Trading the Co-Movement

The design

Same signal, same names — only the label differs

# identical rules for every pair - the ONLY difference between the two
# groups is whether the embedding model put both names in the same cluster
spread = log(P_a) - beta * log(P_b)      # beta: trailing 120d, walk-forward
z      = (spread - mean_60d) / std_60d   # trailing stats only, no look-ahead
enter when |z| crosses 2.0               # short the rich leg, long the cheap
exit  when |z| < 0.5, or after 40 days   # 10bps per side round-trip cost
# treatment: 383 within-cluster pairs     placebo: 383 random cross-cluster
# pairs drawn from the SAME 92 names

Everything in the signal path is walk-forward (trailing windows only). If embedding co-membership carries no information, the two groups should perform identically. They don't.

Result 1

After a divergence, cluster pairs converge — random pairs don't

The event study: at every entry signal (|z| crossing 2), what did the beta-hedged convergence position earn over the next days, gross of costs?

The magnitudes are honest: single-digit basis points per event, a persistent positive gap at every horizon rather than a table-pounding t-stat. Mean reversion at this vanilla level is a thin edge — the interesting part is where it concentrates.

Result 2

The closer the embedding, the stronger the reversion

Splitting the cluster pairs by embedding cosine similarity: the top quartile — the pairs the model is most confident about — carries the edge, and random pairs sit below zero:

Result 3

Reversion is a property of the cluster, and the model tells you which

The aggregate hides a sharp split. Commodity, rate and fee complexes — where same-cluster members share the same external driver — revert reliably. Story clusters, where divergences reflect one name winning, trend instead:

Result 4

The after-cost portfolio

Running every pair simultaneously, equal-weight across active positions, 20bps round-trip costs. Unoptimized on purpose — no cluster filter, no similarity filter, entry/exit thresholds untouched:

Cluster pairs finish at +1.9% (Sharpe 0.08), the placebo at -1.7% (Sharpe -0.03). Neither line is a strategy anyone should run as-is; the spread between them is the point — and Results 2 and 3 say exactly which subset a real implementation would keep.

Anatomy

One pair, five years

VZ / MSI — the spread z-score with the entry (±2) and exit (±0.5) bands. Every excursion past the band is a simulated trade:

Best pairs

Highest 5-year P&L, within-cluster

Caveats, honestly held: pair formation uses embeddings built from 2025/26 filings, so pair selection has hindsight even though the signal path is fully walk-forward (business descriptions move slowly, but the bias is real). Five years, one parameter set, no borrow costs or slippage beyond the 20bps; survivorship: names must exist through the window. Event t-stats treat overlapping events as independent, which overstates them. Educational study of a strategy class — not investment advice, and not a recommendation of any security or pair.