["Journal of Public Economic Theory, Volume 28, Issue 2, April 2026. ", "\nABSTRACT\nWe study when ex‐post efficient bilateral trade is possible under two‐sided asymmetric information with two agents and two assets, subject to balanced budget and voluntary participation constraints. We characterize how the interaction between asset characteristics and ownership structure determines the possibility of efficiency. Our main finding reveals a fundamental misalignment principle when goods are heterogeneous: efficiency is possible precisely when complementarity and ownership structure are misaligned. Under concentrated ownership (one agent owns both assets), efficiency is possible when assets are substitutes but impossible when they are complements. Under dispersed ownership (each agent owns one asset), the opposite holds: efficiency is possible when assets are complements but impossible when they are substitutes. This misalignment creates asymmetric valuations that overcome the participation constraints binding efficiency. Our results shed new light on the classic Myerson‐Satterthwaite impossibility and Cramton–Gibbons–Klemperer possibility theorems to multi‐asset environments, showing that the structure of asset bundles fundamentally alters the rents that we need to provide to ensure truthfulness and voluntary participation.\n"]