We derive fundamental limits to demand analysis in financial markets from two foundational principles of asset pricing: (i) investors value assets for their payoffs, and (ii) prices satisfy no arbitrage. Given these principles, we show that (iii) asset demand curves are not structural objects and that even perfectly exogenous supply shocks provide incorrect price variation for demand estimation. The only exception is the knife-edge case where beliefs over payoffs are never revised. We conclude that asset demand functions are model-dependent objects that rest on unverifiable assumptions about investor beliefs.