Asset Embeddings

Each manager’s portfolio is treated as a “sentence” and each stock (PERMCO) as a “word,” ordered by holding conviction; Word2Vec then learns a dense vector per stock from co-holding patterns — the Asset Embeddings idea from Gabaix et al. I train a skip-gram model with negative sampling.

Configuration. Each portfolio is ordered by active weight — portfolio weight minus market weight — which demotes the mega-caps nearly everyone holds and surfaces idiosyncratic positions. The context window is ±10, and the embedding dimension is d = 100.

Measuring reproducibility. The embedding axes are arbitrary (the space is only defined up to rotation), so I measure a rotation-invariant, seed-vs-seed top-10 nearest-neighbor Jaccard overlap — how much each stock’s neighborhood survives re-training under a new random seed.

A whole-book window collapses the space — every vector ends up nearly parallel (cos ≈ 0.99, Jaccard 0.13). The ±10 window is the real fix, lifting it to 0.47; dimension adds a smaller gain, plateauing around 0.57–0.60, with d = 100 sitting on that plateau.

Even fully tuned, Jaccard is only ~0.5 — about a third of each stock’s nearest neighbors change with the seed. I read this as the co-holding data under-determining the geometry (non-identifiability), not a bug.

The fix: ensembling. A K-seed, Procrustes-aligned ensemble raises the floor from 0.51 (single seed) to ~0.77 at K = 10, with diminishing returns beyond — so I run K = 10.

The ensemble is what feeds the trading stage — and it improves the P&L there too, not just the Jaccard.

Next: cross-quarter drift. Independent per-quarter fits drift in their coordinate frame over time. I plan to adapt Bamler–Mandt’s dynamic word embeddings to impose temporal coherence while keeping the nonlinear representation.

Code: code/asemb/embed.