Demand for any of N assets can influence every other price, generating N^2 cross-impact slopes. Which interactions are determined by economic first principles and which reflect investor behavior? Using no arbitrage alone—without needing to specify a particular equilibrium—a new "Irrelevance of Uncorrelated Portfolios" axiom is necessary and sufficient to isolate N factor portfolios whose demand moves only its own price of risk, collapsing the description to N factor-specific slopes. Two further restrictions yield contrasting simplifications: equal slopes reproduce the familiar mean-variance formula, whereas a demand-based APT compresses the model to a few factor slopes plus one idiosyncratic elasticity.