{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T05:55:50Z","timestamp":1790574950726,"version":"4.1.0"},"posted":{"date-parts":[[2026]]},"group-title":"SSRN","reference-count":0,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>Trading moves prices against the trader, and this price impact is concave. For one asset, Brokmann et al. (2025) show that a linear trading rule calibrated to an \"effective\" quadratic cost loses only about 0.5-2% of net Sharpe ratio. We ask the same question for correlated multi-asset portfolios, where the cost can be charged on the whole portfolio package or on each name separately. The literature uses both forms, and neither is settled empirically. The central result is that impact pooling changes how the measured value of a nonlinear rule scales with diversification. Under package pricing, its achieved gain over the best linear rule falls roughly as one over the number of independent directions traded: at p = 1.3, from 2.1% at two names to 0.6% at ten. Under name-by-name pricing it stays near 3%. A broad book executed name by name looks safest, yet it is exactly the case in which the measured gain does not shrink. We certify the two-asset cost of linearity from both sides, with a nonlinear policy below and an information-relaxation dual bound above: 0.66-2.39% at the square-root law and 2.14-7.23% at stronger curvature. A closed-form elasticity predicts how nonlinear the rule should be across a 400-fold range of costs. Fitting a separate cost coefficient for each kind of trade adds at most 0.45% anywhere measured-less than one-fifth of the 2.3-percentage-point measured effect of choosing the cost model. At an aggregate-zero point, per-asset impact generally adds a leverage-score condition for one coefficient to suffice; we prove this local separation. The practical order is to identify how execution is charged, then decide on nonlinearity, and only then refine the cost coefficient.<\/jats:p>","DOI":"10.2139\/ssrn.7525561","type":"posted-content","created":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T05:13:47Z","timestamp":1790572427000},"source":"Crossref","is-referenced-by-count":0,"title":["When Does Diversification Help? Aggregate versus Per-Asset Nonlinear Impact in Multi-Asset Trading"],"prefix":"10.2139","author":[{"given":"Xin","family":"Heng","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","container-title":[],"original-title":[],"deposited":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T05:13:47Z","timestamp":1790572427000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ssrn.com\/abstract=7525561"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"references-count":0,"URL":"https:\/\/doi.org\/10.2139\/ssrn.7525561","relation":{},"subject":[],"published":{"date-parts":[[2026]]},"subtype":"preprint"}}