year over eighteen windows in the gate table and 7.9 percent there.

Against the ruler. The sector cells beat holding all ten equally by +2.1, +0.1 and +2.0 a year at 3, 6 and 12 months, standard errors near 3, in 9, 8 and 9 windows of 17; the country cells by -0.6, +1.2 and +0.7 in 6, 7 and 8; the residual cells by +0.2, +1.6 and +0.0 in 9, 9 and 9. No cell in the family, gated or not, beat the ruler in more than 10 windows of 17. Over the seventeen windows compounded, the sector arm at 12 months turned one dollar into 5.95 against 3.83 for the ruler; the same arm over all eighteen windows, 2008 included, 3.90 against 2.04. The family table on this page shows a larger growth against the dispersion-gated sector cell at twelve months than against the host. On the seventeen windows the two share they are the same walk, +11.7 a year each and 5.95 against 5.90 compounded; the difference on the page is the 2008 window, which the gated cell never ran because its threshold needed three years of dispersion history and which cost the host 34.4 points. A growth column is each walk over its own windows and does not rank walks of different lengths. The residual arm was killed by a criterion written before the walk, and the case for the sector arm is not its mean either: the difference from the ruler sits inside one standard error for every arm, and what separates the sector arm is the compounding, the drawdown and the Sharpe. Deflated against the declared family of thirty, the host cell's pooled Sharpe of 0.50 carries a 51 percent probability of being real. The correction is built for the largest draw of a search, and this cell is not it: the highest pooled daily Sharpe in the family is 0.69, on the dispersion-gated sector cell at twelve months, which deflates to 76 percent against the same thirty. Pooled daily Sharpe, the family table and the headline card, is a different statistic from the mean window Sharpe in Tables 1 and 2, and this paragraph names which one it uses each time.

Residual against country, paired on the shared windows. At 3 months the residual ranking added +0.8 a year, standard error 0.61, ahead in 10 of 17 windows; at 6 months +0.3 (0.98, 6 of 17); at 12 months -0.8 (1.04, 10 of 17). Sector against country: +2.7, -1.1 and +1.2 at 3, 6 and 12 months, with standard errors near 4 because the two books hold different instruments; sector against residual +1.9, -1.5 and +2.0. The contrasts that clear a sign test are under the trend gate: sector against residual at 12 months, +3.2 a year in 14 of 17 windows, p 0.01; sector against country there, +2.3 in 13 of 17, p 0.02; and sector against country at 3 months, 12 of 16, p 0.04.

The gates on the shared windows. The trend gate cost every arm at every lookback, 5.6 points a year on average, and led the ungated cell in 1 to 4 windows. Its worst year on the sector arm at twelve months was 2020, when the gate returned -15.7 against +16.4 ungated: it sold after the fall and was in bills for the recovery. The dispersion gate cost 0.7 points a year on average and led in 5 to 9 windows of 17. Raising its threshold to the 70th percentile, rerun at six months only, changed nothing on the country and residual arms, within a point, and added +2.0 on the sector arm, 11 of 15 windows. The registered criterion asked whether the gate works at one threshold only. It does not: it works at neither on two arms and helps one sector cell, so it survives the criterion, and it costs 0.7 points a year to keep.

The trend gate with 2008 in. The shared-window rule removes the one window the gate exists for, so the cells that ran 2008, the country and sector arms, are compared again on all 18. Sector arm at 12 months: ungated +9.1 a year, 3.90x compounded, -34.4 in 2008, worst window drawdown 46 percent; trend-gated +6.5 a year, 2.71x, -6.2 in 2008, worst window drawdown 30 percent, ahead of the ungated cell in 5 windows of 18. Country arm at 12 months: ungated +7.7 and 2.46x with -38.7 in 2008, gated +4.2 and 1.66x with -9.4. The gate bought its protection in 2008 and paid for it in the other seventeen: over eighteen windows it kept 69 percent of the ungated terminal wealth on the sector arm and 67 on the country arm.

The kill criteria, as registered. Reconstruction: the median in-sample R squared is 0.73, above the 0.6 floor; survives. The gap: episodic, 0.07 to 0.21, with its pattern reversed; survives as a finding, with the sign the registration did not expect. The residual arm against holding all ten equally after costs: +0.2, +1.6 and +0.0 a year, ahead in 9, 9 and 9 windows of 17, within one standard error of zero at every lookback; that is not beating the ruler, and the arm is killed by its own criterion. The dispersion gate at one threshold only: it is the same at both thresholds on two arms and helps one sector cell; survives, and costs 0.7 points a year. Break-even trading costs, computed from each cell's own cost ladder as the charge per side at which the arm would only match the ruler: the sector arm 43 basis points at 12 months, 30 at 3 and 11 at 6; the residual arm 29 at 6 months, 12 at 3 and 9 at 12; the country arm 25 at 6 months, 22 at 12 and 5 at 3. A liquid US-listed fund trades at 2 to 5 basis points of spread, so eight of the nine clear that charge, by 4 to 38 basis points. The ninth does not: the country arm at three months breaks even at 4.6 basis points a side, inside the spread itself, and fails the criterion it was registered against. The gated cells' ladders ride their lane, so their break-even is not stated.

The answer to the question as registered is yes, mostly. A European country fund is three-quarters a long-only sector portfolio, and the quarter it is not does not pay to rotate on. The sector arm returned more than the country arm at 3 and 12 months and less at 6, with the standard error near 4 points a year at all three. What separates them is the drawdown and the Sharpe, and that ordering holds at every lookback: ten global sector funds are a wider and less correlated set than ten European country funds that share the same banks and the same currency. Over eighteen windows the difference compounds to 3.9x against 2.5x. The wrapper does not explain it: the sector funds charge 0.13 points a year less than the country funds, against arm differences of +2.7, -1.1 and +1.2 at the three lookbacks.

The mimic leaves 19 to 32 percent of each country's variance unexplained, and the correlation gap says the unexplained part moves countries apart rather than together, by 0.07 to 0.21 of correlation a year. It is largest in the calm years, when a country can go its own way, and smallest in 2008, 2011 and 2022, when everything European fell as one. That is a fact about diversification. What a country adds to a European book is there in the years a reader does not need it. The residual has no trailing-return signal worth a top-three book. Ranking on it added +0.8 points a year over the raw country ranking at 3 months and +0.3 at 6, and lost +0.8 at twelve.

Heston and Rouwenhorst (1994) found country effects dominating industry effects in European returns; Cavaglia, Brightman and Aked (2000) found industry factors overtaking country factors by the late 1990s; Bekaert, Hodrick and Zhang (2009) found the country factor alive in comovement. This walk is on the tradeable version of the question, ten funds a retail investor can hold, and reads as the middle paper: the sectors explain most of a country, the rest is real, and only the first part is a rotation.

The risk engine, graded. Before every rebalance the forward tester fits a Monte Carlo cone and a 95 percent VaR on data before the segment it then scores. Over the host walk 197 of 216 cones contained the outcome, 91 percent against a 90 percent claim, and the VaR was breached on 5.24 percent of 4,313 days against 5 expected, each within one standard error of its claim over eighteen years.

Two primitives were written for this study and sit in the Custom group of the platform's palette, where any later study can wire them: the sector mimic, a stockset-to-stockset node that fits the countries to the sectors as of the anchor and hands the forward residual momentum down as the ranking metric, and the dispersion gate, a regime node the router reads. Their behaviour was pinned by tests before the walk: a synthetic country built from two sectors is recovered exactly with a forward R squared of one, the gate labels a hand-built calm panel and a hand-built stressed panel the right way round, and the monthly label holds between month-ends. Every cell is a sealed study on this platform with its 18 windows, its registered claim and its per-step record; the fit tables and the gap series are computed once from the same loader and frozen with the paper.

The residual is largest where the mimic fits worst, Austria at 0.68 and Spain at 0.69. The second tier of country funds that list from 2010 and 2012 is smaller and less bank-heavy still, and that is the next walk.

Ten countries and ten sectors, in dollars: a country's residual includes its currency against the dollar, and a euro-based reader would see a different residual. The second tier of country funds was kept out of the arms by its listing dates.

Seventeen shared windows are few. The standard error of each arm mean, printed in the caption of Table 1, runs 4.9 to 5.4 points a year on the country and residual arms and 2.6 to 2.8 on the sector arm; the paper's claims rest on the drawdown and Sharpe ordering, which holds at every lookback, on the compounding, and on the residual arm's failure to beat the equal-weight ruler. Deflated against thirty cells, the host's pooled Sharpe has a 51 percent probability of being real, and the family's highest, 0.69 on the dispersion-gated sector cell at twelve months, deflates to 76 percent; the reader should carry that number, not the raw Sharpe.

The ten residual cells and the four dispersion-gated sector cells have no 2008 window, so their compounding runs over seventeen windows and their lines on the family figure start in 2009; the figure rebases every line on the first session all of them share, and the family table prints each walk over its own windows with the exclusion counted. A residual cell's compounding is compared with the others on the shared windows only.

Costs are 10 basis points a side; break-even costs are stated for the ungated cells, whose cost ladder is the book's own, and withheld for the gated cells. The implied correlation the mimic reports is partly the long-only constraint's doing, so the level of the gap is overstated and only its movement through time is read. The European rulers were computed outside the engine from the same loader on the walk's own sessions and are total return.

The dispersion gate decides at month-ends and its threshold uses a trailing window of three years; the trend gate's bill sleeve is one fund. Neither gate was tuned; the trend gate cost 5.6 points a year on the shared windows and bought its protection in 2008 alone.

1. Heston, S. L. and Rouwenhorst, K. G. (1994). Does industrial structure explain the benefits of international diversification? Journal of Financial Economics, 36(1), 3 to 27. Country effects dominated industry effects in twelve European markets, 1978 to 1992.
2. Cavaglia, S., Brightman, C. and Aked, M. (2000). The increasing importance of industry factors. Financial Analysts Journal, 56(5), 41 to 54. Industry factors overtook country factors in developed-market returns during the late 1990s.
3. Bekaert, G., Hodrick, R. J. and Zhang, X. (2009). International stock return comovements. The Journal of Finance, 64(6), 2591 to 2626. A country factor remains in the comovement of developed-market returns after industry factors.
4. Asness, C. S., Moskowitz, T. J. and Pedersen, L. H. (2013). Value and momentum everywhere. The Journal of Finance, 68(3), 929 to 985. Momentum in country equity indices, among other asset classes, with the rankings the country arm here uses.