A topological way to build portfolios

Start with a pool of 882,000 systematic strategies: 7 signal families crossed with 100 Binance USDT-perpetual pairs, traded on the 1-hour bar, each one walk-forward optimized and ledgered trade-by-trade out of sample, net of taker fees, slippage and funding. Single-strategy edge in that pool is real and thin. 25.5% of the strategies finish out-of-sample profitable against 21.8% for a random-strategy baseline built from the same machinery. Roughly four points of skill over noise, no more.

Can portfolio construction take a pool that thin and turn it into something worth trading? One specific idea works, a geometric one. You select the strategies that sit at the edge of the correlation structure rather than the ones with the best track record. The edge sharpens.

How the pipeline runs

One walk-forward loop runs the whole construction; the diagram below maps the rest of the article. Every strategy's out-of-sample trade ledger collapses to weekly block returns. Those stack into a matrix of 749,895 strategies by 322 weeks. Weekly is the granularity that made construction pay. From there the loop rolls week by week. At each week it prefilters to the top 200 strategies by trailing 52-week Sharpe, then builds their trailing correlation matrix. Now the one step that matters: eigendecompose that matrix, read off the common market mode from the top eigenvector, keep the positive-edge strategies that load on it least. Those survivors get equal capital. The basket is held for the next week, the return recorded, the window rolled forward. Selection at week m sees only weeks before m, with an embargoed gap, so nothing downstream knows the future. The stitched return series at the end is what every metric here is computed on.

The concepts, in plain terms

Before the figures, the vocabulary they lean on. None of it needs topology beyond the everyday sense of shape and distance.

Correlation distance. Two strategies that rise and fall together are close; two that move independently are far apart. The formula d = √(2(1−ρ)) turns a correlation ρ into an actual distance, zero for identical behaviour and larger as the two decouple. Every picture in this article is built on that one distance.

The market mode. Break the correlation matrix into its eigenvectors and the largest one points along the direction almost every strategy shares, the common bet the whole pool is making. That direction is the market mode. How strongly a strategy lines up with it, its loading, says how much of its return is the crowd's bet rather than something of its own.

The Marchenko–Pastur bound. With a few hundred strategies and only so many weeks of data, a correlation matrix shows apparent structure even when there is none, the way a short run of coin flips can look streaky. Random-matrix theory says exactly how large the eigenvalues of a pure-noise matrix of that shape can get. Everything inside that band, the Marchenko–Pastur bound, is noise. An eigenvalue sitting far outside it is real, and here that outlier is the market mode.

Minimum spanning tree. Link each strategy to its nearest neighbour under the correlation distance, keep adding links until everything connects, and allow no loops. What falls out is a tree: a dense knot of mutually correlated strategies in the middle, lone leaves around the edge. The leaves are the diversifiers.

MDS embedding. Multidimensional scaling pins that same set of distances onto a flat plane, as faithfully as two dimensions allow, so the crowded core and the orthogonal rim show up at a glance.

The two construction methods. Market-neutral spectral selection (MNS) keeps the positive-edge strategies that load least on the market mode and weights them equally. Nested clustered optimization (NCO) groups the strategies first, then sets position sizes with minimum-variance weights within and across the groups, on a covariance matrix scrubbed of its noise eigenvalues.

Regime detection. A rule that reads only past market volatility and labels the coming week calm or turbulent, so the book can shrink before the weeks the whole market-neutral crowd tends to bleed together.

A pool with a shape

Strategies are not independent draws. They share signals, they trade the same coins, and most of them are long the same thing at the same time. That shared exposure has a geometry. The geometry is what construction has to work with. The first figure draws it directly: the minimum spanning tree of the 180 highest-Sharpe strategies in a recent week, with each strategy linked to its nearest neighbour under the correlation distance d = √(2(1−ρ)).

A dense knot sits near the centre, mostly the vol-compression family loading on one common factor. Out at the leaves are the diversifiers, the strategies tied weakly to everything else. Node size is trailing Sharpe, so the leaves are not the weak performers. They are good strategies that happen to be doing something different from the crowd. Those leaves are what the winning methods reach for.

Why ranking by Sharpe fails

Rank strategies by trailing Sharpe, hold the top handful, rebalance as the ranking moves. That is the obvious construction, and it loses money out of sample. The reason is the same geometry. High-Sharpe strategies are crowded into one factor.

To see that factor, look at the eigenvalue spectrum of the correlation matrix. Most of the eigenvalues fall under the Marchenko–Pastur bound, the band a pure-noise matrix of the same shape would produce. Those carry no reliable structure. One eigenvalue sits far outside the band.

That outlier is the market mode, the common direction every crowded strategy loads on. It dominates in-sample variance. It does not persist: the thing that made the top-Sharpe strategies look good last quarter is a shared bet that decays. Rank by Sharpe and you are buying a basket of the same bet, denoised of nothing. This is the López de Prado reading of random-matrix theory, applied to a strategy pool rather than an asset universe. It carries over cleanly.

The market mode also explains the single worst result in the study. Rolling the single best trailing-Sharpe strategy week to week returns −113.6%, with a −0.67 annualized Sharpe and a 146.9% max drawdown. You cannot re-pick the right strategy from one week to the next. Chasing the leader is chasing the decaying factor at its most concentrated.

Rank by Sharpe and you are buying a basket of the same bet, denoised of nothing.

The topological idea

If the market mode is the problem, the fix is to select against it. Three methods do this. They are the same idea in three languages.

Market-neutral spectral selection (MNS). Project each strategy onto the top eigenvector and measure the absolute loading. Keep positive-edge strategies with the lowest loading, the ones most orthogonal to the common factor. The loading distribution shows what gets kept and what gets dropped.

Blue tail on the left is the market-neutral region the selector draws from. The red bulk is the crowd. Most high-Sharpe strategies live in the red.

Nested clustered optimization (NCO). Run hierarchical clustering on the correlation distance, then allocate minimum-variance weights within each cluster and across clusters on the denoised covariance. The dendrogram is the structure NCO exploits.

Allocating block by block keeps the optimizer from concentrating into one correlated cluster, which is the failure mode of a naive min-variance solve on a noisy covariance matrix.

Minimum-spanning-tree periphery. Take the leaves and low-degree nodes of the network in the first figure. They are the diversifiers by construction. This is the same selection as MNS, read off the network instead of the spectrum.

A two-dimensional embedding of the correlation distance puts all three on one picture. Strategies near the centre are crowded into the market mode; strategies at the rim are orthogonal to it.

Red core and blue rim are the same split the loading histogram drew, now laid out in space. Every topological method is a rule for preferring the rim.

The weekly flip

Rebalancing granularity decided the verdict, and at first it pointed the wrong way. At monthly rebalancing, portfolios looked worse than single strategies. That was an artifact of the block size, not a property of construction. The weekly run reversed it.

At weekly rebalancing, market-neutral MNS selection into equal-weight portfolios of 10 lifts the profitable-out-of-sample fraction from 28.7% of single strategies to 45.1% of portfolios. The fraction clearing Sharpe greater than 1 rises from 3.2% to 4.2%. The two panels below sort every single strategy by out-of-sample Sharpe on the left and every constructed portfolio on the right. The right panel is visibly bluer.

The meta-walk-forward leaderboard makes the survivability case in three numbers per method: return on investment, annualized Sharpe, and max drawdown, all out of sample with selection done only on trailing weeks.

Both topological methods clear the single-strategy benchmark, mainly by not blowing up. The single-best line self-destructs because its drawdown runs to 147%. NCO holds its drawdown to 12.7%, the lowest of anything tested.

Timing the regime

Everything so far holds the market on. The MNS book is fully invested every week, and its 0.16 Sharpe is the blend of the good weeks and the weeks the whole market-neutral crowd bleeds together. A natural question is whether those weeks can be sorted ahead of time and the book de-risked going into the bad ones. That is a different lever from selection. It is the first one that lifts the ceiling.

Keep the two topological ideas apart first, because the regime test stresses them differently. MNS is selection: which strategies to hold, the low-loading market-neutral names, equal-weighted. NCO is weighting: how much of each, minimum-variance weights on the denoised covariance. The weekly book described above is MNS. NCO is the alternative for the weighting step, and under regime stress it turns out to be the unstable one.

Detection runs two ways, both seeing only past weeks. The market factor is the cross-sectional mean of the strategies' weekly returns, the average week the pool had. The static detector flags a week turbulent when its trailing 13-week volatility runs above the trailing 52-week rolling median of that same volatility. The HMM detector fits a two-state Gaussian hidden Markov model on the volatility feature and refits it walk-forward, letting the data name the calm and turbulent states instead of a fixed threshold.

Then two ways to act on the regime. Exposure timing scales the whole book down in turbulent weeks and holds it normal otherwise. Regime-matched selection keeps the strategies that performed best in the current regime, on the theory that what works in turbulence keeps working through it.

Regime-matched selection fails, and it fails the same way for both detectors. Static-matched selection returns a −0.51 Sharpe; HMM-matched, −0.84. Conditioning on what worked in this regime is the thin-edge curse one level up: the strategies that led the last turbulent stretch persist no better than the ones that led on raw Sharpe. You are re-selecting a decaying winner, sorted by regime instead of by return.

Exposure timing with the static threshold is the one that works. De-risking MNS through the flagged weeks lifts its Sharpe from 0.16 to 0.28, and to 0.31 if the book sits fully out of turbulent weeks rather than merely trimming. Max drawdown halves, 20.3% to 10.0%. The effect is monotonic in how hard you de-risk: holding 0% of normal exposure through turbulent weeks gives 0.31, 20% gives 0.29, 30% gives 0.28, 50% gives 0.24. Less time in the bad weeks, more Sharpe, with no inflection that would smell of a fit.

The HMM does worse than doing nothing. Its exposure-timed Sharpe is about 0.05, under the plain 0.16 weekly baseline. The inferred states are noisier and lag the turn, so the model de-risks on the wrong weeks: it cuts exposure after the turbulence has already landed and restores it before the calm is real. A two-line volatility threshold beats the fitted state model here, the opposite of what the extra machinery promises.

Two controls pin down what the signal is. It is market volatility, not the book's own. Continuous self-vol-targeting, scaling exposure by the portfolio's realized vol, lands at 0.12, below baseline. The weighting choice matters too. NCO's minimum-variance weighting is the erratic method under this stress, negative under both the plain weekly run and the static overlay, where MNS's equal weighting stays positive and improves. Equal-weighting the market-neutral selection is the pairing that holds up.

None of this raises the alpha. The raw Sharpe ceiling sits near 0.16 to 0.26 across monthly, weekly and daily granularities. The regime overlay does not break it. What the overlay does is sit out the weeks the market-neutral book bleeds in. That roughly doubles the risk-adjusted return and halves the drawdown without finding a single new dollar of edge. The market-vol regime says when to be small; being small in the right weeks is worth about as much here as the selection rule itself.

Holding up on a second pool

One pool can flatter a method. So the whole construction reran on an independently built pool, call it v4: 26 Binance perp pairs against v5's 100, a different family generation, 154,000 strategies after the same trade-count filter, the same 2020 to 2026 window, the same lookahead-safe code. Nothing in the harness changed except the input ledgers.

The orderings carry over cleanly. On v4, market-neutral MNS again posts the lowest drawdown of anything tested, 18.1%, against 41.7% for equal-weighting the whole pool and 82.3% for rolling the single best strategy. It again beats every naive selector on Sharpe. The static-vol overlay again de-risks, cutting MNS's drawdown to 12.3% and lifting its Sharpe from −0.42 to −0.28, or to −0.13 sitting fully out of the turbulent weeks. Regime-matched selection again fails hardest at −1.69, and the HMM again adds nothing the static threshold doesn't. Every qualitative result from the v5 pool repeats.

The level does not repeat. MNS on v4 comes in at −0.42, well under water. The reason is the pool: equal-weighting all of v4 returns a −2.7 Sharpe, and the cross-sectional average strategy loses week over week. There is no positive book to build from a pool whose average member bleeds, and market-neutral selection cannot conjure one.

Some of that gap is breadth. v5 carries 100 pairs to v4's 26. More names means a richer periphery to draw diversifiers from. Restricting v5 to v4's exact 26 pairs drops MNS from 0.16 to 0.08: halving the universe roughly halves the edge. It does not flip the sign. The remaining distance, +0.08 on v5's pairs against −0.42 on v4's, is the pool itself. The v4 strategies are weaker on the same coins over the same weeks than v5's are. Construction reads the geometry the pool hands it. It does not improve the pool.

Neither pool, as it happens, has a positive average strategy. The v5 market factor mean is also negative; MNS earns its 0.16 there by isolating the thin orthogonal tail that does carry edge. On v4 that tail is too thin to clear costs. The method is identical on both, and what differs is whether the pool holds anything for it to find.

What construction buys, and what it does not

Honest read: topological construction buys survivability and sharpens the edge without raising the Sharpe ceiling. The best out-of-sample Sharpe from construction alone is about 0.16, and the selection geometry did not move it. What moved was the drawdown that kills you before the edge can pay, plus the fraction of constructed portfolios that finish in the black, up about 16 points from 28.7% to 45.1%. Diversification sharpens a thin edge. It does not manufacture a thick one, and the v4 pool makes that concrete: with nothing in the pool to extract, the same construction that lifts v5 only loses less.

The regime overlay is the lever that lifts the risk-adjusted number, without touching the alpha. Standing down in the high market-vol weeks takes MNS from 0.16 to roughly 0.30 and halves the drawdown. That is risk timing, not new signal. The simple volatility threshold does it better than the fitted HMM does.

Held over a fixed monthly window the best strategy returns +52%. Try to actually trade it and the weekly reality is −113%. The paper number is a mirage of hindsight selection. The geometry is the part that holds up.

That caveat matters because of how good single-strategy trading looks on paper. Held over a fixed monthly window the best strategy returns +52%. Try to actually trade it, re-selecting the leader as the ranking churns, and the weekly reality is −113%. The paper number is hindsight selection, nothing more. The geometry is the part that holds up: pick from the periphery of the correlation network, stay orthogonal to the market mode, then stand down when market volatility says the market-neutral book is about to bleed. A pool too thin to trade one strategy at a time becomes a pool you can survive in.